category_theory.sites.sheafification | Mathlib porting status

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

70fd9563

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

4f4a1c87

bump to nightly-2024-04-14-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

f736ea6b

Diff

@@ -477,7 +477,7 @@ theorem exists_of_sep (P : Cᵒᵖ ⥤ D)
 #align category_theory.grothendieck_topology.plus.exists_of_sep CategoryTheory.GrothendieckTopology.Plus.exists_of_sep
 -/
 
-variable [ReflectsIsomorphisms (forget D)]
+variable [CategoryTheory.Functor.ReflectsIsomorphisms (forget D)]
 
 #print CategoryTheory.GrothendieckTopology.Plus.isSheaf_of_sep /-
 /-- If `P` is separated, then `P⁺` is a sheaf. -/
@@ -711,7 +711,8 @@ variable (J)
 variable [ConcreteCategory.{max v u} D] [PreservesLimits (forget D)]
   [∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : J.cover X), HasMultiequalizer (S.index P)]
   [∀ X : C, HasColimitsOfShape (J.cover X)ᵒᵖ D]
-  [∀ X : C, PreservesColimitsOfShape (J.cover X)ᵒᵖ (forget D)] [ReflectsIsomorphisms (forget D)]
+  [∀ X : C, PreservesColimitsOfShape (J.cover X)ᵒᵖ (forget D)]
+  [CategoryTheory.Functor.ReflectsIsomorphisms (forget D)]
 
 #print CategoryTheory.GrothendieckTopology.sheafify_isSheaf /-
 theorem GrothendieckTopology.sheafify_isSheaf (P : Cᵒᵖ ⥤ D) : Presheaf.IsSheaf J (J.sheafify P) :=

4f4a1c87

bump to nightly-2024-03-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

22f01ce4

Diff

@@ -290,7 +290,7 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq
     obtain ⟨W, h1, h2, hh⟩ := concrete.colimit_exists_of_rep_eq _ _ _ h
     use W.unop, h1.unop, h2.unop
     ext I
-    apply_fun multiequalizer.ι (W.unop.index P) I at hh 
+    apply_fun multiequalizer.ι (W.unop.index P) I at hh
     convert hh
     all_goals
       dsimp [diagram]
@@ -301,7 +301,7 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq
     use op S, h1.op, h2.op
     apply concrete.multiequalizer_ext
     intro i
-    apply_fun fun ee => ee i at e 
+    apply_fun fun ee => ee i at e
     convert e
     all_goals
       dsimp [diagram]
@@ -318,7 +318,7 @@ theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj
   -- First, we choose representatives for x and y.
   obtain ⟨Sx, x, rfl⟩ := exists_rep x
   obtain ⟨Sy, y, rfl⟩ := exists_rep y
-  simp only [res_mk_eq_mk_pullback] at h 
+  simp only [res_mk_eq_mk_pullback] at h
   -- Next, using our assumption,
   -- choose covers over which the pullbacks of these representatives become equal.
   choose W h1 h2 hh using fun I : S.arrow => (eq_mk_iff_exists _ _).mp (h I)
@@ -353,7 +353,7 @@ theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj
   let IS : S.arrow := I.from_middle
   specialize hh IS
   let IW : (W IS).arrow := I.to_middle
-  apply_fun fun e => e IW at hh 
+  apply_fun fun e => e IW at hh
   convert hh
   · let Rx : Sx.relation :=
       ⟨I.Y, I.Y, I.Y, 𝟙 _, 𝟙 _, I.f, I.to_middle_hom ≫ I.from_middle_hom, _, _, by
@@ -376,12 +376,12 @@ theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
     (X : C) : Function.Injective ((J.toPlus P).app (op X)) :=
   by
   intro x y h
-  simp only [to_plus_eq_mk] at h 
-  rw [eq_mk_iff_exists] at h 
+  simp only [to_plus_eq_mk] at h
+  rw [eq_mk_iff_exists] at h
   obtain ⟨W, h1, h2, hh⟩ := h
   apply hsep X W
   intro I
-  apply_fun fun e => e I at hh 
+  apply_fun fun e => e I at hh
   exact hh
 #align category_theory.grothendieck_topology.plus.inj_of_sep CategoryTheory.GrothendieckTopology.Plus.inj_of_sep
 -/
@@ -495,8 +495,8 @@ theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)
   · intro x y h
     apply sep P S _ _
     intro I
-    apply_fun meq.equiv _ _ at h 
-    apply_fun fun e => e I at h 
+    apply_fun meq.equiv _ _ at h
+    apply_fun fun e => e I at h
     convert h
     · erw [meq.equiv_apply, ← comp_apply, multiequalizer.lift_ι]
     · erw [meq.equiv_apply, ← comp_apply, multiequalizer.lift_ι]

4f4a1c87

bump to nightly-2024-01-11-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

c7c71e9e

Diff

@@ -721,30 +721,30 @@ theorem GrothendieckTopology.sheafify_isSheaf (P : Cᵒᵖ ⥤ D) : Presheaf.IsS
 
 variable (D)
 
-#print CategoryTheory.presheafToSheaf /-
+#print CategoryTheory.plusPlusSheaf /-
 /-- The sheafification functor, as a functor taking values in `Sheaf`. -/
 @[simps]
-def presheafToSheaf : (Cᵒᵖ ⥤ D) ⥤ Sheaf J D
+def plusPlusSheaf : (Cᵒᵖ ⥤ D) ⥤ Sheaf J D
     where
   obj P := ⟨J.sheafify P, J.sheafify_isSheaf P⟩
   map P Q η := ⟨J.sheafifyMap η⟩
   map_id' P := Sheaf.Hom.ext _ _ <| J.sheafifyMap_id _
   map_comp' P Q R f g := Sheaf.Hom.ext _ _ <| J.sheafifyMap_comp _ _
-#align category_theory.presheaf_to_Sheaf CategoryTheory.presheafToSheaf
+#align category_theory.presheaf_to_Sheaf CategoryTheory.plusPlusSheaf
 -/
 
-#print CategoryTheory.presheafToSheaf_preservesZeroMorphisms /-
-instance presheafToSheaf_preservesZeroMorphisms [Preadditive D] :
-    (presheafToSheaf J D).PreservesZeroMorphisms
+#print CategoryTheory.plusPlusSheaf_preservesZeroMorphisms /-
+instance plusPlusSheaf_preservesZeroMorphisms [Preadditive D] :
+    (plusPlusSheaf J D).PreservesZeroMorphisms
     where map_zero' F G := by ext;
     erw [colimit.ι_map, comp_zero, J.plus_map_zero, J.diagram_nat_trans_zero, zero_comp]
-#align category_theory.presheaf_to_Sheaf_preserves_zero_morphisms CategoryTheory.presheafToSheaf_preservesZeroMorphisms
+#align category_theory.presheaf_to_Sheaf_preserves_zero_morphisms CategoryTheory.plusPlusSheaf_preservesZeroMorphisms
 -/
 
-#print CategoryTheory.sheafificationAdjunction /-
+#print CategoryTheory.plusPlusAdjunction /-
 /-- The sheafification functor is left adjoint to the forgetful functor. -/
 @[simps unit_app counit_app_val]
-def sheafificationAdjunction : presheafToSheaf J D ⊣ sheafToPresheaf J D :=
+def plusPlusAdjunction : plusPlusSheaf J D ⊣ sheafToPresheaf J D :=
   Adjunction.mkOfHomEquiv
     { homEquiv := fun P Q =>
         { toFun := fun e => J.toSheafify P ≫ e.val
@@ -755,12 +755,12 @@ def sheafificationAdjunction : presheafToSheaf J D ⊣ sheafToPresheaf J D :=
         intro P Q R η γ; ext1; dsimp; symm
         apply J.sheafify_map_sheafify_lift
       homEquiv_naturality_right := fun P Q R η γ => by dsimp; rw [category.assoc] }
-#align category_theory.sheafification_adjunction CategoryTheory.sheafificationAdjunction
+#align category_theory.sheafification_adjunction CategoryTheory.plusPlusAdjunction
 -/
 
 #print CategoryTheory.sheafToPresheafIsRightAdjoint /-
 instance sheafToPresheafIsRightAdjoint : IsRightAdjoint (sheafToPresheaf J D) :=
-  ⟨_, sheafificationAdjunction J D⟩
+  ⟨_, plusPlusAdjunction J D⟩
 #align category_theory.Sheaf_to_presheaf_is_right_adjoint CategoryTheory.sheafToPresheafIsRightAdjoint
 -/
 
@@ -781,7 +781,7 @@ variable {J D}
 #print CategoryTheory.sheafificationIso /-
 /-- A sheaf `P` is isomorphic to its own sheafification. -/
 @[simps]
-def sheafificationIso (P : Sheaf J D) : P ≅ (presheafToSheaf J D).obj P.val
+def sheafificationIso (P : Sheaf J D) : P ≅ (plusPlusSheaf J D).obj P.val
     where
   Hom := ⟨(J.isoSheafify P.2).Hom⟩
   inv := ⟨(J.isoSheafify P.2).inv⟩
@@ -792,13 +792,13 @@ def sheafificationIso (P : Sheaf J D) : P ≅ (presheafToSheaf J D).obj P.val
 
 #print CategoryTheory.isIso_sheafificationAdjunction_counit /-
 instance isIso_sheafificationAdjunction_counit (P : Sheaf J D) :
-    IsIso ((sheafificationAdjunction J D).counit.app P) :=
+    IsIso ((plusPlusAdjunction J D).counit.app P) :=
   isIso_of_fully_faithful (sheafToPresheaf J D) _
 #align category_theory.is_iso_sheafification_adjunction_counit CategoryTheory.isIso_sheafificationAdjunction_counit
 -/
 
 #print CategoryTheory.sheafification_reflective /-
-instance sheafification_reflective : IsIso (sheafificationAdjunction J D).counit :=
+instance sheafification_reflective : IsIso (plusPlusAdjunction J D).counit :=
   NatIso.isIso_of_isIso_app _
 #align category_theory.sheafification_reflective CategoryTheory.sheafification_reflective
 -/

4f4a1c87

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 -/
-import Mathbin.CategoryTheory.Adjunction.FullyFaithful
-import Mathbin.CategoryTheory.Sites.Plus
-import Mathbin.CategoryTheory.Limits.ConcreteCategory
-import Mathbin.CategoryTheory.ConcreteCategory.Elementwise
+import CategoryTheory.Adjunction.FullyFaithful
+import CategoryTheory.Sites.Plus
+import CategoryTheory.Limits.ConcreteCategory
+import CategoryTheory.ConcreteCategory.Elementwise
 
 #align_import category_theory.sites.sheafification from "leanprover-community/mathlib"@"4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b"

4f4a1c87

bump to nightly-2023-08-02-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

7aca3f15

Diff

@@ -447,7 +447,7 @@ theorem exists_of_sep (P : Cᵒᵖ ⥤ D)
   simp only [res_mk_eq_mk_pullback, eq_mk_iff_exists]
   -- It suffices to prove equality for representatives over a
   -- convenient sufficiently large cover...
-  use (J.pullback II.f).obj (T I)
+  use(J.pullback II.f).obj (T I)
   let e0 : (J.pullback II.f).obj (T I) ⟶ (J.pullback II.f).obj ((J.pullback I.f).obj B) :=
     hom_of_le
       (by

4f4a1c87

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
-
-! This file was ported from Lean 3 source module category_theory.sites.sheafification
-! leanprover-community/mathlib commit 4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Adjunction.FullyFaithful
 import Mathbin.CategoryTheory.Sites.Plus
 import Mathbin.CategoryTheory.Limits.ConcreteCategory
 import Mathbin.CategoryTheory.ConcreteCategory.Elementwise
 
+#align_import category_theory.sites.sheafification from "leanprover-community/mathlib"@"4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b"
+
 /-!
 
 # Sheafification

4f4a1c87

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -66,30 +66,39 @@ instance {X} (P : Cᵒᵖ ⥤ D) (S : J.cover X) :
     CoeFun (Meq P S) fun x => ∀ I : S.arrow, P.obj (op I.y) :=
   ⟨fun x => x.1⟩
 
+#print CategoryTheory.Meq.ext /-
 @[ext]
 theorem ext {X} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x y : Meq P S) (h : ∀ I : S.arrow, x I = y I) :
     x = y :=
   Subtype.ext <| funext <| h
 #align category_theory.meq.ext CategoryTheory.Meq.ext
+-/
 
+#print CategoryTheory.Meq.condition /-
 theorem condition {X} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (I : S.Relation) :
     P.map I.g₁.op (x ((S.index P).fstTo I)) = P.map I.g₂.op (x ((S.index P).sndTo I)) :=
   x.2 _
 #align category_theory.meq.condition CategoryTheory.Meq.condition
+-/
 
+#print CategoryTheory.Meq.refine /-
 /-- Refine a term of `meq P T` with respect to a refinement `S ⟶ T` of covers. -/
 def refine {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P T) (e : S ⟶ T) : Meq P S :=
   ⟨fun I => x ⟨I.y, I.f, (leOfHom e) _ I.hf⟩, fun I =>
     x.condition
       ⟨I.y₁, I.y₂, I.z, I.g₁, I.g₂, I.f₁, I.f₂, (leOfHom e) _ I.h₁, (leOfHom e) _ I.h₂, I.w⟩⟩
 #align category_theory.meq.refine CategoryTheory.Meq.refine
+-/
 
+#print CategoryTheory.Meq.refine_apply /-
 @[simp]
 theorem refine_apply {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P T) (e : S ⟶ T)
     (I : S.arrow) : x.refine e I = x ⟨I.y, I.f, (leOfHom e) _ I.hf⟩ :=
   rfl
 #align category_theory.meq.refine_apply CategoryTheory.Meq.refine_apply
+-/
 
+#print CategoryTheory.Meq.pullback /-
 /-- Pull back a term of `meq P S` with respect to a morphism `f : Y ⟶ X` in `C`. -/
 def pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y ⟶ X) :
     Meq P ((J.pullback f).obj S) :=
@@ -97,29 +106,38 @@ def pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y
     x.condition
       ⟨I.y₁, I.y₂, I.z, I.g₁, I.g₂, I.f₁ ≫ f, I.f₂ ≫ f, I.h₁, I.h₂, by simp [reassoc_of I.w]⟩⟩
 #align category_theory.meq.pullback CategoryTheory.Meq.pullback
+-/
 
+#print CategoryTheory.Meq.pullback_apply /-
 @[simp]
 theorem pullback_apply {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y ⟶ X)
     (I : ((J.pullback f).obj S).arrow) : x.pullback f I = x ⟨_, I.f ≫ f, I.hf⟩ :=
   rfl
 #align category_theory.meq.pullback_apply CategoryTheory.Meq.pullback_apply
+-/
 
+#print CategoryTheory.Meq.pullback_refine /-
 @[simp]
 theorem pullback_refine {Y X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (h : S ⟶ T) (f : Y ⟶ X)
     (x : Meq P T) : (x.pullback f).refine ((J.pullback f).map h) = (refine x h).pullback _ :=
   rfl
 #align category_theory.meq.pullback_refine CategoryTheory.Meq.pullback_refine
+-/
 
+#print CategoryTheory.Meq.mk /-
 /-- Make a term of `meq P S`. -/
 def mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) : Meq P S :=
   ⟨fun I => P.map I.f.op x, fun I => by dsimp;
     simp only [← comp_apply, ← P.map_comp, ← op_comp, I.w]⟩
 #align category_theory.meq.mk CategoryTheory.Meq.mk
+-/
 
+#print CategoryTheory.Meq.mk_apply /-
 theorem mk_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) (I : S.arrow) :
     mk S x I = P.map I.f.op x :=
   rfl
 #align category_theory.meq.mk_apply CategoryTheory.Meq.mk_apply
+-/
 
 variable [PreservesLimits (forget D)]
 
@@ -131,13 +149,16 @@ noncomputable def equiv {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) [HasMultiequ
 #align category_theory.meq.equiv CategoryTheory.Meq.equiv
 -/
 
+#print CategoryTheory.Meq.equiv_apply /-
 @[simp]
 theorem equiv_apply {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} [HasMultiequalizer (S.index P)]
     (x : multiequalizer (S.index P)) (I : S.arrow) :
     equiv P S x I = Multiequalizer.ι (S.index P) I x :=
   rfl
 #align category_theory.meq.equiv_apply CategoryTheory.Meq.equiv_apply
+-/
 
+#print CategoryTheory.Meq.equiv_symm_eq_apply /-
 @[simp]
 theorem equiv_symm_eq_apply {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} [HasMultiequalizer (S.index P)]
     (x : Meq P S) (I : S.arrow) : Multiequalizer.ι (S.index P) I ((Meq.equiv P S).symm x) = x I :=
@@ -146,6 +167,7 @@ theorem equiv_symm_eq_apply {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} [HasMult
   rw [← equiv_apply]
   simp
 #align category_theory.meq.equiv_symm_eq_apply CategoryTheory.Meq.equiv_symm_eq_apply
+-/
 
 end Meq
 
@@ -165,11 +187,14 @@ variable [∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : J.cover X), HasMultiequalizer (S.
 
 noncomputable section
 
+#print CategoryTheory.GrothendieckTopology.Plus.mk /-
 /-- Make a term of `(J.plus_obj P).obj (op X)` from `x : meq P S`. -/
 def mk {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) : (J.plusObj P).obj (op X) :=
   colimit.ι (J.diagram P X) (op S) ((Meq.equiv P S).symm x)
 #align category_theory.grothendieck_topology.plus.mk CategoryTheory.GrothendieckTopology.Plus.mk
+-/
 
+#print CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback /-
 theorem res_mk_eq_mk_pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y ⟶ X) :
     (J.plusObj P).map f.op (mk x) = mk (x.pullback f) :=
   by
@@ -184,7 +209,9 @@ theorem res_mk_eq_mk_pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x :
   erw [multiequalizer.lift_ι, meq.equiv_symm_eq_apply]
   cases i; rfl
 #align category_theory.grothendieck_topology.plus.res_mk_eq_mk_pullback CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback
+-/
 
+#print CategoryTheory.GrothendieckTopology.Plus.toPlus_mk /-
 theorem toPlus_mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) :
     (J.toPlus P).app _ x = mk (Meq.mk S x) :=
   by
@@ -200,7 +227,9 @@ theorem toPlus_mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X))
   simpa only [← comp_apply, category.assoc, multiequalizer.lift_ι, category.comp_id,
     meq.equiv_symm_eq_apply]
 #align category_theory.grothendieck_topology.plus.to_plus_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_mk
+-/
 
+#print CategoryTheory.GrothendieckTopology.Plus.toPlus_apply /-
 theorem toPlus_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : Meq P S) (I : S.arrow) :
     (J.toPlus P).app _ (x I) = (J.plusObj P).map I.f.op (mk x) :=
   by
@@ -225,7 +254,9 @@ theorem toPlus_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : Meq P S) (
   erw [x.condition RR]
   simpa [RR]
 #align category_theory.grothendieck_topology.plus.to_plus_apply CategoryTheory.GrothendieckTopology.Plus.toPlus_apply
+-/
 
+#print CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mk /-
 theorem toPlus_eq_mk {X : C} {P : Cᵒᵖ ⥤ D} (x : P.obj (op X)) :
     (J.toPlus P).app _ x = mk (Meq.mk ⊤ x) :=
   by
@@ -237,9 +268,11 @@ theorem toPlus_eq_mk {X : C} {P : Cᵒᵖ ⥤ D} (x : P.obj (op X)) :
   ext i
   simpa
 #align category_theory.grothendieck_topology.plus.to_plus_eq_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mk
+-/
 
 variable [∀ X : C, PreservesColimitsOfShape (J.cover X)ᵒᵖ (forget D)]
 
+#print CategoryTheory.GrothendieckTopology.Plus.exists_rep /-
 theorem exists_rep {X : C} {P : Cᵒᵖ ⥤ D} (x : (J.plusObj P).obj (op X)) :
     ∃ (S : J.cover X) (y : Meq P S), x = mk y :=
   by
@@ -249,7 +282,9 @@ theorem exists_rep {X : C} {P : Cᵒᵖ ⥤ D} (x : (J.plusObj P).obj (op X)) :
   dsimp [mk]
   simp
 #align category_theory.grothendieck_topology.plus.exists_rep CategoryTheory.GrothendieckTopology.Plus.exists_rep
+-/
 
+#print CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_exists /-
 theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P S) (y : Meq P T) :
     mk x = mk y ↔ ∃ (W : J.cover X) (h1 : W ⟶ S) (h2 : W ⟶ T), x.refine h1 = y.refine h2 :=
   by
@@ -276,7 +311,9 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq
       simp only [← comp_apply, multiequalizer.lift_ι, meq.equiv_symm_eq_apply]
       cases i; rfl
 #align category_theory.grothendieck_topology.plus.eq_mk_iff_exists CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_exists
+-/
 
+#print CategoryTheory.GrothendieckTopology.Plus.sep /-
 /-- `P⁺` is always separated. -/
 theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj (op X))
     (h : ∀ I : S.arrow, (J.plusObj P).map I.f.op x = (J.plusObj P).map I.f.op y) : x = y :=
@@ -332,7 +369,9 @@ theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj
     have := y.condition Ry
     simpa using this
 #align category_theory.grothendieck_topology.plus.sep CategoryTheory.GrothendieckTopology.Plus.sep
+-/
 
+#print CategoryTheory.GrothendieckTopology.Plus.inj_of_sep /-
 theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
     (hsep :
       ∀ (X : C) (S : J.cover X) (x y : P.obj (op X)),
@@ -348,7 +387,9 @@ theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
   apply_fun fun e => e I at hh 
   exact hh
 #align category_theory.grothendieck_topology.plus.inj_of_sep CategoryTheory.GrothendieckTopology.Plus.inj_of_sep
+-/
 
+#print CategoryTheory.GrothendieckTopology.Plus.meqOfSep /-
 /-- An auxiliary definition to be used in the proof of `exists_of_sep` below.
   Given a compatible family of local sections for `P⁺`, and representatives of said sections,
   construct a compatible family of local sections of `P` over the combination of the covers
@@ -377,7 +418,9 @@ def meqOfSep (P : Cᵒᵖ ⥤ D)
     swap; · simp only [category.assoc, II.fst.middle_spec, II.snd.middle_spec]; apply II.w
     exact s.condition IR
 #align category_theory.grothendieck_topology.plus.meq_of_sep CategoryTheory.GrothendieckTopology.Plus.meqOfSep
+-/
 
+#print CategoryTheory.GrothendieckTopology.Plus.exists_of_sep /-
 theorem exists_of_sep (P : Cᵒᵖ ⥤ D)
     (hsep :
       ∀ (X : C) (S : J.cover X) (x y : P.obj (op X)),
@@ -435,9 +478,11 @@ theorem exists_of_sep (P : Cᵒᵖ ⥤ D)
   convert s.condition IR
   cases I; rfl
 #align category_theory.grothendieck_topology.plus.exists_of_sep CategoryTheory.GrothendieckTopology.Plus.exists_of_sep
+-/
 
 variable [ReflectsIsomorphisms (forget D)]
 
+#print CategoryTheory.GrothendieckTopology.Plus.isSheaf_of_sep /-
 /-- If `P` is separated, then `P⁺` is a sheaf. -/
 theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)
     (hsep :
@@ -469,9 +514,11 @@ theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)
     rw [← comp_apply, multiequalizer.lift_ι]
     rfl
 #align category_theory.grothendieck_topology.plus.is_sheaf_of_sep CategoryTheory.GrothendieckTopology.Plus.isSheaf_of_sep
+-/
 
 variable (J)
 
+#print CategoryTheory.GrothendieckTopology.Plus.isSheaf_plus_plus /-
 /-- `P⁺⁺` is always a sheaf. -/
 theorem isSheaf_plus_plus (P : Cᵒᵖ ⥤ D) : Presheaf.IsSheaf J (J.plusObj (J.plusObj P)) :=
   by
@@ -479,6 +526,7 @@ theorem isSheaf_plus_plus (P : Cᵒᵖ ⥤ D) : Presheaf.IsSheaf J (J.plusObj (J
   intro X S x y
   apply sep
 #align category_theory.grothendieck_topology.plus.is_sheaf_plus_plus CategoryTheory.GrothendieckTopology.Plus.isSheaf_plus_plus
+-/
 
 end Plus
 
@@ -487,71 +535,94 @@ variable (J)
 variable [∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : J.cover X), HasMultiequalizer (S.index P)]
   [∀ X : C, HasColimitsOfShape (J.cover X)ᵒᵖ D]
 
+#print CategoryTheory.GrothendieckTopology.sheafify /-
 /-- The sheafification of a presheaf `P`.
 *NOTE:* Additional hypotheses are needed to obtain a proof that this is a sheaf! -/
 def sheafify (P : Cᵒᵖ ⥤ D) : Cᵒᵖ ⥤ D :=
   J.plusObj (J.plusObj P)
 #align category_theory.grothendieck_topology.sheafify CategoryTheory.GrothendieckTopology.sheafify
+-/
 
+#print CategoryTheory.GrothendieckTopology.toSheafify /-
 /-- The canonical map from `P` to its sheafification. -/
 def toSheafify (P : Cᵒᵖ ⥤ D) : P ⟶ J.sheafify P :=
   J.toPlus P ≫ J.plusMap (J.toPlus P)
 #align category_theory.grothendieck_topology.to_sheafify CategoryTheory.GrothendieckTopology.toSheafify
+-/
 
+#print CategoryTheory.GrothendieckTopology.sheafifyMap /-
 /-- The canonical map on sheafifications induced by a morphism. -/
 def sheafifyMap {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) : J.sheafify P ⟶ J.sheafify Q :=
   J.plusMap <| J.plusMap η
 #align category_theory.grothendieck_topology.sheafify_map CategoryTheory.GrothendieckTopology.sheafifyMap
+-/
 
+#print CategoryTheory.GrothendieckTopology.sheafifyMap_id /-
 @[simp]
 theorem sheafifyMap_id (P : Cᵒᵖ ⥤ D) : J.sheafifyMap (𝟙 P) = 𝟙 (J.sheafify P) := by
   dsimp [sheafify_map, sheafify]; simp
 #align category_theory.grothendieck_topology.sheafify_map_id CategoryTheory.GrothendieckTopology.sheafifyMap_id
+-/
 
+#print CategoryTheory.GrothendieckTopology.sheafifyMap_comp /-
 @[simp]
 theorem sheafifyMap_comp {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q ⟶ R) :
     J.sheafifyMap (η ≫ γ) = J.sheafifyMap η ≫ J.sheafifyMap γ := by dsimp [sheafify_map, sheafify];
   simp
 #align category_theory.grothendieck_topology.sheafify_map_comp CategoryTheory.GrothendieckTopology.sheafifyMap_comp
+-/
 
+#print CategoryTheory.GrothendieckTopology.toSheafify_naturality /-
 @[simp, reassoc]
 theorem toSheafify_naturality {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) :
     η ≫ J.toSheafify _ = J.toSheafify _ ≫ J.sheafifyMap η := by
   dsimp [sheafify_map, sheafify, to_sheafify]; simp
 #align category_theory.grothendieck_topology.to_sheafify_naturality CategoryTheory.GrothendieckTopology.toSheafify_naturality
+-/
 
 variable (D)
 
+#print CategoryTheory.GrothendieckTopology.sheafification /-
 /-- The sheafification of a presheaf `P`, as a functor.
 *NOTE:* Additional hypotheses are needed to obtain a proof that this is a sheaf! -/
 def sheafification : (Cᵒᵖ ⥤ D) ⥤ Cᵒᵖ ⥤ D :=
   J.plusFunctor D ⋙ J.plusFunctor D
 #align category_theory.grothendieck_topology.sheafification CategoryTheory.GrothendieckTopology.sheafification
+-/
 
+#print CategoryTheory.GrothendieckTopology.sheafification_obj /-
 @[simp]
 theorem sheafification_obj (P : Cᵒᵖ ⥤ D) : (J.sheafification D).obj P = J.sheafify P :=
   rfl
 #align category_theory.grothendieck_topology.sheafification_obj CategoryTheory.GrothendieckTopology.sheafification_obj
+-/
 
+#print CategoryTheory.GrothendieckTopology.sheafification_map /-
 @[simp]
 theorem sheafification_map {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) :
     (J.sheafification D).map η = J.sheafifyMap η :=
   rfl
 #align category_theory.grothendieck_topology.sheafification_map CategoryTheory.GrothendieckTopology.sheafification_map
+-/
 
+#print CategoryTheory.GrothendieckTopology.toSheafification /-
 /-- The canonical map from `P` to its sheafification, as a natural transformation.
 *Note:* We only show this is a sheaf under additional hypotheses on `D`. -/
 def toSheafification : 𝟭 _ ⟶ sheafification J D :=
   J.toPlusNatTrans D ≫ whiskerRight (J.toPlusNatTrans D) (J.plusFunctor D)
 #align category_theory.grothendieck_topology.to_sheafification CategoryTheory.GrothendieckTopology.toSheafification
+-/
 
+#print CategoryTheory.GrothendieckTopology.toSheafification_app /-
 @[simp]
 theorem toSheafification_app (P : Cᵒᵖ ⥤ D) : (J.toSheafification D).app P = J.toSheafify P :=
   rfl
 #align category_theory.grothendieck_topology.to_sheafification_app CategoryTheory.GrothendieckTopology.toSheafification_app
+-/
 
 variable {D}
 
+#print CategoryTheory.GrothendieckTopology.isIso_toSheafify /-
 theorem isIso_toSheafify {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) : IsIso (J.toSheafify P) :=
   by
   dsimp [to_sheafify]
@@ -559,30 +630,40 @@ theorem isIso_toSheafify {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) : IsIso
   haveI : is_iso ((J.plus_functor D).map (J.to_plus P)) := by apply functor.map_is_iso
   exact @is_iso.comp_is_iso _ _ _ _ _ (J.to_plus P) ((J.plus_functor D).map (J.to_plus P)) _ _
 #align category_theory.grothendieck_topology.is_iso_to_sheafify CategoryTheory.GrothendieckTopology.isIso_toSheafify
+-/
 
+#print CategoryTheory.GrothendieckTopology.isoSheafify /-
 /-- If `P` is a sheaf, then `P` is isomorphic to `J.sheafify P`. -/
 def isoSheafify {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) : P ≅ J.sheafify P :=
   letI := is_iso_to_sheafify J hP
   as_iso (J.to_sheafify P)
 #align category_theory.grothendieck_topology.iso_sheafify CategoryTheory.GrothendieckTopology.isoSheafify
+-/
 
+#print CategoryTheory.GrothendieckTopology.isoSheafify_hom /-
 @[simp]
 theorem isoSheafify_hom {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) :
     (J.isoSheafify hP).Hom = J.toSheafify P :=
   rfl
 #align category_theory.grothendieck_topology.iso_sheafify_hom CategoryTheory.GrothendieckTopology.isoSheafify_hom
+-/
 
+#print CategoryTheory.GrothendieckTopology.sheafifyLift /-
 /-- Given a sheaf `Q` and a morphism `P ⟶ Q`, construct a morphism from
 `J.sheafifcation P` to `Q`. -/
 def sheafifyLift {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.IsSheaf J Q) : J.sheafify P ⟶ Q :=
   J.plusLift (J.plusLift η hQ) hQ
 #align category_theory.grothendieck_topology.sheafify_lift CategoryTheory.GrothendieckTopology.sheafifyLift
+-/
 
+#print CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLift /-
 @[simp, reassoc]
 theorem toSheafify_sheafifyLift {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.IsSheaf J Q) :
     J.toSheafify P ≫ sheafifyLift J η hQ = η := by dsimp only [sheafify_lift, to_sheafify]; simp
 #align category_theory.grothendieck_topology.to_sheafify_sheafify_lift CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLift
+-/
 
+#print CategoryTheory.GrothendieckTopology.sheafifyLift_unique /-
 theorem sheafifyLift_unique {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.IsSheaf J Q)
     (γ : J.sheafify P ⟶ Q) : J.toSheafify P ≫ γ = η → γ = sheafifyLift J η hQ :=
   by
@@ -592,7 +673,9 @@ theorem sheafifyLift_unique {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.
   rw [← category.assoc, ← plus_map_to_plus]
   exact h
 #align category_theory.grothendieck_topology.sheafify_lift_unique CategoryTheory.GrothendieckTopology.sheafifyLift_unique
+-/
 
+#print CategoryTheory.GrothendieckTopology.isoSheafify_inv /-
 @[simp]
 theorem isoSheafify_inv {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) :
     (J.isoSheafify hP).inv = J.sheafifyLift (𝟙 _) hP :=
@@ -600,7 +683,9 @@ theorem isoSheafify_inv {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) :
   apply J.sheafify_lift_unique
   simp [iso.comp_inv_eq]
 #align category_theory.grothendieck_topology.iso_sheafify_inv CategoryTheory.GrothendieckTopology.isoSheafify_inv
+-/
 
+#print CategoryTheory.GrothendieckTopology.sheafify_hom_ext /-
 theorem sheafify_hom_ext {P Q : Cᵒᵖ ⥤ D} (η γ : J.sheafify P ⟶ Q) (hQ : Presheaf.IsSheaf J Q)
     (h : J.toSheafify P ≫ η = J.toSheafify P ≫ γ) : η = γ :=
   by
@@ -609,7 +694,9 @@ theorem sheafify_hom_ext {P Q : Cᵒᵖ ⥤ D} (η γ : J.sheafify P ⟶ Q) (hQ
   rw [← category.assoc, ← category.assoc, ← plus_map_to_plus]
   exact h
 #align category_theory.grothendieck_topology.sheafify_hom_ext CategoryTheory.GrothendieckTopology.sheafify_hom_ext
+-/
 
+#print CategoryTheory.GrothendieckTopology.sheafifyMap_sheafifyLift /-
 @[simp, reassoc]
 theorem sheafifyMap_sheafifyLift {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q ⟶ R)
     (hR : Presheaf.IsSheaf J R) :
@@ -618,6 +705,7 @@ theorem sheafifyMap_sheafifyLift {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q
   apply J.sheafify_lift_unique
   rw [← category.assoc, ← J.to_sheafify_naturality, category.assoc, to_sheafify_sheafify_lift]
 #align category_theory.grothendieck_topology.sheafify_map_sheafify_lift CategoryTheory.GrothendieckTopology.sheafifyMap_sheafifyLift
+-/
 
 end GrothendieckTopology
 
@@ -628,12 +716,15 @@ variable [ConcreteCategory.{max v u} D] [PreservesLimits (forget D)]
   [∀ X : C, HasColimitsOfShape (J.cover X)ᵒᵖ D]
   [∀ X : C, PreservesColimitsOfShape (J.cover X)ᵒᵖ (forget D)] [ReflectsIsomorphisms (forget D)]
 
+#print CategoryTheory.GrothendieckTopology.sheafify_isSheaf /-
 theorem GrothendieckTopology.sheafify_isSheaf (P : Cᵒᵖ ⥤ D) : Presheaf.IsSheaf J (J.sheafify P) :=
   GrothendieckTopology.Plus.isSheaf_plus_plus _ _
 #align category_theory.grothendieck_topology.sheafify_is_sheaf CategoryTheory.GrothendieckTopology.sheafify_isSheaf
+-/
 
 variable (D)
 
+#print CategoryTheory.presheafToSheaf /-
 /-- The sheafification functor, as a functor taking values in `Sheaf`. -/
 @[simps]
 def presheafToSheaf : (Cᵒᵖ ⥤ D) ⥤ Sheaf J D
@@ -643,13 +734,17 @@ def presheafToSheaf : (Cᵒᵖ ⥤ D) ⥤ Sheaf J D
   map_id' P := Sheaf.Hom.ext _ _ <| J.sheafifyMap_id _
   map_comp' P Q R f g := Sheaf.Hom.ext _ _ <| J.sheafifyMap_comp _ _
 #align category_theory.presheaf_to_Sheaf CategoryTheory.presheafToSheaf
+-/
 
+#print CategoryTheory.presheafToSheaf_preservesZeroMorphisms /-
 instance presheafToSheaf_preservesZeroMorphisms [Preadditive D] :
     (presheafToSheaf J D).PreservesZeroMorphisms
     where map_zero' F G := by ext;
     erw [colimit.ι_map, comp_zero, J.plus_map_zero, J.diagram_nat_trans_zero, zero_comp]
 #align category_theory.presheaf_to_Sheaf_preserves_zero_morphisms CategoryTheory.presheafToSheaf_preservesZeroMorphisms
+-/
 
+#print CategoryTheory.sheafificationAdjunction /-
 /-- The sheafification functor is left adjoint to the forgetful functor. -/
 @[simps unit_app counit_app_val]
 def sheafificationAdjunction : presheafToSheaf J D ⊣ sheafToPresheaf J D :=
@@ -664,21 +759,29 @@ def sheafificationAdjunction : presheafToSheaf J D ⊣ sheafToPresheaf J D :=
         apply J.sheafify_map_sheafify_lift
       homEquiv_naturality_right := fun P Q R η γ => by dsimp; rw [category.assoc] }
 #align category_theory.sheafification_adjunction CategoryTheory.sheafificationAdjunction
+-/
 
+#print CategoryTheory.sheafToPresheafIsRightAdjoint /-
 instance sheafToPresheafIsRightAdjoint : IsRightAdjoint (sheafToPresheaf J D) :=
   ⟨_, sheafificationAdjunction J D⟩
 #align category_theory.Sheaf_to_presheaf_is_right_adjoint CategoryTheory.sheafToPresheafIsRightAdjoint
+-/
 
+#print CategoryTheory.presheaf_mono_of_mono /-
 instance presheaf_mono_of_mono {F G : Sheaf J D} (f : F ⟶ G) [Mono f] : Mono f.1 :=
   (sheafToPresheaf J D).map_mono _
 #align category_theory.presheaf_mono_of_mono CategoryTheory.presheaf_mono_of_mono
+-/
 
+#print CategoryTheory.Sheaf.Hom.mono_iff_presheaf_mono /-
 theorem Sheaf.Hom.mono_iff_presheaf_mono {F G : Sheaf J D} (f : F ⟶ G) : Mono f ↔ Mono f.1 :=
   ⟨fun m => by skip; infer_instance, fun m => by skip; exact Sheaf.hom.mono_of_presheaf_mono J D f⟩
 #align category_theory.Sheaf.hom.mono_iff_presheaf_mono CategoryTheory.Sheaf.Hom.mono_iff_presheaf_mono
+-/
 
 variable {J D}
 
+#print CategoryTheory.sheafificationIso /-
 /-- A sheaf `P` is isomorphic to its own sheafification. -/
 @[simps]
 def sheafificationIso (P : Sheaf J D) : P ≅ (presheafToSheaf J D).obj P.val
@@ -688,15 +791,20 @@ def sheafificationIso (P : Sheaf J D) : P ≅ (presheafToSheaf J D).obj P.val
   hom_inv_id' := by ext1; apply (J.iso_sheafify P.2).hom_inv_id
   inv_hom_id' := by ext1; apply (J.iso_sheafify P.2).inv_hom_id
 #align category_theory.sheafification_iso CategoryTheory.sheafificationIso
+-/
 
+#print CategoryTheory.isIso_sheafificationAdjunction_counit /-
 instance isIso_sheafificationAdjunction_counit (P : Sheaf J D) :
     IsIso ((sheafificationAdjunction J D).counit.app P) :=
   isIso_of_fully_faithful (sheafToPresheaf J D) _
 #align category_theory.is_iso_sheafification_adjunction_counit CategoryTheory.isIso_sheafificationAdjunction_counit
+-/
 
+#print CategoryTheory.sheafification_reflective /-
 instance sheafification_reflective : IsIso (sheafificationAdjunction J D).counit :=
   NatIso.isIso_of_isIso_app _
 #align category_theory.sheafification_reflective CategoryTheory.sheafification_reflective
+-/
 
 end CategoryTheory

4f4a1c87

bump to nightly-2023-06-13-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

c9322c77

Diff

@@ -138,7 +138,6 @@ theorem equiv_apply {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} [HasMultiequaliz
   rfl
 #align category_theory.meq.equiv_apply CategoryTheory.Meq.equiv_apply
 
-#print CategoryTheory.Meq.equiv_symm_eq_apply /-
 @[simp]
 theorem equiv_symm_eq_apply {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} [HasMultiequalizer (S.index P)]
     (x : Meq P S) (I : S.arrow) : Multiequalizer.ι (S.index P) I ((Meq.equiv P S).symm x) = x I :=
@@ -147,7 +146,6 @@ theorem equiv_symm_eq_apply {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} [HasMult
   rw [← equiv_apply]
   simp
 #align category_theory.meq.equiv_symm_eq_apply CategoryTheory.Meq.equiv_symm_eq_apply
--/
 
 end Meq

4f4a1c87

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -260,7 +260,7 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq
     obtain ⟨W, h1, h2, hh⟩ := concrete.colimit_exists_of_rep_eq _ _ _ h
     use W.unop, h1.unop, h2.unop
     ext I
-    apply_fun multiequalizer.ι (W.unop.index P) I  at hh 
+    apply_fun multiequalizer.ι (W.unop.index P) I at hh 
     convert hh
     all_goals
       dsimp [diagram]
@@ -271,7 +271,7 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq
     use op S, h1.op, h2.op
     apply concrete.multiequalizer_ext
     intro i
-    apply_fun fun ee => ee i  at e 
+    apply_fun fun ee => ee i at e 
     convert e
     all_goals
       dsimp [diagram]
@@ -321,7 +321,7 @@ theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj
   let IS : S.arrow := I.from_middle
   specialize hh IS
   let IW : (W IS).arrow := I.to_middle
-  apply_fun fun e => e IW  at hh 
+  apply_fun fun e => e IW at hh 
   convert hh
   · let Rx : Sx.relation :=
       ⟨I.Y, I.Y, I.Y, 𝟙 _, 𝟙 _, I.f, I.to_middle_hom ≫ I.from_middle_hom, _, _, by
@@ -347,7 +347,7 @@ theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
   obtain ⟨W, h1, h2, hh⟩ := h
   apply hsep X W
   intro I
-  apply_fun fun e => e I  at hh 
+  apply_fun fun e => e I at hh 
   exact hh
 #align category_theory.grothendieck_topology.plus.inj_of_sep CategoryTheory.GrothendieckTopology.Plus.inj_of_sep
 
@@ -455,8 +455,8 @@ theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)
   · intro x y h
     apply sep P S _ _
     intro I
-    apply_fun meq.equiv _ _  at h 
-    apply_fun fun e => e I  at h 
+    apply_fun meq.equiv _ _ at h 
+    apply_fun fun e => e I at h 
     convert h
     · erw [meq.equiv_apply, ← comp_apply, multiequalizer.lift_ι]
     · erw [meq.equiv_apply, ← comp_apply, multiequalizer.lift_ι]

4f4a1c87

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -243,7 +243,7 @@ theorem toPlus_eq_mk {X : C} {P : Cᵒᵖ ⥤ D} (x : P.obj (op X)) :
 variable [∀ X : C, PreservesColimitsOfShape (J.cover X)ᵒᵖ (forget D)]
 
 theorem exists_rep {X : C} {P : Cᵒᵖ ⥤ D} (x : (J.plusObj P).obj (op X)) :
-    ∃ (S : J.cover X)(y : Meq P S), x = mk y :=
+    ∃ (S : J.cover X) (y : Meq P S), x = mk y :=
   by
   obtain ⟨S, y, h⟩ := concrete.colimit_exists_rep (J.diagram P X) x
   use S.unop, meq.equiv _ _ y
@@ -253,14 +253,14 @@ theorem exists_rep {X : C} {P : Cᵒᵖ ⥤ D} (x : (J.plusObj P).obj (op X)) :
 #align category_theory.grothendieck_topology.plus.exists_rep CategoryTheory.GrothendieckTopology.Plus.exists_rep
 
 theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P S) (y : Meq P T) :
-    mk x = mk y ↔ ∃ (W : J.cover X)(h1 : W ⟶ S)(h2 : W ⟶ T), x.refine h1 = y.refine h2 :=
+    mk x = mk y ↔ ∃ (W : J.cover X) (h1 : W ⟶ S) (h2 : W ⟶ T), x.refine h1 = y.refine h2 :=
   by
   constructor
   · intro h
     obtain ⟨W, h1, h2, hh⟩ := concrete.colimit_exists_of_rep_eq _ _ _ h
     use W.unop, h1.unop, h2.unop
     ext I
-    apply_fun multiequalizer.ι (W.unop.index P) I  at hh
+    apply_fun multiequalizer.ι (W.unop.index P) I  at hh 
     convert hh
     all_goals
       dsimp [diagram]
@@ -271,7 +271,7 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq
     use op S, h1.op, h2.op
     apply concrete.multiequalizer_ext
     intro i
-    apply_fun fun ee => ee i  at e
+    apply_fun fun ee => ee i  at e 
     convert e
     all_goals
       dsimp [diagram]
@@ -286,7 +286,7 @@ theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj
   -- First, we choose representatives for x and y.
   obtain ⟨Sx, x, rfl⟩ := exists_rep x
   obtain ⟨Sy, y, rfl⟩ := exists_rep y
-  simp only [res_mk_eq_mk_pullback] at h
+  simp only [res_mk_eq_mk_pullback] at h 
   -- Next, using our assumption,
   -- choose covers over which the pullbacks of these representatives become equal.
   choose W h1 h2 hh using fun I : S.arrow => (eq_mk_iff_exists _ _).mp (h I)
@@ -321,7 +321,7 @@ theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj
   let IS : S.arrow := I.from_middle
   specialize hh IS
   let IW : (W IS).arrow := I.to_middle
-  apply_fun fun e => e IW  at hh
+  apply_fun fun e => e IW  at hh 
   convert hh
   · let Rx : Sx.relation :=
       ⟨I.Y, I.Y, I.Y, 𝟙 _, 𝟙 _, I.f, I.to_middle_hom ≫ I.from_middle_hom, _, _, by
@@ -342,12 +342,12 @@ theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
     (X : C) : Function.Injective ((J.toPlus P).app (op X)) :=
   by
   intro x y h
-  simp only [to_plus_eq_mk] at h
-  rw [eq_mk_iff_exists] at h
+  simp only [to_plus_eq_mk] at h 
+  rw [eq_mk_iff_exists] at h 
   obtain ⟨W, h1, h2, hh⟩ := h
   apply hsep X W
   intro I
-  apply_fun fun e => e I  at hh
+  apply_fun fun e => e I  at hh 
   exact hh
 #align category_theory.grothendieck_topology.plus.inj_of_sep CategoryTheory.GrothendieckTopology.Plus.inj_of_sep
 
@@ -455,8 +455,8 @@ theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)
   · intro x y h
     apply sep P S _ _
     intro I
-    apply_fun meq.equiv _ _  at h
-    apply_fun fun e => e I  at h
+    apply_fun meq.equiv _ _  at h 
+    apply_fun fun e => e I  at h 
     convert h
     · erw [meq.equiv_apply, ← comp_apply, multiequalizer.lift_ι]
     · erw [meq.equiv_apply, ← comp_apply, multiequalizer.lift_ι]

4f4a1c87

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -66,29 +66,17 @@ instance {X} (P : Cᵒᵖ ⥤ D) (S : J.cover X) :
     CoeFun (Meq P S) fun x => ∀ I : S.arrow, P.obj (op I.y) :=
   ⟨fun x => x.1⟩
 
-/- warning: category_theory.meq.ext -> CategoryTheory.Meq.ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.meq.ext CategoryTheory.Meq.extₓ'. -/
 @[ext]
 theorem ext {X} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x y : Meq P S) (h : ∀ I : S.arrow, x I = y I) :
     x = y :=
   Subtype.ext <| funext <| h
 #align category_theory.meq.ext CategoryTheory.Meq.ext
 
-/- warning: category_theory.meq.condition -> CategoryTheory.Meq.condition is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.meq.condition CategoryTheory.Meq.conditionₓ'. -/
 theorem condition {X} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (I : S.Relation) :
     P.map I.g₁.op (x ((S.index P).fstTo I)) = P.map I.g₂.op (x ((S.index P).sndTo I)) :=
   x.2 _
 #align category_theory.meq.condition CategoryTheory.Meq.condition
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.meq.refine CategoryTheory.Meq.refineₓ'. -/
 /-- Refine a term of `meq P T` with respect to a refinement `S ⟶ T` of covers. -/
 def refine {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P T) (e : S ⟶ T) : Meq P S :=
   ⟨fun I => x ⟨I.y, I.f, (leOfHom e) _ I.hf⟩, fun I =>
@@ -96,21 +84,12 @@ def refine {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P T) (e : S 
       ⟨I.y₁, I.y₂, I.z, I.g₁, I.g₂, I.f₁, I.f₂, (leOfHom e) _ I.h₁, (leOfHom e) _ I.h₂, I.w⟩⟩
 #align category_theory.meq.refine CategoryTheory.Meq.refine
 
-/- warning: category_theory.meq.refine_apply -> CategoryTheory.Meq.refine_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.meq.refine_apply CategoryTheory.Meq.refine_applyₓ'. -/
 @[simp]
 theorem refine_apply {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P T) (e : S ⟶ T)
     (I : S.arrow) : x.refine e I = x ⟨I.y, I.f, (leOfHom e) _ I.hf⟩ :=
   rfl
 #align category_theory.meq.refine_apply CategoryTheory.Meq.refine_apply
 
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 /-- Pull back a term of `meq P S` with respect to a morphism `f : Y ⟶ X` in `C`. -/
 def pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y ⟶ X) :
     Meq P ((J.pullback f).obj S) :=
@@ -119,39 +98,24 @@ def pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y
       ⟨I.y₁, I.y₂, I.z, I.g₁, I.g₂, I.f₁ ≫ f, I.f₂ ≫ f, I.h₁, I.h₂, by simp [reassoc_of I.w]⟩⟩
 #align category_theory.meq.pullback CategoryTheory.Meq.pullback
 
-/- warning: category_theory.meq.pullback_apply -> CategoryTheory.Meq.pullback_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.meq.pullback_apply CategoryTheory.Meq.pullback_applyₓ'. -/
 @[simp]
 theorem pullback_apply {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y ⟶ X)
     (I : ((J.pullback f).obj S).arrow) : x.pullback f I = x ⟨_, I.f ≫ f, I.hf⟩ :=
   rfl
 #align category_theory.meq.pullback_apply CategoryTheory.Meq.pullback_apply
 
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 @[simp]
 theorem pullback_refine {Y X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (h : S ⟶ T) (f : Y ⟶ X)
     (x : Meq P T) : (x.pullback f).refine ((J.pullback f).map h) = (refine x h).pullback _ :=
   rfl
 #align category_theory.meq.pullback_refine CategoryTheory.Meq.pullback_refine
 
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 /-- Make a term of `meq P S`. -/
 def mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) : Meq P S :=
   ⟨fun I => P.map I.f.op x, fun I => by dsimp;
     simp only [← comp_apply, ← P.map_comp, ← op_comp, I.w]⟩
 #align category_theory.meq.mk CategoryTheory.Meq.mk
 
-/- warning: category_theory.meq.mk_apply -> CategoryTheory.Meq.mk_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.meq.mk_apply CategoryTheory.Meq.mk_applyₓ'. -/
 theorem mk_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) (I : S.arrow) :
     mk S x I = P.map I.f.op x :=
   rfl
@@ -167,9 +131,6 @@ noncomputable def equiv {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) [HasMultiequ
 #align category_theory.meq.equiv CategoryTheory.Meq.equiv
 -/
 
-/- warning: category_theory.meq.equiv_apply -> CategoryTheory.Meq.equiv_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.meq.equiv_apply CategoryTheory.Meq.equiv_applyₓ'. -/
 @[simp]
 theorem equiv_apply {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} [HasMultiequalizer (S.index P)]
     (x : multiequalizer (S.index P)) (I : S.arrow) :
@@ -206,20 +167,11 @@ variable [∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : J.cover X), HasMultiequalizer (S.
 
 noncomputable section
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.mk CategoryTheory.GrothendieckTopology.Plus.mkₓ'. -/
 /-- Make a term of `(J.plus_obj P).obj (op X)` from `x : meq P S`. -/
 def mk {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) : (J.plusObj P).obj (op X) :=
   colimit.ι (J.diagram P X) (op S) ((Meq.equiv P S).symm x)
 #align category_theory.grothendieck_topology.plus.mk CategoryTheory.GrothendieckTopology.Plus.mk
 
-/- warning: category_theory.grothendieck_topology.plus.res_mk_eq_mk_pullback -> CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.res_mk_eq_mk_pullback CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullbackₓ'. -/
 theorem res_mk_eq_mk_pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y ⟶ X) :
     (J.plusObj P).map f.op (mk x) = mk (x.pullback f) :=
   by
@@ -235,9 +187,6 @@ theorem res_mk_eq_mk_pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x :
   cases i; rfl
 #align category_theory.grothendieck_topology.plus.res_mk_eq_mk_pullback CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback
 
-/- warning: category_theory.grothendieck_topology.plus.to_plus_mk -> CategoryTheory.GrothendieckTopology.Plus.toPlus_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.to_plus_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_mkₓ'. -/
 theorem toPlus_mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) :
     (J.toPlus P).app _ x = mk (Meq.mk S x) :=
   by
@@ -254,9 +203,6 @@ theorem toPlus_mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X))
     meq.equiv_symm_eq_apply]
 #align category_theory.grothendieck_topology.plus.to_plus_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_mk
 
-/- warning: category_theory.grothendieck_topology.plus.to_plus_apply -> CategoryTheory.GrothendieckTopology.Plus.toPlus_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.to_plus_apply CategoryTheory.GrothendieckTopology.Plus.toPlus_applyₓ'. -/
 theorem toPlus_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : Meq P S) (I : S.arrow) :
     (J.toPlus P).app _ (x I) = (J.plusObj P).map I.f.op (mk x) :=
   by
@@ -282,9 +228,6 @@ theorem toPlus_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : Meq P S) (
   simpa [RR]
 #align category_theory.grothendieck_topology.plus.to_plus_apply CategoryTheory.GrothendieckTopology.Plus.toPlus_apply
 
-/- warning: category_theory.grothendieck_topology.plus.to_plus_eq_mk -> CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mk is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.to_plus_eq_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mkₓ'. -/
 theorem toPlus_eq_mk {X : C} {P : Cᵒᵖ ⥤ D} (x : P.obj (op X)) :
     (J.toPlus P).app _ x = mk (Meq.mk ⊤ x) :=
   by
@@ -299,9 +242,6 @@ theorem toPlus_eq_mk {X : C} {P : Cᵒᵖ ⥤ D} (x : P.obj (op X)) :
 
 variable [∀ X : C, PreservesColimitsOfShape (J.cover X)ᵒᵖ (forget D)]
 
-/- warning: category_theory.grothendieck_topology.plus.exists_rep -> CategoryTheory.GrothendieckTopology.Plus.exists_rep is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.exists_rep CategoryTheory.GrothendieckTopology.Plus.exists_repₓ'. -/
 theorem exists_rep {X : C} {P : Cᵒᵖ ⥤ D} (x : (J.plusObj P).obj (op X)) :
     ∃ (S : J.cover X)(y : Meq P S), x = mk y :=
   by
@@ -312,9 +252,6 @@ theorem exists_rep {X : C} {P : Cᵒᵖ ⥤ D} (x : (J.plusObj P).obj (op X)) :
   simp
 #align category_theory.grothendieck_topology.plus.exists_rep CategoryTheory.GrothendieckTopology.Plus.exists_rep
 
-/- warning: category_theory.grothendieck_topology.plus.eq_mk_iff_exists -> CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_exists is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.eq_mk_iff_exists CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_existsₓ'. -/
 theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P S) (y : Meq P T) :
     mk x = mk y ↔ ∃ (W : J.cover X)(h1 : W ⟶ S)(h2 : W ⟶ T), x.refine h1 = y.refine h2 :=
   by
@@ -342,9 +279,6 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq
       cases i; rfl
 #align category_theory.grothendieck_topology.plus.eq_mk_iff_exists CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_exists
 
-/- warning: category_theory.grothendieck_topology.plus.sep -> CategoryTheory.GrothendieckTopology.Plus.sep is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.sep CategoryTheory.GrothendieckTopology.Plus.sepₓ'. -/
 /-- `P⁺` is always separated. -/
 theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj (op X))
     (h : ∀ I : S.arrow, (J.plusObj P).map I.f.op x = (J.plusObj P).map I.f.op y) : x = y :=
@@ -401,9 +335,6 @@ theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj
     simpa using this
 #align category_theory.grothendieck_topology.plus.sep CategoryTheory.GrothendieckTopology.Plus.sep
 
-/- warning: category_theory.grothendieck_topology.plus.inj_of_sep -> CategoryTheory.GrothendieckTopology.Plus.inj_of_sep is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.inj_of_sep CategoryTheory.GrothendieckTopology.Plus.inj_of_sepₓ'. -/
 theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
     (hsep :
       ∀ (X : C) (S : J.cover X) (x y : P.obj (op X)),
@@ -420,9 +351,6 @@ theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
   exact hh
 #align category_theory.grothendieck_topology.plus.inj_of_sep CategoryTheory.GrothendieckTopology.Plus.inj_of_sep
 
-/- warning: category_theory.grothendieck_topology.plus.meq_of_sep -> CategoryTheory.GrothendieckTopology.Plus.meqOfSep is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.meq_of_sep CategoryTheory.GrothendieckTopology.Plus.meqOfSepₓ'. -/
 /-- An auxiliary definition to be used in the proof of `exists_of_sep` below.
   Given a compatible family of local sections for `P⁺`, and representatives of said sections,
   construct a compatible family of local sections of `P` over the combination of the covers
@@ -452,9 +380,6 @@ def meqOfSep (P : Cᵒᵖ ⥤ D)
     exact s.condition IR
 #align category_theory.grothendieck_topology.plus.meq_of_sep CategoryTheory.GrothendieckTopology.Plus.meqOfSep
 
-/- warning: category_theory.grothendieck_topology.plus.exists_of_sep -> CategoryTheory.GrothendieckTopology.Plus.exists_of_sep is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.exists_of_sep CategoryTheory.GrothendieckTopology.Plus.exists_of_sepₓ'. -/
 theorem exists_of_sep (P : Cᵒᵖ ⥤ D)
     (hsep :
       ∀ (X : C) (S : J.cover X) (x y : P.obj (op X)),
@@ -515,9 +440,6 @@ theorem exists_of_sep (P : Cᵒᵖ ⥤ D)
 
 variable [ReflectsIsomorphisms (forget D)]
 
-/- warning: category_theory.grothendieck_topology.plus.is_sheaf_of_sep -> CategoryTheory.GrothendieckTopology.Plus.isSheaf_of_sep is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.is_sheaf_of_sep CategoryTheory.GrothendieckTopology.Plus.isSheaf_of_sepₓ'. -/
 /-- If `P` is separated, then `P⁺` is a sheaf. -/
 theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)
     (hsep :
@@ -552,12 +474,6 @@ theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)
 
 variable (J)
 
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 /-- `P⁺⁺` is always a sheaf. -/
 theorem isSheaf_plus_plus (P : Cᵒᵖ ⥤ D) : Presheaf.IsSheaf J (J.plusObj (J.plusObj P)) :=
   by
@@ -573,63 +489,33 @@ variable (J)
 variable [∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : J.cover X), HasMultiequalizer (S.index P)]
   [∀ X : C, HasColimitsOfShape (J.cover X)ᵒᵖ D]
 
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 /-- The sheafification of a presheaf `P`.
 *NOTE:* Additional hypotheses are needed to obtain a proof that this is a sheaf! -/
 def sheafify (P : Cᵒᵖ ⥤ D) : Cᵒᵖ ⥤ D :=
   J.plusObj (J.plusObj P)
 #align category_theory.grothendieck_topology.sheafify CategoryTheory.GrothendieckTopology.sheafify
 
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 /-- The canonical map from `P` to its sheafification. -/
 def toSheafify (P : Cᵒᵖ ⥤ D) : P ⟶ J.sheafify P :=
   J.toPlus P ≫ J.plusMap (J.toPlus P)
 #align category_theory.grothendieck_topology.to_sheafify CategoryTheory.GrothendieckTopology.toSheafify
 
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 /-- The canonical map on sheafifications induced by a morphism. -/
 def sheafifyMap {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) : J.sheafify P ⟶ J.sheafify Q :=
   J.plusMap <| J.plusMap η
 #align category_theory.grothendieck_topology.sheafify_map CategoryTheory.GrothendieckTopology.sheafifyMap
 
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 @[simp]
 theorem sheafifyMap_id (P : Cᵒᵖ ⥤ D) : J.sheafifyMap (𝟙 P) = 𝟙 (J.sheafify P) := by
   dsimp [sheafify_map, sheafify]; simp
 #align category_theory.grothendieck_topology.sheafify_map_id CategoryTheory.GrothendieckTopology.sheafifyMap_id
 
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-<too large>
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 @[simp]
 theorem sheafifyMap_comp {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q ⟶ R) :
     J.sheafifyMap (η ≫ γ) = J.sheafifyMap η ≫ J.sheafifyMap γ := by dsimp [sheafify_map, sheafify];
   simp
 #align category_theory.grothendieck_topology.sheafify_map_comp CategoryTheory.GrothendieckTopology.sheafifyMap_comp
 
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-<too large>
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 @[simp, reassoc]
 theorem toSheafify_naturality {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) :
     η ≫ J.toSheafify _ = J.toSheafify _ ≫ J.sheafifyMap η := by
@@ -638,53 +524,29 @@ theorem toSheafify_naturality {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) :
 
 variable (D)
 
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 /-- The sheafification of a presheaf `P`, as a functor.
 *NOTE:* Additional hypotheses are needed to obtain a proof that this is a sheaf! -/
 def sheafification : (Cᵒᵖ ⥤ D) ⥤ Cᵒᵖ ⥤ D :=
   J.plusFunctor D ⋙ J.plusFunctor D
 #align category_theory.grothendieck_topology.sheafification CategoryTheory.GrothendieckTopology.sheafification
 
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 @[simp]
 theorem sheafification_obj (P : Cᵒᵖ ⥤ D) : (J.sheafification D).obj P = J.sheafify P :=
   rfl
 #align category_theory.grothendieck_topology.sheafification_obj CategoryTheory.GrothendieckTopology.sheafification_obj
 
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 @[simp]
 theorem sheafification_map {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) :
     (J.sheafification D).map η = J.sheafifyMap η :=
   rfl
 #align category_theory.grothendieck_topology.sheafification_map CategoryTheory.GrothendieckTopology.sheafification_map
 
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 /-- The canonical map from `P` to its sheafification, as a natural transformation.
 *Note:* We only show this is a sheaf under additional hypotheses on `D`. -/
 def toSheafification : 𝟭 _ ⟶ sheafification J D :=
   J.toPlusNatTrans D ≫ whiskerRight (J.toPlusNatTrans D) (J.plusFunctor D)
 #align category_theory.grothendieck_topology.to_sheafification CategoryTheory.GrothendieckTopology.toSheafification
 
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 @[simp]
 theorem toSheafification_app (P : Cᵒᵖ ⥤ D) : (J.toSheafification D).app P = J.toSheafify P :=
   rfl
@@ -692,12 +554,6 @@ theorem toSheafification_app (P : Cᵒᵖ ⥤ D) : (J.toSheafification D).app P
 
 variable {D}
 
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 theorem isIso_toSheafify {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) : IsIso (J.toSheafify P) :=
   by
   dsimp [to_sheafify]
@@ -706,56 +562,29 @@ theorem isIso_toSheafify {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) : IsIso
   exact @is_iso.comp_is_iso _ _ _ _ _ (J.to_plus P) ((J.plus_functor D).map (J.to_plus P)) _ _
 #align category_theory.grothendieck_topology.is_iso_to_sheafify CategoryTheory.GrothendieckTopology.isIso_toSheafify
 
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 /-- If `P` is a sheaf, then `P` is isomorphic to `J.sheafify P`. -/
 def isoSheafify {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) : P ≅ J.sheafify P :=
   letI := is_iso_to_sheafify J hP
   as_iso (J.to_sheafify P)
 #align category_theory.grothendieck_topology.iso_sheafify CategoryTheory.GrothendieckTopology.isoSheafify
 
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 @[simp]
 theorem isoSheafify_hom {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) :
     (J.isoSheafify hP).Hom = J.toSheafify P :=
   rfl
 #align category_theory.grothendieck_topology.iso_sheafify_hom CategoryTheory.GrothendieckTopology.isoSheafify_hom
 
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 /-- Given a sheaf `Q` and a morphism `P ⟶ Q`, construct a morphism from
 `J.sheafifcation P` to `Q`. -/
 def sheafifyLift {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.IsSheaf J Q) : J.sheafify P ⟶ Q :=
   J.plusLift (J.plusLift η hQ) hQ
 #align category_theory.grothendieck_topology.sheafify_lift CategoryTheory.GrothendieckTopology.sheafifyLift
 
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 @[simp, reassoc]
 theorem toSheafify_sheafifyLift {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.IsSheaf J Q) :
     J.toSheafify P ≫ sheafifyLift J η hQ = η := by dsimp only [sheafify_lift, to_sheafify]; simp
 #align category_theory.grothendieck_topology.to_sheafify_sheafify_lift CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLift
 
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 theorem sheafifyLift_unique {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.IsSheaf J Q)
     (γ : J.sheafify P ⟶ Q) : J.toSheafify P ≫ γ = η → γ = sheafifyLift J η hQ :=
   by
@@ -766,12 +595,6 @@ theorem sheafifyLift_unique {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.
   exact h
 #align category_theory.grothendieck_topology.sheafify_lift_unique CategoryTheory.GrothendieckTopology.sheafifyLift_unique
 
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 @[simp]
 theorem isoSheafify_inv {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) :
     (J.isoSheafify hP).inv = J.sheafifyLift (𝟙 _) hP :=
@@ -780,9 +603,6 @@ theorem isoSheafify_inv {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) :
   simp [iso.comp_inv_eq]
 #align category_theory.grothendieck_topology.iso_sheafify_inv CategoryTheory.GrothendieckTopology.isoSheafify_inv
 
-/- warning: category_theory.grothendieck_topology.sheafify_hom_ext -> CategoryTheory.GrothendieckTopology.sheafify_hom_ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_hom_ext CategoryTheory.GrothendieckTopology.sheafify_hom_extₓ'. -/
 theorem sheafify_hom_ext {P Q : Cᵒᵖ ⥤ D} (η γ : J.sheafify P ⟶ Q) (hQ : Presheaf.IsSheaf J Q)
     (h : J.toSheafify P ≫ η = J.toSheafify P ≫ γ) : η = γ :=
   by
@@ -792,9 +612,6 @@ theorem sheafify_hom_ext {P Q : Cᵒᵖ ⥤ D} (η γ : J.sheafify P ⟶ Q) (hQ
   exact h
 #align category_theory.grothendieck_topology.sheafify_hom_ext CategoryTheory.GrothendieckTopology.sheafify_hom_ext
 
-/- warning: category_theory.grothendieck_topology.sheafify_map_sheafify_lift -> CategoryTheory.GrothendieckTopology.sheafifyMap_sheafifyLift is a dubious translation:
-<too large>
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 @[simp, reassoc]
 theorem sheafifyMap_sheafifyLift {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q ⟶ R)
     (hR : Presheaf.IsSheaf J R) :
@@ -813,24 +630,12 @@ variable [ConcreteCategory.{max v u} D] [PreservesLimits (forget D)]
   [∀ X : C, HasColimitsOfShape (J.cover X)ᵒᵖ D]
   [∀ X : C, PreservesColimitsOfShape (J.cover X)ᵒᵖ (forget D)] [ReflectsIsomorphisms (forget D)]
 
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 theorem GrothendieckTopology.sheafify_isSheaf (P : Cᵒᵖ ⥤ D) : Presheaf.IsSheaf J (J.sheafify P) :=
   GrothendieckTopology.Plus.isSheaf_plus_plus _ _
 #align category_theory.grothendieck_topology.sheafify_is_sheaf CategoryTheory.GrothendieckTopology.sheafify_isSheaf
 
 variable (D)
 
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 /-- The sheafification functor, as a functor taking values in `Sheaf`. -/
 @[simps]
 def presheafToSheaf : (Cᵒᵖ ⥤ D) ⥤ Sheaf J D
@@ -841,24 +646,12 @@ def presheafToSheaf : (Cᵒᵖ ⥤ D) ⥤ Sheaf J D
   map_comp' P Q R f g := Sheaf.Hom.ext _ _ <| J.sheafifyMap_comp _ _
 #align category_theory.presheaf_to_Sheaf CategoryTheory.presheafToSheaf
 
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 instance presheafToSheaf_preservesZeroMorphisms [Preadditive D] :
     (presheafToSheaf J D).PreservesZeroMorphisms
     where map_zero' F G := by ext;
     erw [colimit.ι_map, comp_zero, J.plus_map_zero, J.diagram_nat_trans_zero, zero_comp]
 #align category_theory.presheaf_to_Sheaf_preserves_zero_morphisms CategoryTheory.presheafToSheaf_preservesZeroMorphisms
 
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 /-- The sheafification functor is left adjoint to the forgetful functor. -/
 @[simps unit_app counit_app_val]
 def sheafificationAdjunction : presheafToSheaf J D ⊣ sheafToPresheaf J D :=
@@ -874,44 +667,20 @@ def sheafificationAdjunction : presheafToSheaf J D ⊣ sheafToPresheaf J D :=
       homEquiv_naturality_right := fun P Q R η γ => by dsimp; rw [category.assoc] }
 #align category_theory.sheafification_adjunction CategoryTheory.sheafificationAdjunction
 
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 instance sheafToPresheafIsRightAdjoint : IsRightAdjoint (sheafToPresheaf J D) :=
   ⟨_, sheafificationAdjunction J D⟩
 #align category_theory.Sheaf_to_presheaf_is_right_adjoint CategoryTheory.sheafToPresheafIsRightAdjoint
 
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 instance presheaf_mono_of_mono {F G : Sheaf J D} (f : F ⟶ G) [Mono f] : Mono f.1 :=
   (sheafToPresheaf J D).map_mono _
 #align category_theory.presheaf_mono_of_mono CategoryTheory.presheaf_mono_of_mono
 
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 theorem Sheaf.Hom.mono_iff_presheaf_mono {F G : Sheaf J D} (f : F ⟶ G) : Mono f ↔ Mono f.1 :=
   ⟨fun m => by skip; infer_instance, fun m => by skip; exact Sheaf.hom.mono_of_presheaf_mono J D f⟩
 #align category_theory.Sheaf.hom.mono_iff_presheaf_mono CategoryTheory.Sheaf.Hom.mono_iff_presheaf_mono
 
 variable {J D}
 
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 /-- A sheaf `P` is isomorphic to its own sheafification. -/
 @[simps]
 def sheafificationIso (P : Sheaf J D) : P ≅ (presheafToSheaf J D).obj P.val
@@ -922,17 +691,11 @@ def sheafificationIso (P : Sheaf J D) : P ≅ (presheafToSheaf J D).obj P.val
   inv_hom_id' := by ext1; apply (J.iso_sheafify P.2).inv_hom_id
 #align category_theory.sheafification_iso CategoryTheory.sheafificationIso
 
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 instance isIso_sheafificationAdjunction_counit (P : Sheaf J D) :
     IsIso ((sheafificationAdjunction J D).counit.app P) :=
   isIso_of_fully_faithful (sheafToPresheaf J D) _
 #align category_theory.is_iso_sheafification_adjunction_counit CategoryTheory.isIso_sheafificationAdjunction_counit
 
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-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.sheafification_reflective CategoryTheory.sheafification_reflectiveₓ'. -/
 instance sheafification_reflective : IsIso (sheafificationAdjunction J D).counit :=
   NatIso.isIso_of_isIso_app _
 #align category_theory.sheafification_reflective CategoryTheory.sheafification_reflective

4f4a1c87

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -145,8 +145,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align category_theory.meq.mk CategoryTheory.Meq.mkₓ'. -/
 /-- Make a term of `meq P S`. -/
 def mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) : Meq P S :=
-  ⟨fun I => P.map I.f.op x, fun I => by
-    dsimp
+  ⟨fun I => P.map I.f.op x, fun I => by dsimp;
     simp only [← comp_apply, ← P.map_comp, ← op_comp, I.w]⟩
 #align category_theory.meq.mk CategoryTheory.Meq.mk
 
@@ -449,9 +448,7 @@ def meqOfSep (P : Cᵒᵖ ⥤ D)
     let IR : S.relation :=
       ⟨_, _, _, II.g₁ ≫ II.fst.to_middle_hom, II.g₂ ≫ II.snd.to_middle_hom, II.fst.from_middle_hom,
         II.snd.from_middle_hom, II.fst.from_middle_condition, II.snd.from_middle_condition, _⟩
-    swap;
-    · simp only [category.assoc, II.fst.middle_spec, II.snd.middle_spec]
-      apply II.w
+    swap; · simp only [category.assoc, II.fst.middle_spec, II.snd.middle_spec]; apply II.w
     exact s.condition IR
 #align category_theory.grothendieck_topology.plus.meq_of_sep CategoryTheory.GrothendieckTopology.Plus.meqOfSep
 
@@ -503,8 +500,7 @@ theorem exists_of_sep (P : Cᵒᵖ ⥤ D)
   · refine' ⟨I.Y, _, _, I.hf, _, rfl⟩
     apply sieve.downward_closed
     convert II.hf
-    cases I
-    rfl
+    cases I; rfl
   let IB : S.arrow := IA.from_middle
   let IC : (T IB).arrow := IA.to_middle
   let ID : (T I).arrow := ⟨IV.Y, IV.f ≫ II.f, sieve.downward_closed (T I) II.hf IV.f⟩
@@ -546,8 +542,7 @@ theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)
     obtain ⟨t, ht⟩ := exists_of_sep P hsep X S (meq.equiv _ _ x)
     use t
     apply_fun meq.equiv _ _
-    swap
-    · infer_instance
+    swap; · infer_instance
     rw [← ht]
     ext i
     dsimp
@@ -619,10 +614,8 @@ but is expected to have type
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)) (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P P (CategoryTheory.CategoryStruct.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P)) (CategoryTheory.CategoryStruct.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_map_id CategoryTheory.GrothendieckTopology.sheafifyMap_idₓ'. -/
 @[simp]
-theorem sheafifyMap_id (P : Cᵒᵖ ⥤ D) : J.sheafifyMap (𝟙 P) = 𝟙 (J.sheafify P) :=
-  by
-  dsimp [sheafify_map, sheafify]
-  simp
+theorem sheafifyMap_id (P : Cᵒᵖ ⥤ D) : J.sheafifyMap (𝟙 P) = 𝟙 (J.sheafify P) := by
+  dsimp [sheafify_map, sheafify]; simp
 #align category_theory.grothendieck_topology.sheafify_map_id CategoryTheory.GrothendieckTopology.sheafifyMap_id
 
 /- warning: category_theory.grothendieck_topology.sheafify_map_comp -> CategoryTheory.GrothendieckTopology.sheafifyMap_comp is a dubious translation:
@@ -630,9 +623,7 @@ theorem sheafifyMap_id (P : Cᵒᵖ ⥤ D) : J.sheafifyMap (𝟙 P) = 𝟙 (J.sh
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_map_comp CategoryTheory.GrothendieckTopology.sheafifyMap_compₓ'. -/
 @[simp]
 theorem sheafifyMap_comp {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q ⟶ R) :
-    J.sheafifyMap (η ≫ γ) = J.sheafifyMap η ≫ J.sheafifyMap γ :=
-  by
-  dsimp [sheafify_map, sheafify]
+    J.sheafifyMap (η ≫ γ) = J.sheafifyMap η ≫ J.sheafifyMap γ := by dsimp [sheafify_map, sheafify];
   simp
 #align category_theory.grothendieck_topology.sheafify_map_comp CategoryTheory.GrothendieckTopology.sheafifyMap_comp
 
@@ -641,10 +632,8 @@ theorem sheafifyMap_comp {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q ⟶ R) :
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.to_sheafify_naturality CategoryTheory.GrothendieckTopology.toSheafify_naturalityₓ'. -/
 @[simp, reassoc]
 theorem toSheafify_naturality {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) :
-    η ≫ J.toSheafify _ = J.toSheafify _ ≫ J.sheafifyMap η :=
-  by
-  dsimp [sheafify_map, sheafify, to_sheafify]
-  simp
+    η ≫ J.toSheafify _ = J.toSheafify _ ≫ J.sheafifyMap η := by
+  dsimp [sheafify_map, sheafify, to_sheafify]; simp
 #align category_theory.grothendieck_topology.to_sheafify_naturality CategoryTheory.GrothendieckTopology.toSheafify_naturality
 
 variable (D)
@@ -761,10 +750,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.to_sheafify_sheafify_lift CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLiftₓ'. -/
 @[simp, reassoc]
 theorem toSheafify_sheafifyLift {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.IsSheaf J Q) :
-    J.toSheafify P ≫ sheafifyLift J η hQ = η :=
-  by
-  dsimp only [sheafify_lift, to_sheafify]
-  simp
+    J.toSheafify P ≫ sheafifyLift J η hQ = η := by dsimp only [sheafify_lift, to_sheafify]; simp
 #align category_theory.grothendieck_topology.to_sheafify_sheafify_lift CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLift
 
 /- warning: category_theory.grothendieck_topology.sheafify_lift_unique -> CategoryTheory.GrothendieckTopology.sheafifyLift_unique is a dubious translation:
@@ -863,8 +849,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align category_theory.presheaf_to_Sheaf_preserves_zero_morphisms CategoryTheory.presheafToSheaf_preservesZeroMorphismsₓ'. -/
 instance presheafToSheaf_preservesZeroMorphisms [Preadditive D] :
     (presheafToSheaf J D).PreservesZeroMorphisms
-    where map_zero' F G := by
-    ext
+    where map_zero' F G := by ext;
     erw [colimit.ι_map, comp_zero, J.plus_map_zero, J.diagram_nat_trans_zero, zero_comp]
 #align category_theory.presheaf_to_Sheaf_preserves_zero_morphisms CategoryTheory.presheafToSheaf_preservesZeroMorphisms
 
@@ -886,10 +871,7 @@ def sheafificationAdjunction : presheafToSheaf J D ⊣ sheafToPresheaf J D :=
       homEquiv_naturality_left_symm := by
         intro P Q R η γ; ext1; dsimp; symm
         apply J.sheafify_map_sheafify_lift
-      homEquiv_naturality_right := fun P Q R η γ =>
-        by
-        dsimp
-        rw [category.assoc] }
+      homEquiv_naturality_right := fun P Q R η γ => by dsimp; rw [category.assoc] }
 #align category_theory.sheafification_adjunction CategoryTheory.sheafificationAdjunction
 
 /- warning: category_theory.Sheaf_to_presheaf_is_right_adjoint -> CategoryTheory.sheafToPresheafIsRightAdjoint is a dubious translation:
@@ -919,11 +901,7 @@ but is expected to have type
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {F : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2} {G : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2} (f : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) F G), Iff (CategoryTheory.Mono.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) F G f) (CategoryTheory.Mono.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 F) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 G) (CategoryTheory.Sheaf.Hom.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 F G f))
 Case conversion may be inaccurate. Consider using '#align category_theory.Sheaf.hom.mono_iff_presheaf_mono CategoryTheory.Sheaf.Hom.mono_iff_presheaf_monoₓ'. -/
 theorem Sheaf.Hom.mono_iff_presheaf_mono {F G : Sheaf J D} (f : F ⟶ G) : Mono f ↔ Mono f.1 :=
-  ⟨fun m => by
-    skip
-    infer_instance, fun m => by
-    skip
-    exact Sheaf.hom.mono_of_presheaf_mono J D f⟩
+  ⟨fun m => by skip; infer_instance, fun m => by skip; exact Sheaf.hom.mono_of_presheaf_mono J D f⟩
 #align category_theory.Sheaf.hom.mono_iff_presheaf_mono CategoryTheory.Sheaf.Hom.mono_iff_presheaf_mono
 
 variable {J D}
@@ -940,12 +918,8 @@ def sheafificationIso (P : Sheaf J D) : P ≅ (presheafToSheaf J D).obj P.val
     where
   Hom := ⟨(J.isoSheafify P.2).Hom⟩
   inv := ⟨(J.isoSheafify P.2).inv⟩
-  hom_inv_id' := by
-    ext1
-    apply (J.iso_sheafify P.2).hom_inv_id
-  inv_hom_id' := by
-    ext1
-    apply (J.iso_sheafify P.2).inv_hom_id
+  hom_inv_id' := by ext1; apply (J.iso_sheafify P.2).hom_inv_id
+  inv_hom_id' := by ext1; apply (J.iso_sheafify P.2).inv_hom_id
 #align category_theory.sheafification_iso CategoryTheory.sheafificationIso
 
 /- warning: category_theory.is_iso_sheafification_adjunction_counit -> CategoryTheory.isIso_sheafificationAdjunction_counit is a dubious translation:

4f4a1c87

bump to nightly-2023-05-28-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6c6011cf

Diff

@@ -67,10 +67,7 @@ instance {X} (P : Cᵒᵖ ⥤ D) (S : J.cover X) :
   ⟨fun x => x.1⟩
 
 /- warning: category_theory.meq.ext -> CategoryTheory.Meq.ext is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align category_theory.meq.ext CategoryTheory.Meq.extₓ'. -/
 @[ext]
 theorem ext {X} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x y : Meq P S) (h : ∀ I : S.arrow, x I = y I) :
@@ -79,10 +76,7 @@ theorem ext {X} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x y : Meq P S) (h : ∀ I :
 #align category_theory.meq.ext CategoryTheory.Meq.ext
 
 /- warning: category_theory.meq.condition -> CategoryTheory.Meq.condition is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.meq.condition CategoryTheory.Meq.conditionₓ'. -/
 theorem condition {X} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (I : S.Relation) :
     P.map I.g₁.op (x ((S.index P).fstTo I)) = P.map I.g₂.op (x ((S.index P).sndTo I)) :=
@@ -103,10 +97,7 @@ def refine {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P T) (e : S 
 #align category_theory.meq.refine CategoryTheory.Meq.refine
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.meq.refine_apply CategoryTheory.Meq.refine_applyₓ'. -/
 @[simp]
 theorem refine_apply {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P T) (e : S ⟶ T)
@@ -129,10 +120,7 @@ def pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y
 #align category_theory.meq.pullback CategoryTheory.Meq.pullback
 
 /- warning: category_theory.meq.pullback_apply -> CategoryTheory.Meq.pullback_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.meq.pullback_apply CategoryTheory.Meq.pullback_applyₓ'. -/
 @[simp]
 theorem pullback_apply {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y ⟶ X)
@@ -141,10 +129,7 @@ theorem pullback_apply {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P
 #align category_theory.meq.pullback_apply CategoryTheory.Meq.pullback_apply
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.meq.pullback_refine CategoryTheory.Meq.pullback_refineₓ'. -/
 @[simp]
 theorem pullback_refine {Y X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (h : S ⟶ T) (f : Y ⟶ X)
@@ -166,10 +151,7 @@ def mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) : Meq P S
 #align category_theory.meq.mk CategoryTheory.Meq.mk
 
 /- warning: category_theory.meq.mk_apply -> CategoryTheory.Meq.mk_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.meq.mk_apply CategoryTheory.Meq.mk_applyₓ'. -/
 theorem mk_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) (I : S.arrow) :
     mk S x I = P.map I.f.op x :=
@@ -187,10 +169,7 @@ noncomputable def equiv {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) [HasMultiequ
 -/
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.meq.equiv_apply CategoryTheory.Meq.equiv_applyₓ'. -/
 @[simp]
 theorem equiv_apply {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} [HasMultiequalizer (S.index P)]
@@ -240,10 +219,7 @@ def mk {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) : (J.plusObj P)
 #align category_theory.grothendieck_topology.plus.mk CategoryTheory.GrothendieckTopology.Plus.mk
 
 /- warning: category_theory.grothendieck_topology.plus.res_mk_eq_mk_pullback -> CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.res_mk_eq_mk_pullback CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullbackₓ'. -/
 theorem res_mk_eq_mk_pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y ⟶ X) :
     (J.plusObj P).map f.op (mk x) = mk (x.pullback f) :=
@@ -261,10 +237,7 @@ theorem res_mk_eq_mk_pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x :
 #align category_theory.grothendieck_topology.plus.res_mk_eq_mk_pullback CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback
 
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J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (CategoryTheory.GrothendieckTopology.toPlus.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X)) x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S x))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.to_plus_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_mkₓ'. -/
 theorem toPlus_mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) :
     (J.toPlus P).app _ x = mk (Meq.mk S x) :=
@@ -283,10 +256,7 @@ theorem toPlus_mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X))
 #align category_theory.grothendieck_topology.plus.to_plus_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_mk
 
 /- warning: category_theory.grothendieck_topology.plus.to_plus_apply -> CategoryTheory.GrothendieckTopology.Plus.toPlus_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.to_plus_apply CategoryTheory.GrothendieckTopology.Plus.toPlus_applyₓ'. -/
 theorem toPlus_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : Meq P S) (I : S.arrow) :
     (J.toPlus P).app _ (x I) = (J.plusObj P).map I.f.op (mk x) :=
@@ -314,10 +284,7 @@ theorem toPlus_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : Meq P S) (
 #align category_theory.grothendieck_topology.plus.to_plus_apply CategoryTheory.GrothendieckTopology.Plus.toPlus_apply
 
 /- warning: category_theory.grothendieck_topology.plus.to_plus_eq_mk -> CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mk is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.to_plus_eq_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mkₓ'. -/
 theorem toPlus_eq_mk {X : C} {P : Cᵒᵖ ⥤ D} (x : P.obj (op X)) :
     (J.toPlus P).app _ x = mk (Meq.mk ⊤ x) :=
@@ -334,10 +301,7 @@ theorem toPlus_eq_mk {X : C} {P : Cᵒᵖ ⥤ D} (x : P.obj (op X)) :
 variable [∀ X : C, PreservesColimitsOfShape (J.cover X)ᵒᵖ (forget D)]
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.exists_rep CategoryTheory.GrothendieckTopology.Plus.exists_repₓ'. -/
 theorem exists_rep {X : C} {P : Cᵒᵖ ⥤ D} (x : (J.plusObj P).obj (op X)) :
     ∃ (S : J.cover X)(y : Meq P S), x = mk y :=
@@ -350,10 +314,7 @@ theorem exists_rep {X : C} {P : Cᵒᵖ ⥤ D} (x : (J.plusObj P).obj (op X)) :
 #align category_theory.grothendieck_topology.plus.exists_rep CategoryTheory.GrothendieckTopology.Plus.exists_rep
 
 /- warning: category_theory.grothendieck_topology.plus.eq_mk_iff_exists -> CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_exists is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.eq_mk_iff_exists CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_existsₓ'. -/
 theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P S) (y : Meq P T) :
     mk x = mk y ↔ ∃ (W : J.cover X)(h1 : W ⟶ S)(h2 : W ⟶ T), x.refine h1 = y.refine h2 :=
@@ -383,10 +344,7 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq
 #align category_theory.grothendieck_topology.plus.eq_mk_iff_exists CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_exists
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.sep CategoryTheory.GrothendieckTopology.Plus.sepₓ'. -/
 /-- `P⁺` is always separated. -/
 theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj (op X))
@@ -445,10 +403,7 @@ theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj
 #align category_theory.grothendieck_topology.plus.sep CategoryTheory.GrothendieckTopology.Plus.sep
 
 /- warning: category_theory.grothendieck_topology.plus.inj_of_sep -> CategoryTheory.GrothendieckTopology.Plus.inj_of_sep is a dubious translation:
-lean 3 declaration is
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C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.inj_of_sep CategoryTheory.GrothendieckTopology.Plus.inj_of_sepₓ'. -/
 theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
     (hsep :
@@ -467,10 +422,7 @@ theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
 #align category_theory.grothendieck_topology.plus.inj_of_sep CategoryTheory.GrothendieckTopology.Plus.inj_of_sep
 
 /- warning: category_theory.grothendieck_topology.plus.meq_of_sep -> CategoryTheory.GrothendieckTopology.Plus.meqOfSep is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.meq_of_sep CategoryTheory.GrothendieckTopology.Plus.meqOfSepₓ'. -/
 /-- An auxiliary definition to be used in the proof of `exists_of_sep` below.
   Given a compatible family of local sections for `P⁺`, and representatives of said sections,
@@ -504,10 +456,7 @@ def meqOfSep (P : Cᵒᵖ ⥤ D)
 #align category_theory.grothendieck_topology.plus.meq_of_sep CategoryTheory.GrothendieckTopology.Plus.meqOfSep
 
 /- warning: category_theory.grothendieck_topology.plus.exists_of_sep -> CategoryTheory.GrothendieckTopology.Plus.exists_of_sep is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.exists_of_sep CategoryTheory.GrothendieckTopology.Plus.exists_of_sepₓ'. -/
 theorem exists_of_sep (P : Cᵒᵖ ⥤ D)
     (hsep :
@@ -571,10 +520,7 @@ theorem exists_of_sep (P : Cᵒᵖ ⥤ D)
 variable [ReflectsIsomorphisms (forget D)]
 
 /- warning: category_theory.grothendieck_topology.plus.is_sheaf_of_sep -> CategoryTheory.GrothendieckTopology.Plus.isSheaf_of_sep is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.is_sheaf_of_sep CategoryTheory.GrothendieckTopology.Plus.isSheaf_of_sepₓ'. -/
 /-- If `P` is separated, then `P⁺` is a sheaf. -/
 theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)
@@ -680,10 +626,7 @@ theorem sheafifyMap_id (P : Cᵒᵖ ⥤ D) : J.sheafifyMap (𝟙 P) = 𝟙 (J.sh
 #align category_theory.grothendieck_topology.sheafify_map_id CategoryTheory.GrothendieckTopology.sheafifyMap_id
 
 /- warning: category_theory.grothendieck_topology.sheafify_map_comp -> CategoryTheory.GrothendieckTopology.sheafifyMap_comp is a dubious translation:
-lean 3 declaration is
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(CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {R : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) 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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_map_comp CategoryTheory.GrothendieckTopology.sheafifyMap_compₓ'. -/
 @[simp]
 theorem sheafifyMap_comp {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q ⟶ R) :
@@ -694,10 +637,7 @@ theorem sheafifyMap_comp {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q ⟶ R) :
 #align category_theory.grothendieck_topology.sheafify_map_comp CategoryTheory.GrothendieckTopology.sheafifyMap_comp
 
 /- warning: category_theory.grothendieck_topology.to_sheafify_naturality -> CategoryTheory.GrothendieckTopology.toSheafify_naturality is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.to_sheafify_naturality CategoryTheory.GrothendieckTopology.toSheafify_naturalityₓ'. -/
 @[simp, reassoc]
 theorem toSheafify_naturality {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) :
@@ -733,10 +673,7 @@ theorem sheafification_obj (P : Cᵒᵖ ⥤ D) : (J.sheafification D).obj P = J.
 #align category_theory.grothendieck_topology.sheafification_obj CategoryTheory.GrothendieckTopology.sheafification_obj
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafification_map CategoryTheory.GrothendieckTopology.sheafification_mapₓ'. -/
 @[simp]
 theorem sheafification_map {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) :
@@ -757,10 +694,7 @@ def toSheafification : 𝟭 _ ⟶ sheafification J D :=
 #align category_theory.grothendieck_topology.to_sheafification CategoryTheory.GrothendieckTopology.toSheafification
 
 /- warning: category_theory.grothendieck_topology.to_sheafification_app -> CategoryTheory.GrothendieckTopology.toSheafification_app is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.to_sheafification_app CategoryTheory.GrothendieckTopology.toSheafification_appₓ'. -/
 @[simp]
 theorem toSheafification_app (P : Cᵒᵖ ⥤ D) : (J.toSheafification D).app P = J.toSheafify P :=
@@ -834,10 +768,7 @@ theorem toSheafify_sheafifyLift {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presh
 #align category_theory.grothendieck_topology.to_sheafify_sheafify_lift CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLift
 
 /- warning: category_theory.grothendieck_topology.sheafify_lift_unique -> CategoryTheory.GrothendieckTopology.sheafifyLift_unique is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_lift_unique CategoryTheory.GrothendieckTopology.sheafifyLift_uniqueₓ'. -/
 theorem sheafifyLift_unique {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.IsSheaf J Q)
     (γ : J.sheafify P ⟶ Q) : J.toSheafify P ≫ γ = η → γ = sheafifyLift J η hQ :=
@@ -864,10 +795,7 @@ theorem isoSheafify_inv {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) :
 #align category_theory.grothendieck_topology.iso_sheafify_inv CategoryTheory.GrothendieckTopology.isoSheafify_inv
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_hom_ext CategoryTheory.GrothendieckTopology.sheafify_hom_extₓ'. -/
 theorem sheafify_hom_ext {P Q : Cᵒᵖ ⥤ D} (η γ : J.sheafify P ⟶ Q) (hQ : Presheaf.IsSheaf J Q)
     (h : J.toSheafify P ≫ η = J.toSheafify P ≫ γ) : η = γ :=
@@ -879,10 +807,7 @@ theorem sheafify_hom_ext {P Q : Cᵒᵖ ⥤ D} (η γ : J.sheafify P ⟶ Q) (hQ
 #align category_theory.grothendieck_topology.sheafify_hom_ext CategoryTheory.GrothendieckTopology.sheafify_hom_ext
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_map_sheafify_lift CategoryTheory.GrothendieckTopology.sheafifyMap_sheafifyLiftₓ'. -/
 @[simp, reassoc]
 theorem sheafifyMap_sheafifyLift {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q ⟶ R)
@@ -1024,10 +949,7 @@ def sheafificationIso (P : Sheaf J D) : P ≅ (presheafToSheaf J D).obj P.val
 #align category_theory.sheafification_iso CategoryTheory.sheafificationIso
 
 /- warning: category_theory.is_iso_sheafification_adjunction_counit -> CategoryTheory.isIso_sheafificationAdjunction_counit is a dubious translation:
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u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.is_iso_sheafification_adjunction_counit CategoryTheory.isIso_sheafificationAdjunction_counitₓ'. -/
 instance isIso_sheafificationAdjunction_counit (P : Sheaf J D) :
     IsIso ((sheafificationAdjunction J D).counit.app P) :=
@@ -1035,10 +957,7 @@ instance isIso_sheafificationAdjunction_counit (P : Sheaf J D) :
 #align category_theory.is_iso_sheafification_adjunction_counit CategoryTheory.isIso_sheafificationAdjunction_counit
 
 /- warning: category_theory.sheafification_reflective -> CategoryTheory.sheafification_reflective is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.sheafification_reflective CategoryTheory.sheafification_reflectiveₓ'. -/
 instance sheafification_reflective : IsIso (sheafificationAdjunction J D).counit :=
   NatIso.isIso_of_isIso_app _

4f4a1c87

bump to nightly-2023-05-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

ed98987c

Diff

@@ -699,7 +699,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q)) (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P Q (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q) η (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q)) (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q) (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.to_sheafify_naturality CategoryTheory.GrothendieckTopology.toSheafify_naturalityₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem toSheafify_naturality {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) :
     η ≫ J.toSheafify _ = J.toSheafify _ ≫ J.sheafifyMap η :=
   by
@@ -825,7 +825,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (hQ : CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J Q), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η hQ)) η
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.to_sheafify_sheafify_lift CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLiftₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem toSheafify_sheafifyLift {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.IsSheaf J Q) :
     J.toSheafify P ≫ sheafifyLift J η hQ = η :=
   by
@@ -884,7 +884,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {R : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (γ : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) Q R) (hR : CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J R), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) R) (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q) R (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q R γ hR)) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P R (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P Q R η γ) hR)
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_map_sheafify_lift CategoryTheory.GrothendieckTopology.sheafifyMap_sheafifyLiftₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem sheafifyMap_sheafifyLift {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q ⟶ R)
     (hR : Presheaf.IsSheaf J R) :
     J.sheafifyMap η ≫ J.sheafifyLift γ hR = J.sheafifyLift (η ≫ γ) hR :=

4f4a1c87

bump to nightly-2023-05-19-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

a31df521

Diff

@@ -190,7 +190,7 @@ noncomputable def equiv {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) [HasMultiequ
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} [_inst_5 : CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Limits.multiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) _inst_5)) (I : CategoryTheory.GrothendieckTopology.Cover.Arrow.{u2, u3} C _inst_1 X J S), Eq.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.y.{u2, u3} C _inst_1 X J S I)))) (coeFn.{max 1 (max (succ u3) (succ u2)) (succ (max u2 u3)), max (max (succ u3) (succ u2)) (succ (max u2 u3))} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (fun (x : CategoryTheory.Meq.{u1, u2, u3} C 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(CategoryTheory.Limits.multiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) _inst_5)) -> (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S)) (Equiv.hasCoeToFun.{succ (max u2 u3), max 1 (max (succ u3) (succ u2)) (succ (max u2 u3))} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Limits.multiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) _inst_5)) (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S)) (CategoryTheory.Meq.equiv.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 X P S _inst_5) x) I) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), u1} D (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, u1} D 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Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Limits.multiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) _inst_5)) -> (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Limits.MulticospanIndex.left.{max u3 u2, max u2 u3, u1} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) I))) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3 (CategoryTheory.Limits.multiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) _inst_5) (CategoryTheory.Limits.MulticospanIndex.left.{max u3 u2, max u2 u3, u1} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) I)) (CategoryTheory.Limits.Multiequalizer.ι.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) _inst_5 I) x)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} [_inst_5 : CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D 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C _inst_1 X J D _inst_2 S P) _inst_5 I) x)
 Case conversion may be inaccurate. Consider using '#align category_theory.meq.equiv_apply CategoryTheory.Meq.equiv_applyₓ'. -/
 @[simp]
 theorem equiv_apply {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} [HasMultiequalizer (S.index P)]

4f4a1c87

bump to nightly-2023-05-16-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

9cb92e8c

Diff

@@ -315,7 +315,7 @@ theorem toPlus_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : Meq P S) (
 
 /- warning: category_theory.grothendieck_topology.plus.to_plus_eq_mk -> CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mk is a dubious translation:
 lean 3 declaration is
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C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X))), Eq.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} 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(CategoryTheory.GrothendieckTopology.Cover.orderTop.{u2, u3} C _inst_1 X J))) (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toHasTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.orderTop.{u2, u3} C _inst_1 X J))) x))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X))), Eq.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} 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(CategoryTheory.GrothendieckTopology.toPlus._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (CategoryTheory.NatTrans.app.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toPlus._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S)) P (CategoryTheory.GrothendieckTopology.toPlus._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (CategoryTheory.GrothendieckTopology.toPlus.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) 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(CategoryTheory.GrothendieckTopology.Cover.orderTop.{u2, u3} C _inst_1 X J))) (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toHasTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toHasLe.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.orderTop.{u2, u3} C _inst_1 X J))) x))
 but is expected to have type
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X))), Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ 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D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, succ (max u3 u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, succ (max u3 u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)) (CategoryTheory.NatTrans.app.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (CategoryTheory.GrothendieckTopology.toPlus.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X)) x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.instOrderTopCoverToLEInstPreorderCover.{u2, u3} C _inst_1 X J))) (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.instOrderTopCoverToLEInstPreorderCover.{u2, u3} C _inst_1 X J))) x))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.to_plus_eq_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mkₓ'. -/

4f4a1c87

bump to nightly-2023-05-12-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

fab1af65

Diff

@@ -70,7 +70,7 @@ instance {X} (P : Cᵒᵖ ⥤ D) (S : J.cover X) :
 lean 3 declaration is
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 but is expected to have type
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(CategoryTheory.GrothendieckTopology.Cover.Relation.snd.{u2, u3} C _inst_1 X J S I)))) y I)) -> (Eq.{max (succ u3) (succ u2)} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) x y)
 Case conversion may be inaccurate. Consider using '#align category_theory.meq.ext CategoryTheory.Meq.extₓ'. -/
 @[ext]
 theorem ext {X} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x y : Meq P S) (h : ∀ I : S.arrow, x I = y I) :
@@ -82,7 +82,7 @@ theorem ext {X} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x y : Meq P S) (h : ∀ I :
 lean 3 declaration is
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 but is expected to have type
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(Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Relation.Y₁.{u2, u3} C _inst_1 X J S I))) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Relation.Z.{u2, u3} C _inst_1 X J S I))) (Prefunctor.map.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} 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(CategoryTheory.GrothendieckTopology.Cover.Relation.fst.{u2, u3} C _inst_1 X J S I))) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, 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_inst_1)) (CategoryTheory.GrothendieckTopology.Cover.Relation.Z.{u2, u3} C _inst_1 X J S I) (CategoryTheory.GrothendieckTopology.Cover.Relation.Y₂.{u2, u3} C _inst_1 X J S I) (CategoryTheory.GrothendieckTopology.Cover.Relation.g₂.{u2, u3} C _inst_1 X J S I))) (x (CategoryTheory.GrothendieckTopology.Cover.Relation.snd.{u2, u3} C _inst_1 X J S I)))) x (CategoryTheory.Limits.MulticospanIndex.sndTo.{max u3 u2, max u3 u2, u1} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) I)))
 Case conversion may be inaccurate. Consider using '#align category_theory.meq.condition CategoryTheory.Meq.conditionₓ'. -/
 theorem condition {X} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (I : S.Relation) :
     P.map I.g₁.op (x ((S.index P).fstTo I)) = P.map I.g₂.op (x ((S.index P).sndTo I)) :=
@@ -106,7 +106,7 @@ def refine {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P T) (e : S 
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} {T : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P T) (e : Quiver.Hom.{succ (max u3 u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)))) S T) (I : CategoryTheory.GrothendieckTopology.Cover.Arrow.{u2, u3} C _inst_1 X J S), Eq.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.y.{u2, u3} C _inst_1 X J S I)))) (coeFn.{max 1 (max (succ u3) (succ u2)) (succ (max u2 u3)), max (max (succ u3) (succ u2)) (succ (max u2 u3))} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (fun (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) => forall (I : CategoryTheory.GrothendieckTopology.Cover.Arrow.{u2, u3} C _inst_1 X J S), coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.y.{u2, u3} C _inst_1 X J S I)))) (CategoryTheory.Meq.hasCoeToFun.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S T x e) I) (coeFn.{max 1 (max (succ u3) (succ u2)) (succ (max u2 u3)), max (max (succ u3) (succ u2)) (succ (max u2 u3))} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P T) (fun (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P T) => forall (I : CategoryTheory.GrothendieckTopology.Cover.Arrow.{u2, u3} C _inst_1 X J T), coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.y.{u2, u3} C _inst_1 X J T I)))) (CategoryTheory.Meq.hasCoeToFun.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P T) x (CategoryTheory.GrothendieckTopology.Cover.Arrow.mk.{u2, u3} C _inst_1 X J T (CategoryTheory.GrothendieckTopology.Cover.Arrow.y.{u2, u3} C _inst_1 X J S I) (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 X J S I) (CategoryTheory.leOfHom.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X) S T e (CategoryTheory.GrothendieckTopology.Cover.Arrow.y.{u2, u3} C _inst_1 X J S I) (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 X J S I) (CategoryTheory.GrothendieckTopology.Cover.Arrow.hf.{u2, u3} C _inst_1 X J S I))))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} {T : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P T) (e : Quiver.Hom.{max (succ u3) (succ u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} 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(CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I) (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 X J S I) (CategoryTheory.GrothendieckTopology.Cover.Arrow.hf.{u2, u3} C _inst_1 X J S I))))
 Case conversion may be inaccurate. Consider using '#align category_theory.meq.refine_apply CategoryTheory.Meq.refine_applyₓ'. -/
 @[simp]
 theorem refine_apply {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P T) (e : S ⟶ T)
@@ -132,7 +132,7 @@ def pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y
 lean 3 declaration is
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 but is expected to have type
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(Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J Y)) (CategoryTheory.GrothendieckTopology.pullback.{u2, u3} C _inst_1 X Y J f)) S) I) (CategoryTheory.CategoryStruct.comp.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 Y J (Prefunctor.obj.{max (succ u3) (succ u2), max (succ u3) (succ u2), max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J Y)))) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J Y)) (CategoryTheory.GrothendieckTopology.pullback.{u2, u3} C _inst_1 X Y J f)) S) I) Y X (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 Y J (Prefunctor.obj.{max (succ u3) (succ u2), max (succ u3) (succ u2), max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J Y)))) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J Y)) (CategoryTheory.GrothendieckTopology.pullback.{u2, u3} C _inst_1 X Y J f)) S) I) f) (CategoryTheory.GrothendieckTopology.Cover.Arrow.hf.{u2, u3} C _inst_1 Y J (Prefunctor.obj.{max (succ u3) (succ u2), max (succ u3) (succ u2), max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J Y)))) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J Y)) (CategoryTheory.GrothendieckTopology.pullback.{u2, u3} C _inst_1 X Y J f)) S) I)))
 Case conversion may be inaccurate. Consider using '#align category_theory.meq.pullback_apply CategoryTheory.Meq.pullback_applyₓ'. -/
 @[simp]
 theorem pullback_apply {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y ⟶ X)
@@ -156,7 +156,7 @@ theorem pullback_refine {Y X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (h : S 
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X))) -> (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X))) -> (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X))) -> (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S)
 Case conversion may be inaccurate. Consider using '#align category_theory.meq.mk CategoryTheory.Meq.mkₓ'. -/
 /-- Make a term of `meq P S`. -/
 def mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) : Meq P S :=
@@ -169,7 +169,7 @@ def mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) : Meq P S
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X))) (I : CategoryTheory.GrothendieckTopology.Cover.Arrow.{u2, u3} C _inst_1 X J S), Eq.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.y.{u2, u3} C _inst_1 X J S I)))) (coeFn.{max 1 (max (succ u3) (succ u2)) (succ (max u2 u3)), max (max (succ u3) (succ u2)) (succ (max u2 u3))} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (fun (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) => forall (I : CategoryTheory.GrothendieckTopology.Cover.Arrow.{u2, u3} C _inst_1 X J S), coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.y.{u2, u3} C _inst_1 X J S I)))) (CategoryTheory.Meq.hasCoeToFun.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S x) I) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), u1} D (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, u1} D (CategoryTheory.Category.toCategoryStruct.{max u2 u3, u1} D _inst_2)) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X)) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.y.{u2, u3} C _inst_1 X J S I)))) (fun (f : Quiver.Hom.{succ (max u2 u3), u1} D (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, u1} D 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(CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I) X (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 X J S I))) x)
 Case conversion may be inaccurate. Consider using '#align category_theory.meq.mk_apply CategoryTheory.Meq.mk_applyₓ'. -/
 theorem mk_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) (I : S.arrow) :
     mk S x I = P.map I.f.op x :=
@@ -190,7 +190,7 @@ noncomputable def equiv {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) [HasMultiequ
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} [_inst_5 : CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} 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(CategoryTheory.Limits.multiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) _inst_5)) -> (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S)) (Equiv.hasCoeToFun.{succ (max u2 u3), max 1 (max (succ u3) (succ u2)) (succ (max u2 u3))} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Limits.multiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) _inst_5)) (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S)) (CategoryTheory.Meq.equiv.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 X P S _inst_5) x) I) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), u1} D (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, u1} D 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Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Limits.multiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) _inst_5)) -> (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Limits.MulticospanIndex.left.{max u3 u2, max u2 u3, u1} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) I))) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3 (CategoryTheory.Limits.multiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) _inst_5) (CategoryTheory.Limits.MulticospanIndex.left.{max u3 u2, max u2 u3, u1} D _inst_2 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 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} [_inst_5 : CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D 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(CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (CategoryTheory.Limits.multiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) _inst_5)) (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S)) (CategoryTheory.Meq.equiv.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 X P S _inst_5) x) I) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (CategoryTheory.Limits.multiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) _inst_5) (CategoryTheory.Limits.MulticospanIndex.left.{max u3 u2, max u3 u2, u1} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) I) (CategoryTheory.Limits.Multiequalizer.ι.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P) _inst_5 I) x)
 Case conversion may be inaccurate. Consider using '#align category_theory.meq.equiv_apply CategoryTheory.Meq.equiv_applyₓ'. -/
 @[simp]
 theorem equiv_apply {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} [HasMultiequalizer (S.index P)]
@@ -232,7 +232,7 @@ noncomputable section
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X}, (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) -> (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.Plus.mk._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_6) P (CategoryTheory.GrothendieckTopology.Plus.mk._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_5)) (Opposite.op.{succ u3} C X)))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X}, (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) -> (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X}, (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) -> (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.mk CategoryTheory.GrothendieckTopology.Plus.mkₓ'. -/
 /-- Make a term of `(J.plus_obj P).obj (op X)` from `x : meq P S`. -/
 def mk {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) : (J.plusObj P).obj (op X) :=
@@ -264,7 +264,7 @@ theorem res_mk_eq_mk_pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x :
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X))), Eq.{succ (max 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 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) 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J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (CategoryTheory.GrothendieckTopology.toPlus.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X)) x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S x))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X))), Eq.{max (succ u3) (succ u2)} 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(CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, succ (max u3 u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, succ (max u3 u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)) (CategoryTheory.NatTrans.app.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (CategoryTheory.GrothendieckTopology.toPlus.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X)) x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S x))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.to_plus_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_mkₓ'. -/
 theorem toPlus_mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) :
     (J.toPlus P).app _ x = mk (Meq.mk S x) :=
@@ -286,7 +286,7 @@ theorem toPlus_mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X))
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (I : CategoryTheory.GrothendieckTopology.Cover.Arrow.{u2, u3} C _inst_1 X J S), Eq.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) 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 but is expected to have type
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u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I))) (Prefunctor.map.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I)) (Quiver.Hom.op.{u3, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I) X (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 X J S I))) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S x))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.to_plus_apply CategoryTheory.GrothendieckTopology.Plus.toPlus_applyₓ'. -/
 theorem toPlus_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : Meq P S) (I : S.arrow) :
     (J.toPlus P).app _ (x I) = (J.plusObj P).map I.f.op (mk x) :=
@@ -317,7 +317,7 @@ theorem toPlus_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : Meq P S) (
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X))), Eq.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toPlus._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S)) P (CategoryTheory.GrothendieckTopology.toPlus._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), u1} D (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, u1} D (CategoryTheory.Category.toCategoryStruct.{max u2 u3, u1} D _inst_2)) 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(CategoryTheory.Category.toCategoryStruct.{max u2 u3, u1} D _inst_2)) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X)) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toPlus._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S)) P (CategoryTheory.GrothendieckTopology.toPlus._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) => (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 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(CategoryTheory.GrothendieckTopology.toPlus._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)))) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3 (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X)) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toPlus._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S)) P (CategoryTheory.GrothendieckTopology.toPlus._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (CategoryTheory.NatTrans.app.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toPlus._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S)) P (CategoryTheory.GrothendieckTopology.toPlus._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (CategoryTheory.GrothendieckTopology.toPlus.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X)) x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toHasTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.orderTop.{u2, u3} C _inst_1 X J))) (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toHasTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.orderTop.{u2, u3} C _inst_1 X J))) x))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X))), Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ 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(CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, succ (max u3 u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, succ (max u3 u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)) (CategoryTheory.NatTrans.app.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (CategoryTheory.GrothendieckTopology.toPlus.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X)) x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.instOrderTopCoverToLEInstPreorderCover.{u2, u3} C _inst_1 X J))) (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.instOrderTopCoverToLEInstPreorderCover.{u2, u3} C _inst_1 X J))) x))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X))), Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, succ (max u3 u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, succ (max u3 u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, succ (max u3 u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)) (CategoryTheory.NatTrans.app.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (CategoryTheory.GrothendieckTopology.toPlus.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X)) x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.instOrderTopCoverToLEInstPreorderCover.{u2, u3} C _inst_1 X J))) (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.instOrderTopCoverToLEInstPreorderCover.{u2, u3} C _inst_1 X J))) x))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.to_plus_eq_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mkₓ'. -/
 theorem toPlus_eq_mk {X : C} {P : Cᵒᵖ ⥤ D} (x : P.obj (op X)) :
     (J.toPlus P).app _ x = mk (Meq.mk ⊤ x) :=
@@ -337,7 +337,7 @@ variable [∀ X : C, PreservesColimitsOfShape (J.cover X)ᵒᵖ (forget D)]
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X))), Exists.{max 1 (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (fun (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => Exists.{max 1 (max (succ u3) (succ u2)) (succ (max u2 u3))} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (fun (y : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) => Eq.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X))) x (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S y)))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))), Exists.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (fun (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => Exists.{max (succ u3) (succ u2)} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (fun (y : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) => Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) x (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S y)))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))), Exists.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (fun (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => Exists.{max (succ u3) (succ u2)} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (fun (y : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) => Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) x (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S y)))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.exists_rep CategoryTheory.GrothendieckTopology.Plus.exists_repₓ'. -/
 theorem exists_rep {X : C} {P : Cᵒᵖ ⥤ D} (x : (J.plusObj P).obj (op X)) :
     ∃ (S : J.cover X)(y : Meq P S), x = mk y :=
@@ -353,7 +353,7 @@ theorem exists_rep {X : C} {P : Cᵒᵖ ⥤ D} (x : (J.plusObj P).obj (op X)) :
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} {T : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (y : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P T), Iff (Eq.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.Plus.mk._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S)) P (CategoryTheory.GrothendieckTopology.Plus.mk._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P T y)) (Exists.{max 1 (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (fun (W : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => Exists.{succ (max u3 u2)} (Quiver.Hom.{succ (max u3 u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)))) W S) (fun (h1 : Quiver.Hom.{succ (max u3 u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)))) W S) => Exists.{succ (max u3 u2)} (Quiver.Hom.{succ (max u3 u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)))) W T) (fun (h2 : Quiver.Hom.{succ (max u3 u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)))) W T) => Eq.{max 1 (max (succ u3) (succ u2)) (succ (max u2 u3))} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W S x h1) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W T y h2)))))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} {T : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (y : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P T), Iff (Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P T y)) (Exists.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (fun (W : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => Exists.{max (succ u3) (succ u2)} (Quiver.Hom.{max (succ u3) (succ u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) W S) (fun (h1 : Quiver.Hom.{max (succ u3) (succ u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) W S) => Exists.{max (succ u3) (succ u2)} (Quiver.Hom.{max (succ u3) (succ u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) W T) (fun (h2 : Quiver.Hom.{max (succ u3) (succ u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) W T) => Eq.{max (succ u3) (succ u2)} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W S x h1) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W T y h2)))))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} {T : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (y : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P T), Iff (Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} 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CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P T y)) (Exists.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (fun (W : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => Exists.{max (succ u3) (succ u2)} (Quiver.Hom.{max (succ u3) (succ u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) W S) (fun (h1 : Quiver.Hom.{max (succ u3) (succ u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, 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T) (fun (h2 : Quiver.Hom.{max (succ u3) (succ u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) W T) => Eq.{max (succ u3) (succ u2)} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W S x h1) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W T y h2)))))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.eq_mk_iff_exists CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_existsₓ'. -/
 theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P S) (y : Meq P T) :
     mk x = mk y ↔ ∃ (W : J.cover X)(h1 : W ⟶ S)(h2 : W ⟶ T), x.refine h1 = y.refine h2 :=
@@ -386,7 +386,7 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] {X : C} (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X))) (y : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X))), (forall (I : CategoryTheory.GrothendieckTopology.Cover.Arrow.{u2, u3} C _inst_1 X J S), Eq.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) 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 but is expected to have type
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(CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I)))) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 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: C) => _inst_5 X))) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I))) (Prefunctor.map.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I)) (Quiver.Hom.op.{u3, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I) X (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 X J S I))) x) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} 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C) => _inst_5 X))) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C 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(Opposite.op.{succ u3} C X) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I)) (Quiver.Hom.op.{u3, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I) X (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 X J S I))) y)) -> (Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => 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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.sep CategoryTheory.GrothendieckTopology.Plus.sepₓ'. -/
 /-- `P⁺` is always separated. -/
 theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj (op X))
@@ -448,7 +448,7 @@ theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), (forall (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X))) (y : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.inj_of_sep CategoryTheory.GrothendieckTopology.Plus.inj_of_sepₓ'. -/
 theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
     (hsep :
@@ -470,7 +470,7 @@ theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) 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 but is expected to have type
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_inst_1 X J S I) P (T I) (t I))) -> (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P (CategoryTheory.GrothendieckTopology.Cover.bind.{u2, u3} C _inst_1 J X S T)))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.meq_of_sep CategoryTheory.GrothendieckTopology.Plus.meqOfSepₓ'. -/
 /-- An auxiliary definition to be used in the proof of `exists_of_sep` below.
   Given a compatible family of local sections for `P⁺`, and representatives of said sections,
@@ -507,7 +507,7 @@ def meqOfSep (P : Cᵒᵖ ⥤ D)
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) 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(Opposite.op.{succ u3} C X))) x y)) -> (forall (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (s : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) S), Exists.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, 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 but is expected to have type
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(CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} 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_inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) => Eq.{max (succ u3) (succ u2)} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) S) (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) S t) s))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.exists_of_sep CategoryTheory.GrothendieckTopology.Plus.exists_of_sepₓ'. -/
 theorem exists_of_sep (P : Cᵒᵖ ⥤ D)
     (hsep :
@@ -574,7 +574,7 @@ variable [ReflectsIsomorphisms (forget D)]
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) 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 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} 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+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) 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u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I)) (Quiver.Hom.op.{u3, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I) X (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 X J S I))) x) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I))) (Prefunctor.map.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I)) (Quiver.Hom.op.{u3, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I) X (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 X J S I))) y)) -> (Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X))) x y)) -> (CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.is_sheaf_of_sep CategoryTheory.GrothendieckTopology.Plus.isSheaf_of_sepₓ'. -/
 /-- If `P` is separated, then `P⁺` is a sheaf. -/
 theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)

4f4a1c87

bump to nightly-2023-04-18-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/49b7f94aab3a3bdca1f9f34c5d818afb253b3993

c37d1701

Diff

@@ -232,7 +232,7 @@ noncomputable section
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X}, (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) -> (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.Plus.mk._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_6) P (CategoryTheory.GrothendieckTopology.Plus.mk._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_5)) (Opposite.op.{succ u3} C X)))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X}, (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) -> (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X}, (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) -> (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.mk CategoryTheory.GrothendieckTopology.Plus.mkₓ'. -/
 /-- Make a term of `(J.plus_obj P).obj (op X)` from `x : meq P S`. -/
 def mk {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) : (J.plusObj P).obj (op X) :=
@@ -243,7 +243,7 @@ def mk {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) : (J.plusObj P)
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} 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 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {Y : C} {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (f : Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Y X), Eq.{max (succ u3) (succ u2)} 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_inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C Y)) (Prefunctor.map.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X) (Opposite.op.{succ u3} C Y) (Quiver.Hom.op.{u3, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Y X f)) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S x)) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) Y P (Prefunctor.obj.{max (succ u3) (succ u2), max (succ u3) (succ u2), max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J Y)))) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J Y)) (CategoryTheory.GrothendieckTopology.pullback.{u2, u3} C _inst_1 X Y J f)) S) (CategoryTheory.Meq.pullback.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 Y X P S x f))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {Y : C} {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (f : Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Y X), Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C Y))) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C Y)) (Prefunctor.map.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X) (Opposite.op.{succ u3} C Y) (Quiver.Hom.op.{u3, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Y X f)) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S x)) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) Y P (Prefunctor.obj.{max (succ u3) (succ u2), max (succ u3) (succ u2), max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J Y)))) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J Y)) (CategoryTheory.GrothendieckTopology.pullback.{u2, u3} C _inst_1 X Y J f)) S) (CategoryTheory.Meq.pullback.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 Y X P S x f))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.res_mk_eq_mk_pullback CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullbackₓ'. -/
 theorem res_mk_eq_mk_pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y ⟶ X) :
     (J.plusObj P).map f.op (mk x) = mk (x.pullback f) :=
@@ -264,7 +264,7 @@ theorem res_mk_eq_mk_pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x :
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X))), Eq.{succ (max 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(CategoryTheory.GrothendieckTopology.toPlus._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (CategoryTheory.NatTrans.app.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toPlus._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S)) P (CategoryTheory.GrothendieckTopology.toPlus._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (CategoryTheory.GrothendieckTopology.toPlus.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X)) x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S x))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X))), Eq.{max (succ u3) 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J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (CategoryTheory.GrothendieckTopology.toPlus.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X)) x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S x))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X))), Eq.{max (succ u3) 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(CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, succ (max u3 u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, succ (max u3 u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)) (CategoryTheory.NatTrans.app.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (CategoryTheory.GrothendieckTopology.toPlus.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X)) x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S x))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.to_plus_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_mkₓ'. -/
 theorem toPlus_mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) :
     (J.toPlus P).app _ x = mk (Meq.mk S x) :=
@@ -286,7 +286,7 @@ theorem toPlus_mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X))
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (I : CategoryTheory.GrothendieckTopology.Cover.Arrow.{u2, u3} C _inst_1 X J S), Eq.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) 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 but is expected to have type
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(Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I))) (Prefunctor.map.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I)) (Quiver.Hom.op.{u3, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I) X (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 X J S I))) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S x))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.to_plus_apply CategoryTheory.GrothendieckTopology.Plus.toPlus_applyₓ'. -/
 theorem toPlus_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : Meq P S) (I : S.arrow) :
     (J.toPlus P).app _ (x I) = (J.plusObj P).map I.f.op (mk x) :=
@@ -317,7 +317,7 @@ theorem toPlus_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : Meq P S) (
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X))), Eq.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toPlus._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S)) P (CategoryTheory.GrothendieckTopology.toPlus._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (coeFn.{succ (max u2 u3), succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), u1} D (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, u1} D (CategoryTheory.Category.toCategoryStruct.{max u2 u3, u1} D _inst_2)) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X)) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toPlus._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S)) P (CategoryTheory.GrothendieckTopology.toPlus._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (fun (f : Quiver.Hom.{succ (max u2 u3), u1} D (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, u1} D (CategoryTheory.Category.toCategoryStruct.{max u2 u3, u1} D _inst_2)) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X)) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toPlus._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S)) P (CategoryTheory.GrothendieckTopology.toPlus._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) => (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X))) -> (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toPlus._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S)) P (CategoryTheory.GrothendieckTopology.toPlus._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)))) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3 (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X)) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toPlus._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S)) P (CategoryTheory.GrothendieckTopology.toPlus._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (CategoryTheory.NatTrans.app.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toPlus._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S)) P (CategoryTheory.GrothendieckTopology.toPlus._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (CategoryTheory.GrothendieckTopology.toPlus.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X)) x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toHasTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.orderTop.{u2, u3} C _inst_1 X J))) (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toHasTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.orderTop.{u2, u3} C _inst_1 X J))) x))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X))), Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ 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(CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, succ (max u3 u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, succ (max u3 u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)) (CategoryTheory.NatTrans.app.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (CategoryTheory.GrothendieckTopology.toPlus.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X)) x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.instOrderTopCoverToLEInstPreorderCover.{u2, u3} C _inst_1 X J))) (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.instOrderTopCoverToLEInstPreorderCover.{u2, u3} C _inst_1 X J))) x))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X))), Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, succ (max u3 u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, succ (max u3 u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, succ (max u3 u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)) (CategoryTheory.NatTrans.app.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (CategoryTheory.GrothendieckTopology.toPlus.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X)) x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.instOrderTopCoverToLEInstPreorderCover.{u2, u3} C _inst_1 X J))) (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.instOrderTopCoverToLEInstPreorderCover.{u2, u3} C _inst_1 X J))) x))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.to_plus_eq_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mkₓ'. -/
 theorem toPlus_eq_mk {X : C} {P : Cᵒᵖ ⥤ D} (x : P.obj (op X)) :
     (J.toPlus P).app _ x = mk (Meq.mk ⊤ x) :=
@@ -337,7 +337,7 @@ variable [∀ X : C, PreservesColimitsOfShape (J.cover X)ᵒᵖ (forget D)]
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X))), Exists.{max 1 (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (fun (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => Exists.{max 1 (max (succ u3) (succ u2)) (succ (max u2 u3))} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (fun (y : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) => Eq.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X))) x (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S y)))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))), Exists.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (fun (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => Exists.{max (succ u3) (succ u2)} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (fun (y : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) => Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) x (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S y)))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))), Exists.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (fun (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => Exists.{max (succ u3) (succ u2)} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (fun (y : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) => Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) x (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S y)))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.exists_rep CategoryTheory.GrothendieckTopology.Plus.exists_repₓ'. -/
 theorem exists_rep {X : C} {P : Cᵒᵖ ⥤ D} (x : (J.plusObj P).obj (op X)) :
     ∃ (S : J.cover X)(y : Meq P S), x = mk y :=
@@ -353,7 +353,7 @@ theorem exists_rep {X : C} {P : Cᵒᵖ ⥤ D} (x : (J.plusObj P).obj (op X)) :
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} {T : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (y : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P T), Iff (Eq.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.Plus.mk._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S)) P (CategoryTheory.GrothendieckTopology.Plus.mk._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P T y)) (Exists.{max 1 (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (fun (W : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => Exists.{succ (max u3 u2)} (Quiver.Hom.{succ (max u3 u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)))) W S) (fun (h1 : Quiver.Hom.{succ (max u3 u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)))) W S) => Exists.{succ (max u3 u2)} (Quiver.Hom.{succ (max u3 u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)))) W T) (fun (h2 : Quiver.Hom.{succ (max u3 u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)))) W T) => Eq.{max 1 (max (succ u3) (succ u2)) (succ (max u2 u3))} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W S x h1) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W T y h2)))))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} {T : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (y : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P T), Iff (Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P T y)) (Exists.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (fun (W : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => Exists.{max (succ u3) (succ u2)} (Quiver.Hom.{max (succ u3) (succ u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) W S) (fun (h1 : Quiver.Hom.{max (succ u3) (succ u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) W S) => Exists.{max (succ u3) (succ u2)} (Quiver.Hom.{max (succ u3) (succ u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) W T) (fun (h2 : Quiver.Hom.{max (succ u3) (succ u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) W T) => Eq.{max (succ u3) (succ u2)} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W S x h1) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W T y h2)))))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} {T : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (y : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P T), Iff (Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} 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u3} C _inst_1 J X) => _inst_6 P X S) X P T y)) (Exists.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (fun (W : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => Exists.{max (succ u3) (succ u2)} (Quiver.Hom.{max (succ u3) (succ u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) W S) (fun (h1 : Quiver.Hom.{max (succ u3) (succ u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max 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X)))) W T) (fun (h2 : Quiver.Hom.{max (succ u3) (succ u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) W T) => Eq.{max (succ u3) (succ u2)} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W S x h1) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W T y h2)))))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.eq_mk_iff_exists CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_existsₓ'. -/
 theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P S) (y : Meq P T) :
     mk x = mk y ↔ ∃ (W : J.cover X)(h1 : W ⟶ S)(h2 : W ⟶ T), x.refine h1 = y.refine h2 :=
@@ -386,7 +386,7 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] {X : C} (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : 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 but is expected to have type
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_inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I)))) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 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S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I))) (Prefunctor.map.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I)) (Quiver.Hom.op.{u3, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I) X (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 X J S I))) x) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} 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C) => _inst_5 X))) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C 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(Opposite.op.{succ u3} C X) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I)) (Quiver.Hom.op.{u3, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I) X (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 X J S I))) y)) -> (Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C 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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.sep CategoryTheory.GrothendieckTopology.Plus.sepₓ'. -/
 /-- `P⁺` is always separated. -/
 theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj (op X))
@@ -448,7 +448,7 @@ theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), (forall (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X))) (y : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.inj_of_sep CategoryTheory.GrothendieckTopology.Plus.inj_of_sepₓ'. -/
 theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
     (hsep :
@@ -470,7 +470,7 @@ theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.meq_of_sep CategoryTheory.GrothendieckTopology.Plus.meqOfSepₓ'. -/
 /-- An auxiliary definition to be used in the proof of `exists_of_sep` below.
   Given a compatible family of local sections for `P⁺`, and representatives of said sections,
@@ -507,7 +507,7 @@ def meqOfSep (P : Cᵒᵖ ⥤ D)
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) 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(Opposite.op.{succ u3} C X))) x y)) -> (forall (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (s : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) S), Exists.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, 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 but is expected to have type
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(CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} 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(CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} 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(CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I)))) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} 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(CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I))) (Prefunctor.map.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X) (Opposite.op.{succ u3} 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u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I))) (Prefunctor.map.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I)) (Quiver.Hom.op.{u3, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I) X (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 X J S I))) y)) -> (Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X))) x y)) -> (forall (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (s : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) S), Exists.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (fun (t : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) => Eq.{max (succ u3) (succ u2)} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) S) (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) S t) s))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.exists_of_sep CategoryTheory.GrothendieckTopology.Plus.exists_of_sepₓ'. -/
 theorem exists_of_sep (P : Cᵒᵖ ⥤ D)
     (hsep :
@@ -574,7 +574,7 @@ variable [ReflectsIsomorphisms (forget D)]
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), (forall (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X))) (y : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} 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Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X))) x y)) -> (CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), (forall (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} 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+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) 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(CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I)) (Quiver.Hom.op.{u3, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I) X (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 X J S I))) x) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I))) (Prefunctor.map.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I)) (Quiver.Hom.op.{u3, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I) X (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 X J S I))) y)) -> (Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X))) x y)) -> (CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.is_sheaf_of_sep CategoryTheory.GrothendieckTopology.Plus.isSheaf_of_sepₓ'. -/
 /-- If `P` is separated, then `P⁺` is a sheaf. -/
 theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)
@@ -615,7 +615,7 @@ variable (J)
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (fun (X : C) => _inst_5 X))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (fun (X : C) => _inst_5 X))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (fun (X : C) => _inst_5 X))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.is_sheaf_plus_plus CategoryTheory.GrothendieckTopology.Plus.isSheaf_plus_plusₓ'. -/
 /-- `P⁺⁺` is always a sheaf. -/
 theorem isSheaf_plus_plus (P : Cᵒᵖ ⥤ D) : Presheaf.IsSheaf J (J.plusObj (J.plusObj P)) :=
@@ -636,7 +636,7 @@ variable [∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : J.cover X), HasMultiequalizer (S.
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2], (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) -> (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2], (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) -> (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2], (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) -> (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify CategoryTheory.GrothendieckTopology.sheafifyₓ'. -/
 /-- The sheafification of a presheaf `P`.
 *NOTE:* Additional hypotheses are needed to obtain a proof that this is a sheaf! -/
@@ -648,7 +648,7 @@ def sheafify (P : Cᵒᵖ ⥤ D) : Cᵒᵖ ⥤ D :=
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_3) (CategoryTheory.GrothendieckTopology.toSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_4) P)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.to_sheafify CategoryTheory.GrothendieckTopology.toSheafifyₓ'. -/
 /-- The canonical map from `P` to its sheafification. -/
 def toSheafify (P : Cᵒᵖ ⥤ D) : P ⟶ J.sheafify P :=
@@ -659,7 +659,7 @@ def toSheafify (P : Cᵒᵖ ⥤ D) : P ⟶ J.sheafify P :=
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) -> (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_3) (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_4) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_3.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_3) (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_4.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_4) Q))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) -> (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) -> (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_map CategoryTheory.GrothendieckTopology.sheafifyMapₓ'. -/
 /-- The canonical map on sheafifications induced by a morphism. -/
 def sheafifyMap {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) : J.sheafify P ⟶ J.sheafify Q :=
@@ -670,7 +670,7 @@ def sheafifyMap {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) : J.sheafify P ⟶ J.sheafi
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Eq.{succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_3.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_4.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) P)) (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P P (CategoryTheory.CategoryStruct.id.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P)) (CategoryTheory.CategoryStruct.id.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)) (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P P (CategoryTheory.CategoryStruct.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P)) (CategoryTheory.CategoryStruct.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)) (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P P (CategoryTheory.CategoryStruct.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P)) (CategoryTheory.CategoryStruct.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_map_id CategoryTheory.GrothendieckTopology.sheafifyMap_idₓ'. -/
 @[simp]
 theorem sheafifyMap_id (P : Cᵒᵖ ⥤ D) : J.sheafifyMap (𝟙 P) = 𝟙 (J.sheafify P) :=
@@ -683,7 +683,7 @@ theorem sheafifyMap_id (P : Cᵒᵖ ⥤ D) : J.sheafifyMap (𝟙 P) = 𝟙 (J.sh
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {R : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (γ : Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) Q R), Eq.{succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_3.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_4.{u3, u2, u1} C _inst_1 J D _inst_2 (fun 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 but is expected to have type
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+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {R : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) 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P R (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P Q R η γ)) (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) R) (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η) (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q R γ))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_map_comp CategoryTheory.GrothendieckTopology.sheafifyMap_compₓ'. -/
 @[simp]
 theorem sheafifyMap_comp {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q ⟶ R) :
@@ -697,7 +697,7 @@ theorem sheafifyMap_comp {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q ⟶ R) :
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q), Eq.{succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.toSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) Q)) (CategoryTheory.CategoryStruct.comp.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P Q (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.toSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) Q) η (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q)) (CategoryTheory.CategoryStruct.comp.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.toSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.toSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) Q) (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P 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(fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q) η (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q)) (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q) (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q)) (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P Q (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q) η (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q)) (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q) (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.to_sheafify_naturality CategoryTheory.GrothendieckTopology.toSheafify_naturalityₓ'. -/
 @[simp, reassoc.1]
 theorem toSheafify_naturality {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) :
@@ -713,7 +713,7 @@ variable (D)
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2], CategoryTheory.Functor.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2], CategoryTheory.Functor.{max u3 u2, max u3 u2, max (max (max u1 u3) u3 u2) u2, max (max (max u1 u3) u3 u2) u2} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2], CategoryTheory.Functor.{max u3 u2, max u3 u2, max (max (max u1 u3) u3 u2) u2, max (max (max u1 u3) u3 u2) u2} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafification CategoryTheory.GrothendieckTopology.sheafificationₓ'. -/
 /-- The sheafification of a presheaf `P`, as a functor.
 *NOTE:* Additional hypotheses are needed to obtain a proof that this is a sheaf! -/
@@ -725,7 +725,7 @@ def sheafification : (Cᵒᵖ ⥤ D) ⥤ Cᵒᵖ ⥤ D :=
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Eq.{succ (max u2 (max u2 u3) u3 u1)} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.obj.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.GrothendieckTopology.sheafification.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X)) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Eq.{max (max (succ u3) (succ u2)) (succ u1)} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (Prefunctor.obj.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.GrothendieckTopology.sheafification.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X))) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Eq.{max (max (succ u3) (succ u2)) (succ u1)} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (Prefunctor.obj.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.GrothendieckTopology.sheafification.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X))) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafification_obj CategoryTheory.GrothendieckTopology.sheafification_objₓ'. -/
 @[simp]
 theorem sheafification_obj (P : Cᵒᵖ ⥤ D) : (J.sheafification D).obj P = J.sheafify P :=
@@ -736,7 +736,7 @@ theorem sheafification_obj (P : Cᵒᵖ ⥤ D) : (J.sheafification D).obj P = J.
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q), Eq.{succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.Functor.obj.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.GrothendieckTopology.sheafification.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X)) P) (CategoryTheory.Functor.obj.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.GrothendieckTopology.sheafification.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C 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 but is expected to have type
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(CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) 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D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.GrothendieckTopology.sheafification.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X))) P Q η) (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η)
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafification_map CategoryTheory.GrothendieckTopology.sheafification_mapₓ'. -/
 @[simp]
 theorem sheafification_map {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) :
@@ -748,7 +748,7 @@ theorem sheafification_map {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) :
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2], Quiver.Hom.{succ (max (max u2 (max u2 u3) u3 u1) u2 u3), max (max u2 u3) u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.CategoryStruct.toQuiver.{max (max u2 (max u2 u3) u3 u1) u2 u3, max (max u2 u3) u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.Category.toCategoryStruct.{max (max u2 (max u2 u3) u3 u1) u2 u3, max (max u2 u3) u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.Functor.category.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)))) (CategoryTheory.Functor.id.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.GrothendieckTopology.sheafification.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toSheafification._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_3) (CategoryTheory.GrothendieckTopology.toSheafification._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_4))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2], Quiver.Hom.{max (max (succ u3) (succ u2)) (succ u1), max (max u3 u2) u1} (CategoryTheory.Functor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.CategoryStruct.toQuiver.{max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.Category.toCategoryStruct.{max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.Functor.category.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)))) (CategoryTheory.Functor.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.GrothendieckTopology.sheafification.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2], Quiver.Hom.{max (max (succ u3) (succ u2)) (succ u1), max (max u3 u2) u1} (CategoryTheory.Functor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.CategoryStruct.toQuiver.{max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.Category.toCategoryStruct.{max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.Functor.category.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)))) (CategoryTheory.Functor.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.GrothendieckTopology.sheafification.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.to_sheafification CategoryTheory.GrothendieckTopology.toSheafificationₓ'. -/
 /-- The canonical map from `P` to its sheafification, as a natural transformation.
 *Note:* We only show this is a sheaf under additional hypotheses on `D`. -/
@@ -760,7 +760,7 @@ def toSheafification : 𝟭 _ ⟶ sheafification J D :=
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Eq.{succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.Functor.obj.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.id.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 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 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} 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J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P) (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.GrothendieckTopology.sheafification.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X))) P)) (CategoryTheory.NatTrans.app.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.GrothendieckTopology.sheafification.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X)) (CategoryTheory.GrothendieckTopology.toSheafification.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X)) P) (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.to_sheafification_app CategoryTheory.GrothendieckTopology.toSheafification_appₓ'. -/
 @[simp]
 theorem toSheafification_app (P : Cᵒᵖ ⥤ D) : (J.toSheafification D).app P = J.toSheafify P :=
@@ -773,7 +773,7 @@ variable {D}
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J P) -> (CategoryTheory.IsIso.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.toSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) P) (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J P) -> (CategoryTheory.IsIso.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J P) -> (CategoryTheory.IsIso.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.is_iso_to_sheafify CategoryTheory.GrothendieckTopology.isIso_toSheafifyₓ'. -/
 theorem isIso_toSheafify {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) : IsIso (J.toSheafify P) :=
   by
@@ -787,7 +787,7 @@ theorem isIso_toSheafify {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) : IsIso
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J P) -> (CategoryTheory.Iso.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.isoSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_3) (CategoryTheory.GrothendieckTopology.isoSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_4) P))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J P) -> (CategoryTheory.Iso.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J P) -> (CategoryTheory.Iso.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.iso_sheafify CategoryTheory.GrothendieckTopology.isoSheafifyₓ'. -/
 /-- If `P` is a sheaf, then `P` is isomorphic to `J.sheafify P`. -/
 def isoSheafify {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) : P ≅ J.sheafify P :=
@@ -799,7 +799,7 @@ def isoSheafify {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) : P ≅ J.sheafi
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (hP : CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J P), Eq.{succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.isoSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.isoSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) P)) (CategoryTheory.Iso.hom.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.isoSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.isoSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) P) (CategoryTheory.GrothendieckTopology.isoSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P hP)) (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (hP : CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J P), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)) (CategoryTheory.Iso.hom.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.isoSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P hP)) (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (hP : CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J P), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)) (CategoryTheory.Iso.hom.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.isoSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P hP)) (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.iso_sheafify_hom CategoryTheory.GrothendieckTopology.isoSheafify_homₓ'. -/
 @[simp]
 theorem isoSheafify_hom {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) :
@@ -811,7 +811,7 @@ theorem isoSheafify_hom {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) :
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) -> (CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J Q) -> (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.sheafifyLift._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_3) (CategoryTheory.GrothendieckTopology.sheafifyLift._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_4) P) Q)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) -> (CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J Q) -> (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) -> (CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J Q) -> (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q)
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_lift CategoryTheory.GrothendieckTopology.sheafifyLiftₓ'. -/
 /-- Given a sheaf `Q` and a morphism `P ⟶ Q`, construct a morphism from
 `J.sheafifcation P` to `Q`. -/
@@ -823,7 +823,7 @@ def sheafifyLift {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.IsSheaf J Q
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (hQ : CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J Q), Eq.{succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (CategoryTheory.CategoryStruct.comp.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.toSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) P) Q (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η hQ)) η
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (hQ : CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J Q), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η hQ)) η
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (hQ : CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J Q), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η hQ)) η
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.to_sheafify_sheafify_lift CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLiftₓ'. -/
 @[simp, reassoc.1]
 theorem toSheafify_sheafifyLift {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.IsSheaf J Q) :
@@ -837,7 +837,7 @@ theorem toSheafify_sheafifyLift {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presh
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (hQ : CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J Q) (γ : Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q), (Eq.{succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (CategoryTheory.CategoryStruct.comp.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.toSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) P) Q (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) γ) η) -> (Eq.{succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q) γ (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η hQ))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (hQ : CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J Q) (γ : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q), (Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) γ) η) -> (Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q) γ (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η hQ))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (hQ : CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J Q) (γ : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q), (Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) 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_inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) γ) η) -> (Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q) γ (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η hQ))
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_lift_unique CategoryTheory.GrothendieckTopology.sheafifyLift_uniqueₓ'. -/
 theorem sheafifyLift_unique {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.IsSheaf J Q)
     (γ : J.sheafify P ⟶ Q) : J.toSheafify P ≫ γ = η → γ = sheafifyLift J η hQ :=
@@ -853,7 +853,7 @@ theorem sheafifyLift_unique {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (hP : CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J P), Eq.{succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.isoSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.isoSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) P) P) (CategoryTheory.Iso.inv.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.isoSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.isoSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) P) (CategoryTheory.GrothendieckTopology.isoSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P hP)) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P P (CategoryTheory.CategoryStruct.id.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P) hP)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (hP : CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J P), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) P) (CategoryTheory.Iso.inv.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.isoSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P hP)) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P P (CategoryTheory.CategoryStruct.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P) hP)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (hP : CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J P), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) P) (CategoryTheory.Iso.inv.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.isoSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P hP)) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P P (CategoryTheory.CategoryStruct.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P) hP)
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.iso_sheafify_inv CategoryTheory.GrothendieckTopology.isoSheafify_invₓ'. -/
 @[simp]
 theorem isoSheafify_inv {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) :
@@ -867,7 +867,7 @@ theorem isoSheafify_inv {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) :
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q) (γ : Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) 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 but is expected to have type
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(CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) 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(CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q) η γ)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q) (γ : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q), (CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J Q) -> (Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) η) (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) γ)) -> (Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q) η γ)
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_hom_ext CategoryTheory.GrothendieckTopology.sheafify_hom_extₓ'. -/
 theorem sheafify_hom_ext {P Q : Cᵒᵖ ⥤ D} (η γ : J.sheafify P ⟶ Q) (hQ : Presheaf.IsSheaf J Q)
     (h : J.toSheafify P ≫ η = J.toSheafify P ≫ γ) : η = γ :=
@@ -882,7 +882,7 @@ theorem sheafify_hom_ext {P Q : Cᵒᵖ ⥤ D} (η γ : J.sheafify P ⟶ Q) (hQ
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {R : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (γ : Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) Q R) (hR : CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J R), Eq.{succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) 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u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_4.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) Q) R (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q R γ hR)) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P R (CategoryTheory.CategoryStruct.comp.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P Q R η γ) hR)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {R : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (γ : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) Q R) (hR : CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J R), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) R) (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q) R (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q R γ hR)) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P R (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P Q R η γ) hR)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {R : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (γ : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) Q R) (hR : CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J R), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) R) (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q) R (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) Q R γ hR)) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P R (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P Q R η γ) hR)
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_map_sheafify_lift CategoryTheory.GrothendieckTopology.sheafifyMap_sheafifyLiftₓ'. -/
 @[simp, reassoc.1]
 theorem sheafifyMap_sheafifyLift {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q ⟶ R)
@@ -906,7 +906,7 @@ variable [ConcreteCategory.{max v u} D] [PreservesLimits (forget D)]
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) P)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) P)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) P)
 Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_is_sheaf CategoryTheory.GrothendieckTopology.sheafify_isSheafₓ'. -/
 theorem GrothendieckTopology.sheafify_isSheaf (P : Cᵒᵖ ⥤ D) : Presheaf.IsSheaf J (J.sheafify P) :=
   GrothendieckTopology.Plus.isSheaf_plus_plus _ _
@@ -918,7 +918,7 @@ variable (D)
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)], CategoryTheory.Functor.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u3 u1 u2 u3} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)], CategoryTheory.Functor.{max u3 u2, max u3 u2, max (max (max u1 u3) u3 u2) u2, max (max (max u1 u3) u3 u2) u2} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)], CategoryTheory.Functor.{max u3 u2, max u3 u2, max (max (max u1 u3) u3 u2) u2, max (max (max u1 u3) u3 u2) u2} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2)
 Case conversion may be inaccurate. Consider using '#align category_theory.presheaf_to_Sheaf CategoryTheory.presheafToSheafₓ'. -/
 /-- The sheafification functor, as a functor taking values in `Sheaf`. -/
 @[simps]
@@ -934,7 +934,7 @@ def presheafToSheaf : (Cᵒᵖ ⥤ D) ⥤ Sheaf J D
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_9 : CategoryTheory.Preadditive.{max u2 u3, u1} D _inst_2], CategoryTheory.Functor.PreservesZeroMorphisms.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u3 u1 u2 u3} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Limits.CategoryTheory.Functor.hasZeroMorphisms.{u2, u3, max u2 u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{max u2 u3, u1} D _inst_2 _inst_9)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.preadditive.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2 _inst_9)) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_9 : CategoryTheory.Preadditive.{max u3 u2, u1} D _inst_2], CategoryTheory.Functor.PreservesZeroMorphisms.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Limits.instHasZeroMorphismsFunctorCategory.{u2, u3, max u3 u2, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{max u3 u2, u1} D _inst_2 _inst_9)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.instPreadditiveSheafInstCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 _inst_9)) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_9 : CategoryTheory.Preadditive.{max u3 u2, u1} D _inst_2], CategoryTheory.Functor.PreservesZeroMorphisms.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Limits.instHasZeroMorphismsFunctorCategory.{u2, u3, max u3 u2, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{max u3 u2, u1} D _inst_2 _inst_9)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.instPreadditiveSheafInstCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 _inst_9)) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8)
 Case conversion may be inaccurate. Consider using '#align category_theory.presheaf_to_Sheaf_preserves_zero_morphisms CategoryTheory.presheafToSheaf_preservesZeroMorphismsₓ'. -/
 instance presheafToSheaf_preservesZeroMorphisms [Preadditive D] :
     (presheafToSheaf J D).PreservesZeroMorphisms
@@ -947,7 +947,7 @@ instance presheafToSheaf_preservesZeroMorphisms [Preadditive D] :
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)], CategoryTheory.Adjunction.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u3 u1 u2 u3} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (CategoryTheory.sheafificationAdjunction._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_5) (CategoryTheory.sheafificationAdjunction._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_6) (fun (X : C) => _inst_7 X) _inst_8) (CategoryTheory.sheafToPresheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)], CategoryTheory.Adjunction.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8) (CategoryTheory.sheafToPresheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)], CategoryTheory.Adjunction.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8) (CategoryTheory.sheafToPresheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2)
 Case conversion may be inaccurate. Consider using '#align category_theory.sheafification_adjunction CategoryTheory.sheafificationAdjunctionₓ'. -/
 /-- The sheafification functor is left adjoint to the forgetful functor. -/
 @[simps unit_app counit_app_val]
@@ -971,7 +971,7 @@ def sheafificationAdjunction : presheafToSheaf J D ⊣ sheafToPresheaf J D :=
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)], CategoryTheory.IsRightAdjoint.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u3 u1 u2 u3} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafToPresheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)], CategoryTheory.IsRightAdjoint.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafToPresheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)], CategoryTheory.IsRightAdjoint.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafToPresheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2)
 Case conversion may be inaccurate. Consider using '#align category_theory.Sheaf_to_presheaf_is_right_adjoint CategoryTheory.sheafToPresheafIsRightAdjointₓ'. -/
 instance sheafToPresheafIsRightAdjoint : IsRightAdjoint (sheafToPresheaf J D) :=
   ⟨_, sheafificationAdjunction J D⟩
@@ -981,7 +981,7 @@ instance sheafToPresheafIsRightAdjoint : IsRightAdjoint (sheafToPresheaf J D) :=
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] {F : CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2} {G : CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2} (f : Quiver.Hom.{succ (max u2 u3), max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2))) F G) [_inst_9 : CategoryTheory.Mono.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) F G f], CategoryTheory.Mono.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.val.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2 F) (CategoryTheory.Sheaf.val.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2 G) (CategoryTheory.Sheaf.Hom.val.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2 F G f)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {F : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2} {G : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2} (f : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) F G) [_inst_9 : CategoryTheory.Mono.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) F G f], CategoryTheory.Mono.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 F) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 G) (CategoryTheory.Sheaf.Hom.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 F G f)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {F : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2} {G : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2} (f : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) F G) [_inst_9 : CategoryTheory.Mono.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) F G f], CategoryTheory.Mono.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 F) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 G) (CategoryTheory.Sheaf.Hom.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 F G f)
 Case conversion may be inaccurate. Consider using '#align category_theory.presheaf_mono_of_mono CategoryTheory.presheaf_mono_of_monoₓ'. -/
 instance presheaf_mono_of_mono {F G : Sheaf J D} (f : F ⟶ G) [Mono f] : Mono f.1 :=
   (sheafToPresheaf J D).map_mono _
@@ -991,7 +991,7 @@ instance presheaf_mono_of_mono {F G : Sheaf J D} (f : F ⟶ G) [Mono f] : Mono f
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] {F : CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2} {G : CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2} (f : Quiver.Hom.{succ (max u2 u3), max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2))) F G), Iff (CategoryTheory.Mono.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) F G f) (CategoryTheory.Mono.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.val.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2 F) (CategoryTheory.Sheaf.val.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2 G) (CategoryTheory.Sheaf.Hom.val.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2 F G f))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {F : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2} {G : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2} (f : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) F G), Iff (CategoryTheory.Mono.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) F G f) (CategoryTheory.Mono.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 F) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 G) (CategoryTheory.Sheaf.Hom.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 F G f))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {F : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2} {G : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2} (f : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) F G), Iff (CategoryTheory.Mono.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) F G f) (CategoryTheory.Mono.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 F) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 G) (CategoryTheory.Sheaf.Hom.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 F G f))
 Case conversion may be inaccurate. Consider using '#align category_theory.Sheaf.hom.mono_iff_presheaf_mono CategoryTheory.Sheaf.Hom.mono_iff_presheaf_monoₓ'. -/
 theorem Sheaf.Hom.mono_iff_presheaf_mono {F G : Sheaf J D} (f : F ⟶ G) : Mono f ↔ Mono f.1 :=
   ⟨fun m => by
@@ -1007,7 +1007,7 @@ variable {J D}
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] (P : CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2), CategoryTheory.Iso.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) P (CategoryTheory.Functor.obj.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u3 u1 u2 u3} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (CategoryTheory.sheafificationIso._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_5) (CategoryTheory.sheafificationIso._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_6) (fun (X : C) => _inst_7 X) _inst_8) (CategoryTheory.Sheaf.val.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2 P))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] (P : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2), CategoryTheory.Iso.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) P (Prefunctor.obj.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8)) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 P))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] (P : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2), CategoryTheory.Iso.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) P (Prefunctor.obj.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8)) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 P))
 Case conversion may be inaccurate. Consider using '#align category_theory.sheafification_iso CategoryTheory.sheafificationIsoₓ'. -/
 /-- A sheaf `P` is isomorphic to its own sheafification. -/
 @[simps]
@@ -1027,7 +1027,7 @@ def sheafificationIso (P : Sheaf J D) : P ≅ (presheafToSheaf J D).obj P.val
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] (P : CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2), CategoryTheory.IsIso.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Functor.obj.{max u2 u3, max u2 u3, max u3 u1 u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Functor.comp.{max u2 u3, max u2 u3, max u2 u3, max u3 u1 u2 u3, max u2 (max u2 u3) u3 u1, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafToPresheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 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C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2)) (CategoryTheory.Adjunction.counit.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u3 u1 u2 u3} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (CategoryTheory.sheafificationAdjunction._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S)) (CategoryTheory.sheafificationAdjunction._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_6 X)) (fun (X : C) => _inst_7 X) _inst_8) (CategoryTheory.sheafToPresheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafificationAdjunction.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8)) P)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] (P : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2), CategoryTheory.IsIso.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) 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_inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8) (CategoryTheory.sheafToPresheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafificationAdjunction.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8)) P)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] (P : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2), CategoryTheory.IsIso.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Functor.comp.{max u3 u2, max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafToPresheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8))) P) (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Functor.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) P) (CategoryTheory.NatTrans.app.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Functor.comp.{max u3 u2, max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafToPresheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8)) (CategoryTheory.Functor.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2)) (CategoryTheory.Adjunction.counit.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8) (CategoryTheory.sheafToPresheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafificationAdjunction.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8)) P)
 Case conversion may be inaccurate. Consider using '#align category_theory.is_iso_sheafification_adjunction_counit CategoryTheory.isIso_sheafificationAdjunction_counitₓ'. -/
 instance isIso_sheafificationAdjunction_counit (P : Sheaf J D) :
     IsIso ((sheafificationAdjunction J D).counit.app P) :=
@@ -1038,7 +1038,7 @@ instance isIso_sheafificationAdjunction_counit (P : Sheaf J D) :
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)], CategoryTheory.IsIso.{max (max u3 u1 u2 u3) u2 u3, max (max u2 u3) u3 u1 u2 u3} (CategoryTheory.Functor.{max u2 u3, max u2 u3, max u3 u1 u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2)) (CategoryTheory.Functor.category.{max u2 u3, max u2 u3, max u3 u1 u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2)) (CategoryTheory.Functor.comp.{max u2 u3, max u2 u3, max u2 u3, max u3 u1 u2 u3, max u2 (max u2 u3) u3 u1, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafToPresheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (CategoryTheory.sheafificationAdjunction._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S)) (CategoryTheory.sheafificationAdjunction._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_6 X)) (fun (X : C) => _inst_7 X) _inst_8)) (CategoryTheory.Functor.id.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2)) (CategoryTheory.Adjunction.counit.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u3 u1 u2 u3} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (CategoryTheory.sheafificationAdjunction._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S)) (CategoryTheory.sheafificationAdjunction._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_6 X)) (fun (X : C) => _inst_7 X) _inst_8) (CategoryTheory.sheafToPresheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafificationAdjunction.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8))
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)], CategoryTheory.IsIso.{max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2)) (CategoryTheory.Functor.category.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2)) (CategoryTheory.Functor.comp.{max u3 u2, max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafToPresheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8)) (CategoryTheory.Functor.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2)) (CategoryTheory.Adjunction.counit.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8) (CategoryTheory.sheafToPresheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafificationAdjunction.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)], CategoryTheory.IsIso.{max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2)) (CategoryTheory.Functor.category.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2)) (CategoryTheory.Functor.comp.{max u3 u2, max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafToPresheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8)) (CategoryTheory.Functor.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2)) (CategoryTheory.Adjunction.counit.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8) (CategoryTheory.sheafToPresheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafificationAdjunction.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8))
 Case conversion may be inaccurate. Consider using '#align category_theory.sheafification_reflective CategoryTheory.sheafification_reflectiveₓ'. -/
 instance sheafification_reflective : IsIso (sheafificationAdjunction J D).counit :=
   NatIso.isIso_of_isIso_app _

4f4a1c87

bump to nightly-2023-04-16-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b

63127953

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 
 ! This file was ported from Lean 3 source module category_theory.sites.sheafification
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 4f4a1c875d0baa92ab5d92f3fb1bb258ad9f3e5b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.CategoryTheory.ConcreteCategory.Elementwise
 
 # Sheafification
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We construct the sheafification of a presheaf over a site `C` with values in `D` whenever
 `D` is a concrete category for which the forgetful functor preserves the appropriate (co)limits
 and reflects isomorphisms.

70fd9563

bump to nightly-2023-04-13-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/347636a7a80595d55bedf6e6fbd996a3c39da69a

7a1b67c7

Diff

@@ -42,12 +42,14 @@ variable [ConcreteCategory.{max v u} D]
 
 attribute [local instance] concrete_category.has_coe_to_sort concrete_category.has_coe_to_fun
 
+#print CategoryTheory.Meq /-
 /-- A concrete version of the multiequalizer, to be used below. -/
 @[nolint has_nonempty_instance]
 def Meq {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) :=
   { x : ∀ I : S.arrow, P.obj (op I.y) //
     ∀ I : S.Relation, P.map I.g₁.op (x I.fst) = P.map I.g₂.op (x I.snd) }
 #align category_theory.meq CategoryTheory.Meq
+-/
 
 end
 
@@ -61,17 +63,35 @@ instance {X} (P : Cᵒᵖ ⥤ D) (S : J.cover X) :
     CoeFun (Meq P S) fun x => ∀ I : S.arrow, P.obj (op I.y) :=
   ⟨fun x => x.1⟩
 
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 @[ext]
 theorem ext {X} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x y : Meq P S) (h : ∀ I : S.arrow, x I = y I) :
     x = y :=
   Subtype.ext <| funext <| h
 #align category_theory.meq.ext CategoryTheory.Meq.ext
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.meq.condition CategoryTheory.Meq.conditionₓ'. -/
 theorem condition {X} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (I : S.Relation) :
     P.map I.g₁.op (x ((S.index P).fstTo I)) = P.map I.g₂.op (x ((S.index P).sndTo I)) :=
   x.2 _
 #align category_theory.meq.condition CategoryTheory.Meq.condition
 
+/- warning: category_theory.meq.refine -> CategoryTheory.Meq.refine is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.meq.refine CategoryTheory.Meq.refineₓ'. -/
 /-- Refine a term of `meq P T` with respect to a refinement `S ⟶ T` of covers. -/
 def refine {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P T) (e : S ⟶ T) : Meq P S :=
   ⟨fun I => x ⟨I.y, I.f, (leOfHom e) _ I.hf⟩, fun I =>
@@ -79,12 +99,24 @@ def refine {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P T) (e : S 
       ⟨I.y₁, I.y₂, I.z, I.g₁, I.g₂, I.f₁, I.f₂, (leOfHom e) _ I.h₁, (leOfHom e) _ I.h₂, I.w⟩⟩
 #align category_theory.meq.refine CategoryTheory.Meq.refine
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.meq.refine_apply CategoryTheory.Meq.refine_applyₓ'. -/
 @[simp]
 theorem refine_apply {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P T) (e : S ⟶ T)
     (I : S.arrow) : x.refine e I = x ⟨I.y, I.f, (leOfHom e) _ I.hf⟩ :=
   rfl
 #align category_theory.meq.refine_apply CategoryTheory.Meq.refine_apply
 
+/- warning: category_theory.meq.pullback -> CategoryTheory.Meq.pullback is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] {Y : C} {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X}, (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) -> (forall (f : Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Y X), CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 Y P (CategoryTheory.Functor.obj.{max u3 u2, max u3 u2, max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J Y)) (CategoryTheory.GrothendieckTopology.pullback.{u2, u3} C _inst_1 X Y J f) S))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.meq.pullback CategoryTheory.Meq.pullbackₓ'. -/
 /-- Pull back a term of `meq P S` with respect to a morphism `f : Y ⟶ X` in `C`. -/
 def pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y ⟶ X) :
     Meq P ((J.pullback f).obj S) :=
@@ -93,18 +125,36 @@ def pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y
       ⟨I.y₁, I.y₂, I.z, I.g₁, I.g₂, I.f₁ ≫ f, I.f₂ ≫ f, I.h₁, I.h₂, by simp [reassoc_of I.w]⟩⟩
 #align category_theory.meq.pullback CategoryTheory.Meq.pullback
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.meq.pullback_apply CategoryTheory.Meq.pullback_applyₓ'. -/
 @[simp]
 theorem pullback_apply {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y ⟶ X)
     (I : ((J.pullback f).obj S).arrow) : x.pullback f I = x ⟨_, I.f ≫ f, I.hf⟩ :=
   rfl
 #align category_theory.meq.pullback_apply CategoryTheory.Meq.pullback_apply
 
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D _inst_2 _inst_3 X P S T x h) f)
+Case conversion may be inaccurate. Consider using '#align category_theory.meq.pullback_refine CategoryTheory.Meq.pullback_refineₓ'. -/
 @[simp]
 theorem pullback_refine {Y X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (h : S ⟶ T) (f : Y ⟶ X)
     (x : Meq P T) : (x.pullback f).refine ((J.pullback f).map h) = (refine x h).pullback _ :=
   rfl
 #align category_theory.meq.pullback_refine CategoryTheory.Meq.pullback_refine
 
+/- warning: category_theory.meq.mk -> CategoryTheory.Meq.mk is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P (Opposite.op.{succ u3} C X))) -> (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.meq.mk CategoryTheory.Meq.mkₓ'. -/
 /-- Make a term of `meq P S`. -/
 def mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) : Meq P S :=
   ⟨fun I => P.map I.f.op x, fun I => by
@@ -112,6 +162,12 @@ def mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) : Meq P S
     simp only [← comp_apply, ← P.map_comp, ← op_comp, I.w]⟩
 #align category_theory.meq.mk CategoryTheory.Meq.mk
 
+/- warning: category_theory.meq.mk_apply -> CategoryTheory.Meq.mk_apply is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.meq.mk_apply CategoryTheory.Meq.mk_applyₓ'. -/
 theorem mk_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) (I : S.arrow) :
     mk S x I = P.map I.f.op x :=
   rfl
@@ -119,12 +175,20 @@ theorem mk_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X))
 
 variable [PreservesLimits (forget D)]
 
+#print CategoryTheory.Meq.equiv /-
 /-- The equivalence between the type associated to `multiequalizer (S.index P)` and `meq P S`. -/
 noncomputable def equiv {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) [HasMultiequalizer (S.index P)] :
     (multiequalizer (S.index P) : D) ≃ Meq P S :=
   Limits.Concrete.multiequalizerEquiv _
 #align category_theory.meq.equiv CategoryTheory.Meq.equiv
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.meq.equiv_apply CategoryTheory.Meq.equiv_applyₓ'. -/
 @[simp]
 theorem equiv_apply {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} [HasMultiequalizer (S.index P)]
     (x : multiequalizer (S.index P)) (I : S.arrow) :
@@ -132,6 +196,7 @@ theorem equiv_apply {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} [HasMultiequaliz
   rfl
 #align category_theory.meq.equiv_apply CategoryTheory.Meq.equiv_apply
 
+#print CategoryTheory.Meq.equiv_symm_eq_apply /-
 @[simp]
 theorem equiv_symm_eq_apply {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} [HasMultiequalizer (S.index P)]
     (x : Meq P S) (I : S.arrow) : Multiequalizer.ι (S.index P) I ((Meq.equiv P S).symm x) = x I :=
@@ -140,6 +205,7 @@ theorem equiv_symm_eq_apply {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} [HasMult
   rw [← equiv_apply]
   simp
 #align category_theory.meq.equiv_symm_eq_apply CategoryTheory.Meq.equiv_symm_eq_apply
+-/
 
 end Meq
 
@@ -159,11 +225,23 @@ variable [∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : J.cover X), HasMultiequalizer (S.
 
 noncomputable section
 
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 /-- Make a term of `(J.plus_obj P).obj (op X)` from `x : meq P S`. -/
 def mk {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) : (J.plusObj P).obj (op X) :=
   colimit.ι (J.diagram P X) (op S) ((Meq.equiv P S).symm x)
 #align category_theory.grothendieck_topology.plus.mk CategoryTheory.GrothendieckTopology.Plus.mk
 
+/- warning: category_theory.grothendieck_topology.plus.res_mk_eq_mk_pullback -> CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback is a dubious translation:
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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {Y : C} {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (f : Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Y X), Eq.{max (succ u3) (succ u2)} 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u3} C _inst_1 J Y) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J Y)))) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J Y) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J Y)) (CategoryTheory.GrothendieckTopology.pullback.{u2, u3} C _inst_1 X Y J f)) S) (CategoryTheory.Meq.pullback.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 Y X P S x f))
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.res_mk_eq_mk_pullback CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullbackₓ'. -/
 theorem res_mk_eq_mk_pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x : Meq P S) (f : Y ⟶ X) :
     (J.plusObj P).map f.op (mk x) = mk (x.pullback f) :=
   by
@@ -179,6 +257,12 @@ theorem res_mk_eq_mk_pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} (x :
   cases i; rfl
 #align category_theory.grothendieck_topology.plus.res_mk_eq_mk_pullback CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback
 
+/- warning: category_theory.grothendieck_topology.plus.to_plus_mk -> CategoryTheory.GrothendieckTopology.Plus.toPlus_mk is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} 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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ 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J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (CategoryTheory.GrothendieckTopology.toPlus.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X)) x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S x))
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.to_plus_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_mkₓ'. -/
 theorem toPlus_mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X)) :
     (J.toPlus P).app _ x = mk (Meq.mk S x) :=
   by
@@ -195,6 +279,12 @@ theorem toPlus_mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : P.obj (op X))
     meq.equiv_symm_eq_apply]
 #align category_theory.grothendieck_topology.plus.to_plus_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_mk
 
+/- warning: category_theory.grothendieck_topology.plus.to_plus_apply -> CategoryTheory.GrothendieckTopology.Plus.toPlus_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.to_plus_apply CategoryTheory.GrothendieckTopology.Plus.toPlus_applyₓ'. -/
 theorem toPlus_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : Meq P S) (I : S.arrow) :
     (J.toPlus P).app _ (x I) = (J.plusObj P).map I.f.op (mk x) :=
   by
@@ -220,6 +310,12 @@ theorem toPlus_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.cover X) (x : Meq P S) (
   simpa [RR]
 #align category_theory.grothendieck_topology.plus.to_plus_apply CategoryTheory.GrothendieckTopology.Plus.toPlus_apply
 
+/- warning: category_theory.grothendieck_topology.plus.to_plus_eq_mk -> CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mk is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} 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(CategoryTheory.GrothendieckTopology.Cover.orderTop.{u2, u3} C _inst_1 X J))) (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toHasTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.orderTop.{u2, u3} C _inst_1 X J))) x))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X))), Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ 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(CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) (Prefunctor.map.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} 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J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (CategoryTheory.GrothendieckTopology.toPlus.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X)) x) (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.instOrderTopCoverToLEInstPreorderCover.{u2, u3} C _inst_1 X J))) (CategoryTheory.Meq.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P (Top.top.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (OrderTop.toTop.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.toLE.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)) (CategoryTheory.GrothendieckTopology.Cover.instOrderTopCoverToLEInstPreorderCover.{u2, u3} C _inst_1 X J))) x))
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.to_plus_eq_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mkₓ'. -/
 theorem toPlus_eq_mk {X : C} {P : Cᵒᵖ ⥤ D} (x : P.obj (op X)) :
     (J.toPlus P).app _ x = mk (Meq.mk ⊤ x) :=
   by
@@ -234,6 +330,12 @@ theorem toPlus_eq_mk {X : C} {P : Cᵒᵖ ⥤ D} (x : P.obj (op X)) :
 
 variable [∀ X : C, PreservesColimitsOfShape (J.cover X)ᵒᵖ (forget D)]
 
+/- warning: category_theory.grothendieck_topology.plus.exists_rep -> CategoryTheory.GrothendieckTopology.Plus.exists_rep is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X))), Exists.{max 1 (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (fun (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => Exists.{max 1 (max (succ u3) (succ u2)) (succ (max u2 u3))} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (fun (y : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) => Eq.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (Opposite.op.{succ u3} C X))) x (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S y)))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (x : Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))), Exists.{max (succ u3) (succ u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (fun (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => Exists.{max (succ u3) (succ u2)} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (fun (y : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) => Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} (CategoryTheory.Category.toCategoryStruct.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} CategoryTheory.types.{max u3 u2})) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, u1, succ (max u3 u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.ConcreteCategory.Forget.{max u3 u2, max u3 u2, u1} D _inst_2 _inst_3)) (Prefunctor.obj.{succ u2, max (succ u3) (succ u2), u3, u1} (Opposite.{succ u3} C) (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.toCategoryStruct.{u2, u3} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1))) D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X))) (Opposite.op.{succ u3} C X))) x (CategoryTheory.GrothendieckTopology.Plus.mk.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (X : C) => _inst_5 X) (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) X P S y)))
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.exists_rep CategoryTheory.GrothendieckTopology.Plus.exists_repₓ'. -/
 theorem exists_rep {X : C} {P : Cᵒᵖ ⥤ D} (x : (J.plusObj P).obj (op X)) :
     ∃ (S : J.cover X)(y : Meq P S), x = mk y :=
   by
@@ -244,6 +346,12 @@ theorem exists_rep {X : C} {P : Cᵒᵖ ⥤ D} (x : (J.plusObj P).obj (op X)) :
   simp
 #align category_theory.grothendieck_topology.plus.exists_rep CategoryTheory.GrothendieckTopology.Plus.exists_rep
 
+/- warning: category_theory.grothendieck_topology.plus.eq_mk_iff_exists -> CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_exists is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} {T : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (y : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P T), Iff (Eq.{succ (max u2 u3)} (coeSort.{succ u1, succ (succ (max u2 u3))} D Type.{max u2 u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3) (CategoryTheory.Functor.obj.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 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(Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)))) W T) (fun (h2 : Quiver.Hom.{succ (max u3 u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X)))) W T) => Eq.{max 1 (max (succ u3) (succ u2)) (succ (max u2 u3))} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W S x h1) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W T y h2)))))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {X : C} {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} {T : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X} (x : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P S) (y : CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P T), Iff (Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max u3 u2} 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X)))) W T) (fun (h2 : Quiver.Hom.{max (succ u3) (succ u2), max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X)))) W T) => Eq.{max (succ u3) (succ u2)} (CategoryTheory.Meq.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W S x h1) (CategoryTheory.Meq.refine.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 X P W T y h2)))))
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.eq_mk_iff_exists CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_existsₓ'. -/
 theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq P S) (y : Meq P T) :
     mk x = mk y ↔ ∃ (W : J.cover X)(h1 : W ⟶ S)(h2 : W ⟶ T), x.refine h1 = y.refine h2 :=
   by
@@ -271,6 +379,12 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.cover X} (x : Meq
       cases i; rfl
 #align category_theory.grothendieck_topology.plus.eq_mk_iff_exists CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_exists
 
+/- warning: category_theory.grothendieck_topology.plus.sep -> CategoryTheory.GrothendieckTopology.Plus.sep is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.sep CategoryTheory.GrothendieckTopology.Plus.sepₓ'. -/
 /-- `P⁺` is always separated. -/
 theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj (op X))
     (h : ∀ I : S.arrow, (J.plusObj P).map I.f.op x = (J.plusObj P).map I.f.op y) : x = y :=
@@ -327,6 +441,12 @@ theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) (x y : (J.plusObj P).obj
     simpa using this
 #align category_theory.grothendieck_topology.plus.sep CategoryTheory.GrothendieckTopology.Plus.sep
 
+/- warning: category_theory.grothendieck_topology.plus.inj_of_sep -> CategoryTheory.GrothendieckTopology.Plus.inj_of_sep is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.inj_of_sep CategoryTheory.GrothendieckTopology.Plus.inj_of_sepₓ'. -/
 theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
     (hsep :
       ∀ (X : C) (S : J.cover X) (x y : P.obj (op X)),
@@ -343,6 +463,12 @@ theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
   exact hh
 #align category_theory.grothendieck_topology.plus.inj_of_sep CategoryTheory.GrothendieckTopology.Plus.inj_of_sep
 
+/- warning: category_theory.grothendieck_topology.plus.meq_of_sep -> CategoryTheory.GrothendieckTopology.Plus.meqOfSep is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} 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+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.meq_of_sep CategoryTheory.GrothendieckTopology.Plus.meqOfSepₓ'. -/
 /-- An auxiliary definition to be used in the proof of `exists_of_sep` below.
   Given a compatible family of local sections for `P⁺`, and representatives of said sections,
   construct a compatible family of local sections of `P` over the combination of the covers
@@ -374,6 +500,12 @@ def meqOfSep (P : Cᵒᵖ ⥤ D)
     exact s.condition IR
 #align category_theory.grothendieck_topology.plus.meq_of_sep CategoryTheory.GrothendieckTopology.Plus.meqOfSep
 
+/- warning: category_theory.grothendieck_topology.plus.exists_of_sep -> CategoryTheory.GrothendieckTopology.Plus.exists_of_sep is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} 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+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.exists_of_sep CategoryTheory.GrothendieckTopology.Plus.exists_of_sepₓ'. -/
 theorem exists_of_sep (P : Cᵒᵖ ⥤ D)
     (hsep :
       ∀ (X : C) (S : J.cover X) (x y : P.obj (op X)),
@@ -435,6 +567,12 @@ theorem exists_of_sep (P : Cᵒᵖ ⥤ D)
 
 variable [ReflectsIsomorphisms (forget D)]
 
+/- warning: category_theory.grothendieck_topology.plus.is_sheaf_of_sep -> CategoryTheory.GrothendieckTopology.Plus.isSheaf_of_sep is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) 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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} 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(CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 P) (Opposite.op.{succ u3} C X) (Opposite.op.{succ u3} C (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I)) (Quiver.Hom.op.{u3, succ u2} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.GrothendieckTopology.Cover.Arrow.Y.{u2, u3} C _inst_1 X J S I) X (CategoryTheory.GrothendieckTopology.Cover.Arrow.f.{u2, u3} C _inst_1 X J S I))) y)) -> (Eq.{max (succ u3) (succ u2)} (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), u1, succ (max u3 u2)} D (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, u1} D (CategoryTheory.Category.toCategoryStruct.{max u3 u2, u1} D _inst_2)) Type.{max u3 u2} (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, succ (max u3 u2)} Type.{max 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(CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)))
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.is_sheaf_of_sep CategoryTheory.GrothendieckTopology.Plus.isSheaf_of_sepₓ'. -/
 /-- If `P` is separated, then `P⁺` is a sheaf. -/
 theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)
     (hsep :
@@ -470,6 +608,12 @@ theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)
 
 variable (J)
 
+/- warning: category_theory.grothendieck_topology.plus.is_sheaf_plus_plus -> CategoryTheory.GrothendieckTopology.Plus.isSheaf_plus_plus is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (fun (X : C) => _inst_5 X))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_6 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) (CategoryTheory.GrothendieckTopology.plusObj.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_6 P X S) P (fun (X : C) => _inst_5 X)) (fun (X : C) => _inst_5 X))
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.plus.is_sheaf_plus_plus CategoryTheory.GrothendieckTopology.Plus.isSheaf_plus_plusₓ'. -/
 /-- `P⁺⁺` is always a sheaf. -/
 theorem isSheaf_plus_plus (P : Cᵒᵖ ⥤ D) : Presheaf.IsSheaf J (J.plusObj (J.plusObj P)) :=
   by
@@ -485,22 +629,46 @@ variable (J)
 variable [∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : J.cover X), HasMultiequalizer (S.index P)]
   [∀ X : C, HasColimitsOfShape (J.cover X)ᵒᵖ D]
 
+/- warning: category_theory.grothendieck_topology.sheafify -> CategoryTheory.GrothendieckTopology.sheafify is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2], (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) -> (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2], (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) -> (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify CategoryTheory.GrothendieckTopology.sheafifyₓ'. -/
 /-- The sheafification of a presheaf `P`.
 *NOTE:* Additional hypotheses are needed to obtain a proof that this is a sheaf! -/
 def sheafify (P : Cᵒᵖ ⥤ D) : Cᵒᵖ ⥤ D :=
   J.plusObj (J.plusObj P)
 #align category_theory.grothendieck_topology.sheafify CategoryTheory.GrothendieckTopology.sheafify
 
+/- warning: category_theory.grothendieck_topology.to_sheafify -> CategoryTheory.GrothendieckTopology.toSheafify is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_3) (CategoryTheory.GrothendieckTopology.toSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_4) P)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.to_sheafify CategoryTheory.GrothendieckTopology.toSheafifyₓ'. -/
 /-- The canonical map from `P` to its sheafification. -/
 def toSheafify (P : Cᵒᵖ ⥤ D) : P ⟶ J.sheafify P :=
   J.toPlus P ≫ J.plusMap (J.toPlus P)
 #align category_theory.grothendieck_topology.to_sheafify CategoryTheory.GrothendieckTopology.toSheafify
 
+/- warning: category_theory.grothendieck_topology.sheafify_map -> CategoryTheory.GrothendieckTopology.sheafifyMap is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) -> (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_3) (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_4) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_3.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_3) (CategoryTheory.GrothendieckTopology.sheafifyMap._proof_4.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_4) Q))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_map CategoryTheory.GrothendieckTopology.sheafifyMapₓ'. -/
 /-- The canonical map on sheafifications induced by a morphism. -/
 def sheafifyMap {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) : J.sheafify P ⟶ J.sheafify Q :=
   J.plusMap <| J.plusMap η
 #align category_theory.grothendieck_topology.sheafify_map CategoryTheory.GrothendieckTopology.sheafifyMap
 
+/- warning: category_theory.grothendieck_topology.sheafify_map_id -> CategoryTheory.GrothendieckTopology.sheafifyMap_id is a dubious translation:
+lean 3 declaration is
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CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)) (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P P (CategoryTheory.CategoryStruct.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P)) (CategoryTheory.CategoryStruct.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P))
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_map_id CategoryTheory.GrothendieckTopology.sheafifyMap_idₓ'. -/
 @[simp]
 theorem sheafifyMap_id (P : Cᵒᵖ ⥤ D) : J.sheafifyMap (𝟙 P) = 𝟙 (J.sheafify P) :=
   by
@@ -508,6 +676,12 @@ theorem sheafifyMap_id (P : Cᵒᵖ ⥤ D) : J.sheafifyMap (𝟙 P) = 𝟙 (J.sh
   simp
 #align category_theory.grothendieck_topology.sheafify_map_id CategoryTheory.GrothendieckTopology.sheafifyMap_id
 
+/- warning: category_theory.grothendieck_topology.sheafify_map_comp -> CategoryTheory.GrothendieckTopology.sheafifyMap_comp is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} 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+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_map_comp CategoryTheory.GrothendieckTopology.sheafifyMap_compₓ'. -/
 @[simp]
 theorem sheafifyMap_comp {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q ⟶ R) :
     J.sheafifyMap (η ≫ γ) = J.sheafifyMap η ≫ J.sheafifyMap γ :=
@@ -516,6 +690,12 @@ theorem sheafifyMap_comp {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q ⟶ R) :
   simp
 #align category_theory.grothendieck_topology.sheafify_map_comp CategoryTheory.GrothendieckTopology.sheafifyMap_comp
 
+/- warning: category_theory.grothendieck_topology.to_sheafify_naturality -> CategoryTheory.GrothendieckTopology.toSheafify_naturality is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) 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u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.toSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) P) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.toSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) Q) (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafifyMap.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) 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+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.to_sheafify_naturality CategoryTheory.GrothendieckTopology.toSheafify_naturalityₓ'. -/
 @[simp, reassoc.1]
 theorem toSheafify_naturality {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) :
     η ≫ J.toSheafify _ = J.toSheafify _ ≫ J.sheafifyMap η :=
@@ -526,29 +706,59 @@ theorem toSheafify_naturality {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) :
 
 variable (D)
 
+/- warning: category_theory.grothendieck_topology.sheafification -> CategoryTheory.GrothendieckTopology.sheafification is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafification CategoryTheory.GrothendieckTopology.sheafificationₓ'. -/
 /-- The sheafification of a presheaf `P`, as a functor.
 *NOTE:* Additional hypotheses are needed to obtain a proof that this is a sheaf! -/
 def sheafification : (Cᵒᵖ ⥤ D) ⥤ Cᵒᵖ ⥤ D :=
   J.plusFunctor D ⋙ J.plusFunctor D
 #align category_theory.grothendieck_topology.sheafification CategoryTheory.GrothendieckTopology.sheafification
 
+/- warning: category_theory.grothendieck_topology.sheafification_obj -> CategoryTheory.GrothendieckTopology.sheafification_obj is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafification_obj CategoryTheory.GrothendieckTopology.sheafification_objₓ'. -/
 @[simp]
 theorem sheafification_obj (P : Cᵒᵖ ⥤ D) : (J.sheafification D).obj P = J.sheafify P :=
   rfl
 #align category_theory.grothendieck_topology.sheafification_obj CategoryTheory.GrothendieckTopology.sheafification_obj
 
+/- warning: category_theory.grothendieck_topology.sheafification_map -> CategoryTheory.GrothendieckTopology.sheafification_map is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafification_map CategoryTheory.GrothendieckTopology.sheafification_mapₓ'. -/
 @[simp]
 theorem sheafification_map {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) :
     (J.sheafification D).map η = J.sheafifyMap η :=
   rfl
 #align category_theory.grothendieck_topology.sheafification_map CategoryTheory.GrothendieckTopology.sheafification_map
 
+/- warning: category_theory.grothendieck_topology.to_sheafification -> CategoryTheory.GrothendieckTopology.toSheafification is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.to_sheafification CategoryTheory.GrothendieckTopology.toSheafificationₓ'. -/
 /-- The canonical map from `P` to its sheafification, as a natural transformation.
 *Note:* We only show this is a sheaf under additional hypotheses on `D`. -/
 def toSheafification : 𝟭 _ ⟶ sheafification J D :=
   J.toPlusNatTrans D ≫ whiskerRight (J.toPlusNatTrans D) (J.plusFunctor D)
 #align category_theory.grothendieck_topology.to_sheafification CategoryTheory.GrothendieckTopology.toSheafification
 
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+but is expected to have type
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(CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (Prefunctor.obj.{succ (max u3 u2), succ (max u3 u2), max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C 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J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P)
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.to_sheafification_app CategoryTheory.GrothendieckTopology.toSheafification_appₓ'. -/
 @[simp]
 theorem toSheafification_app (P : Cᵒᵖ ⥤ D) : (J.toSheafification D).app P = J.toSheafify P :=
   rfl
@@ -556,6 +766,12 @@ theorem toSheafification_app (P : Cᵒᵖ ⥤ D) : (J.toSheafification D).app P
 
 variable {D}
 
+/- warning: category_theory.grothendieck_topology.is_iso_to_sheafify -> CategoryTheory.GrothendieckTopology.isIso_toSheafify is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J P) -> (CategoryTheory.IsIso.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.toSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) P) (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J P) -> (CategoryTheory.IsIso.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P))
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.is_iso_to_sheafify CategoryTheory.GrothendieckTopology.isIso_toSheafifyₓ'. -/
 theorem isIso_toSheafify {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) : IsIso (J.toSheafify P) :=
   by
   dsimp [to_sheafify]
@@ -564,24 +780,48 @@ theorem isIso_toSheafify {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) : IsIso
   exact @is_iso.comp_is_iso _ _ _ _ _ (J.to_plus P) ((J.plus_functor D).map (J.to_plus P)) _ _
 #align category_theory.grothendieck_topology.is_iso_to_sheafify CategoryTheory.GrothendieckTopology.isIso_toSheafify
 
+/- warning: category_theory.grothendieck_topology.iso_sheafify -> CategoryTheory.GrothendieckTopology.isoSheafify is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J P) -> (CategoryTheory.Iso.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.isoSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_3) (CategoryTheory.GrothendieckTopology.isoSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_4) P))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J P) -> (CategoryTheory.Iso.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P))
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.iso_sheafify CategoryTheory.GrothendieckTopology.isoSheafifyₓ'. -/
 /-- If `P` is a sheaf, then `P` is isomorphic to `J.sheafify P`. -/
 def isoSheafify {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) : P ≅ J.sheafify P :=
   letI := is_iso_to_sheafify J hP
   as_iso (J.to_sheafify P)
 #align category_theory.grothendieck_topology.iso_sheafify CategoryTheory.GrothendieckTopology.isoSheafify
 
+/- warning: category_theory.grothendieck_topology.iso_sheafify_hom -> CategoryTheory.GrothendieckTopology.isoSheafify_hom is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.iso_sheafify_hom CategoryTheory.GrothendieckTopology.isoSheafify_homₓ'. -/
 @[simp]
 theorem isoSheafify_hom {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) :
     (J.isoSheafify hP).Hom = J.toSheafify P :=
   rfl
 #align category_theory.grothendieck_topology.iso_sheafify_hom CategoryTheory.GrothendieckTopology.isoSheafify_hom
 
+/- warning: category_theory.grothendieck_topology.sheafify_lift -> CategoryTheory.GrothendieckTopology.sheafifyLift is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) -> (CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J Q) -> (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.sheafifyLift._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_3) (CategoryTheory.GrothendieckTopology.sheafifyLift._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_4) P) Q)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2}, (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) -> (CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J Q) -> (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q)
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_lift CategoryTheory.GrothendieckTopology.sheafifyLiftₓ'. -/
 /-- Given a sheaf `Q` and a morphism `P ⟶ Q`, construct a morphism from
 `J.sheafifcation P` to `Q`. -/
 def sheafifyLift {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.IsSheaf J Q) : J.sheafify P ⟶ Q :=
   J.plusLift (J.plusLift η hQ) hQ
 #align category_theory.grothendieck_topology.sheafify_lift CategoryTheory.GrothendieckTopology.sheafifyLift
 
+/- warning: category_theory.grothendieck_topology.to_sheafify_sheafify_lift -> CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLift is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (hQ : CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J Q), Eq.{succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (CategoryTheory.CategoryStruct.comp.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (CategoryTheory.GrothendieckTopology.toSheafify._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S)) (CategoryTheory.GrothendieckTopology.toSheafify._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_4 X)) P) Q (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η hQ)) η
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (hQ : CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J Q), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) P Q) (CategoryTheory.CategoryStruct.comp.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η hQ)) η
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.to_sheafify_sheafify_lift CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLiftₓ'. -/
 @[simp, reassoc.1]
 theorem toSheafify_sheafifyLift {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.IsSheaf J Q) :
     J.toSheafify P ≫ sheafifyLift J η hQ = η :=
@@ -590,6 +830,12 @@ theorem toSheafify_sheafifyLift {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presh
   simp
 #align category_theory.grothendieck_topology.to_sheafify_sheafify_lift CategoryTheory.GrothendieckTopology.toSheafify_sheafifyLift
 
+/- warning: category_theory.grothendieck_topology.sheafify_lift_unique -> CategoryTheory.GrothendieckTopology.sheafifyLift_unique is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) 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(Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q), (Eq.{succ (max u2 u3)} (Quiver.Hom.{succ (max u2 u3), max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, 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(max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q) γ (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P Q η hQ))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} {Q : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (η : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) 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(CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q), (Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) 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_inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) Q (CategoryTheory.GrothendieckTopology.toSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) γ) η) -> (Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 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X) P Q η hQ))
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_lift_unique CategoryTheory.GrothendieckTopology.sheafifyLift_uniqueₓ'. -/
 theorem sheafifyLift_unique {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.IsSheaf J Q)
     (γ : J.sheafify P ⟶ Q) : J.toSheafify P ≫ γ = η → γ = sheafifyLift J η hQ :=
   by
@@ -600,6 +846,12 @@ theorem sheafifyLift_unique {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.
   exact h
 #align category_theory.grothendieck_topology.sheafify_lift_unique CategoryTheory.GrothendieckTopology.sheafifyLift_unique
 
+/- warning: category_theory.grothendieck_topology.iso_sheafify_inv -> CategoryTheory.GrothendieckTopology.isoSheafify_inv is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] {P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2} (hP : CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J P), Eq.{max (succ u3) (succ u2)} (Quiver.Hom.{succ (max u3 u2), max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) P) (CategoryTheory.Iso.inv.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) P (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P) (CategoryTheory.GrothendieckTopology.isoSheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P hP)) (CategoryTheory.GrothendieckTopology.sheafifyLift.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_3 P X S) (fun (X : C) => _inst_4 X) P P (CategoryTheory.CategoryStruct.id.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2)) P) hP)
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.iso_sheafify_inv CategoryTheory.GrothendieckTopology.isoSheafify_invₓ'. -/
 @[simp]
 theorem isoSheafify_inv {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) :
     (J.isoSheafify hP).inv = J.sheafifyLift (𝟙 _) hP :=
@@ -608,6 +860,12 @@ theorem isoSheafify_inv {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) :
   simp [iso.comp_inv_eq]
 #align category_theory.grothendieck_topology.iso_sheafify_inv CategoryTheory.GrothendieckTopology.isoSheafify_inv
 
+/- warning: category_theory.grothendieck_topology.sheafify_hom_ext -> CategoryTheory.GrothendieckTopology.sheafify_hom_ext is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} 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+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_hom_ext CategoryTheory.GrothendieckTopology.sheafify_hom_extₓ'. -/
 theorem sheafify_hom_ext {P Q : Cᵒᵖ ⥤ D} (η γ : J.sheafify P ⟶ Q) (hQ : Presheaf.IsSheaf J Q)
     (h : J.toSheafify P ≫ η = J.toSheafify P ≫ γ) : η = γ :=
   by
@@ -617,6 +875,12 @@ theorem sheafify_hom_ext {P Q : Cᵒᵖ ⥤ D} (η γ : J.sheafify P ⟶ Q) (hQ
   exact h
 #align category_theory.grothendieck_topology.sheafify_hom_ext CategoryTheory.GrothendieckTopology.sheafify_hom_ext
 
+/- warning: category_theory.grothendieck_topology.sheafify_map_sheafify_lift -> CategoryTheory.GrothendieckTopology.sheafifyMap_sheafifyLift is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_4 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} 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+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_map_sheafify_lift CategoryTheory.GrothendieckTopology.sheafifyMap_sheafifyLiftₓ'. -/
 @[simp, reassoc.1]
 theorem sheafifyMap_sheafifyLift {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q ⟶ R)
     (hR : Presheaf.IsSheaf J R) :
@@ -635,12 +899,24 @@ variable [ConcreteCategory.{max v u} D] [PreservesLimits (forget D)]
   [∀ X : C, HasColimitsOfShape (J.cover X)ᵒᵖ D]
   [∀ X : C, PreservesColimitsOfShape (J.cover X)ᵒᵖ (forget D)] [ReflectsIsomorphisms (forget D)]
 
+/- warning: category_theory.grothendieck_topology.sheafify_is_sheaf -> CategoryTheory.GrothendieckTopology.sheafify_isSheaf is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), CategoryTheory.Presheaf.IsSheaf.{u2, max u2 u3, u3, u1} C _inst_1 D _inst_2 J (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) P)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2), CategoryTheory.Presheaf.IsSheaf.{u2, max u3 u2, u3, u1} C _inst_1 D _inst_2 J (CategoryTheory.GrothendieckTopology.sheafify.{u1, u2, u3} C _inst_1 J D _inst_2 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) P)
+Case conversion may be inaccurate. Consider using '#align category_theory.grothendieck_topology.sheafify_is_sheaf CategoryTheory.GrothendieckTopology.sheafify_isSheafₓ'. -/
 theorem GrothendieckTopology.sheafify_isSheaf (P : Cᵒᵖ ⥤ D) : Presheaf.IsSheaf J (J.sheafify P) :=
   GrothendieckTopology.Plus.isSheaf_plus_plus _ _
 #align category_theory.grothendieck_topology.sheafify_is_sheaf CategoryTheory.GrothendieckTopology.sheafify_isSheaf
 
 variable (D)
 
+/- warning: category_theory.presheaf_to_Sheaf -> CategoryTheory.presheafToSheaf is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)], CategoryTheory.Functor.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u3 u1 u2 u3} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)], CategoryTheory.Functor.{max u3 u2, max u3 u2, max (max (max u1 u3) u3 u2) u2, max (max (max u1 u3) u3 u2) u2} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2)
+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf_to_Sheaf CategoryTheory.presheafToSheafₓ'. -/
 /-- The sheafification functor, as a functor taking values in `Sheaf`. -/
 @[simps]
 def presheafToSheaf : (Cᵒᵖ ⥤ D) ⥤ Sheaf J D
@@ -651,6 +927,12 @@ def presheafToSheaf : (Cᵒᵖ ⥤ D) ⥤ Sheaf J D
   map_comp' P Q R f g := Sheaf.Hom.ext _ _ <| J.sheafifyMap_comp _ _
 #align category_theory.presheaf_to_Sheaf CategoryTheory.presheafToSheaf
 
+/- warning: category_theory.presheaf_to_Sheaf_preserves_zero_morphisms -> CategoryTheory.presheafToSheaf_preservesZeroMorphisms is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_9 : CategoryTheory.Preadditive.{max u2 u3, u1} D _inst_2], CategoryTheory.Functor.PreservesZeroMorphisms.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u3 u1 u2 u3} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Limits.CategoryTheory.Functor.hasZeroMorphisms.{u2, u3, max u2 u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{max u2 u3, u1} D _inst_2 _inst_9)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.preadditive.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2 _inst_9)) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_9 : CategoryTheory.Preadditive.{max u3 u2, u1} D _inst_2], CategoryTheory.Functor.PreservesZeroMorphisms.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Limits.instHasZeroMorphismsFunctorCategory.{u2, u3, max u3 u2, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{max u3 u2, u1} D _inst_2 _inst_9)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.instPreadditiveSheafInstCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 _inst_9)) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8)
+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf_to_Sheaf_preserves_zero_morphisms CategoryTheory.presheafToSheaf_preservesZeroMorphismsₓ'. -/
 instance presheafToSheaf_preservesZeroMorphisms [Preadditive D] :
     (presheafToSheaf J D).PreservesZeroMorphisms
     where map_zero' F G := by
@@ -658,6 +940,12 @@ instance presheafToSheaf_preservesZeroMorphisms [Preadditive D] :
     erw [colimit.ι_map, comp_zero, J.plus_map_zero, J.diagram_nat_trans_zero, zero_comp]
 #align category_theory.presheaf_to_Sheaf_preserves_zero_morphisms CategoryTheory.presheafToSheaf_preservesZeroMorphisms
 
+/- warning: category_theory.sheafification_adjunction -> CategoryTheory.sheafificationAdjunction is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)], CategoryTheory.Adjunction.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u3 u1 u2 u3} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (CategoryTheory.sheafificationAdjunction._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_5) (CategoryTheory.sheafificationAdjunction._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_6) (fun (X : C) => _inst_7 X) _inst_8) (CategoryTheory.sheafToPresheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)], CategoryTheory.Adjunction.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8) (CategoryTheory.sheafToPresheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2)
+Case conversion may be inaccurate. Consider using '#align category_theory.sheafification_adjunction CategoryTheory.sheafificationAdjunctionₓ'. -/
 /-- The sheafification functor is left adjoint to the forgetful functor. -/
 @[simps unit_app counit_app_val]
 def sheafificationAdjunction : presheafToSheaf J D ⊣ sheafToPresheaf J D :=
@@ -676,14 +964,32 @@ def sheafificationAdjunction : presheafToSheaf J D ⊣ sheafToPresheaf J D :=
         rw [category.assoc] }
 #align category_theory.sheafification_adjunction CategoryTheory.sheafificationAdjunction
 
+/- warning: category_theory.Sheaf_to_presheaf_is_right_adjoint -> CategoryTheory.sheafToPresheafIsRightAdjoint is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)], CategoryTheory.IsRightAdjoint.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u3 u1 u2 u3} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafToPresheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)], CategoryTheory.IsRightAdjoint.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafToPresheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2)
+Case conversion may be inaccurate. Consider using '#align category_theory.Sheaf_to_presheaf_is_right_adjoint CategoryTheory.sheafToPresheafIsRightAdjointₓ'. -/
 instance sheafToPresheafIsRightAdjoint : IsRightAdjoint (sheafToPresheaf J D) :=
   ⟨_, sheafificationAdjunction J D⟩
 #align category_theory.Sheaf_to_presheaf_is_right_adjoint CategoryTheory.sheafToPresheafIsRightAdjoint
 
+/- warning: category_theory.presheaf_mono_of_mono -> CategoryTheory.presheaf_mono_of_mono is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] {F : CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2} {G : CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2} (f : Quiver.Hom.{succ (max u2 u3), max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2))) F G) [_inst_9 : CategoryTheory.Mono.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) F G f], CategoryTheory.Mono.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.val.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2 F) (CategoryTheory.Sheaf.val.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2 G) (CategoryTheory.Sheaf.Hom.val.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2 F G f)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {F : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2} {G : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2} (f : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) F G) [_inst_9 : CategoryTheory.Mono.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) F G f], CategoryTheory.Mono.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 F) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 G) (CategoryTheory.Sheaf.Hom.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 F G f)
+Case conversion may be inaccurate. Consider using '#align category_theory.presheaf_mono_of_mono CategoryTheory.presheaf_mono_of_monoₓ'. -/
 instance presheaf_mono_of_mono {F G : Sheaf J D} (f : F ⟶ G) [Mono f] : Mono f.1 :=
   (sheafToPresheaf J D).map_mono _
 #align category_theory.presheaf_mono_of_mono CategoryTheory.presheaf_mono_of_mono
 
+/- warning: category_theory.Sheaf.hom.mono_iff_presheaf_mono -> CategoryTheory.Sheaf.Hom.mono_iff_presheaf_mono is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] {F : CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2} {G : CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2} (f : Quiver.Hom.{succ (max u2 u3), max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2))) F G), Iff (CategoryTheory.Mono.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) F G f) (CategoryTheory.Mono.{max u2 u3, max u2 (max u2 u3) u3 u1} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.val.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2 F) (CategoryTheory.Sheaf.val.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2 G) (CategoryTheory.Sheaf.Hom.val.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2 F G f))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] (J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1) (D : Type.{u1}) [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] {F : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2} {G : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2} (f : Quiver.Hom.{max (succ u3) (succ u2), max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) F G), Iff (CategoryTheory.Mono.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) F G f) (CategoryTheory.Mono.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 F) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 G) (CategoryTheory.Sheaf.Hom.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 F G f))
+Case conversion may be inaccurate. Consider using '#align category_theory.Sheaf.hom.mono_iff_presheaf_mono CategoryTheory.Sheaf.Hom.mono_iff_presheaf_monoₓ'. -/
 theorem Sheaf.Hom.mono_iff_presheaf_mono {F G : Sheaf J D} (f : F ⟶ G) : Mono f ↔ Mono f.1 :=
   ⟨fun m => by
     skip
@@ -694,6 +1000,12 @@ theorem Sheaf.Hom.mono_iff_presheaf_mono {F G : Sheaf J D} (f : F ⟶ G) : Mono
 
 variable {J D}
 
+/- warning: category_theory.sheafification_iso -> CategoryTheory.sheafificationIso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] (P : CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2), CategoryTheory.Iso.{max u2 u3, max u3 u1 u2 u3} (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) P (CategoryTheory.Functor.obj.{max u2 u3, max u2 u3, max u2 (max u2 u3) u3 u1, max u3 u1 u2 u3} (CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.CategoryTheory.category.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (CategoryTheory.sheafificationIso._proof_1.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_5) (CategoryTheory.sheafificationIso._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 _inst_6) (fun (X : C) => _inst_7 X) _inst_8) (CategoryTheory.Sheaf.val.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2 P))
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_8 : CategoryTheory.ReflectsIsomorphisms.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] (P : CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2), CategoryTheory.Iso.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) P (Prefunctor.obj.{max (succ u3) (succ u2), max (succ u3) (succ u2), max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2))) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max u3 u2) u1} (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2))) (CategoryTheory.Functor.toPrefunctor.{max u3 u2, max u3 u2, max (max u3 u2) u1, max (max u3 u2) u1} (CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Functor.category.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (CategoryTheory.Sheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.Sheaf.instCategorySheaf.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.presheafToSheaf.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8)) (CategoryTheory.Sheaf.val.{u2, max u3 u2, u3, u1} C _inst_1 J D _inst_2 P))
+Case conversion may be inaccurate. Consider using '#align category_theory.sheafification_iso CategoryTheory.sheafificationIsoₓ'. -/
 /-- A sheaf `P` is isomorphic to its own sheafification. -/
 @[simps]
 def sheafificationIso (P : Sheaf J D) : P ≅ (presheafToSheaf J D).obj P.val
@@ -708,11 +1020,23 @@ def sheafificationIso (P : Sheaf J D) : P ≅ (presheafToSheaf J D).obj P.val
     apply (J.iso_sheafify P.2).inv_hom_id
 #align category_theory.sheafification_iso CategoryTheory.sheafificationIso
 
+/- warning: category_theory.is_iso_sheafification_adjunction_counit -> CategoryTheory.isIso_sheafificationAdjunction_counit is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) 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CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S)) (CategoryTheory.sheafificationAdjunction._proof_2.{u3, u2, u1} C _inst_1 J D _inst_2 (fun (X : C) => _inst_6 X)) (fun (X : C) => _inst_7 X) _inst_8) (CategoryTheory.sheafToPresheaf.{u2, max u2 u3, u3, u1} C _inst_1 J D _inst_2) (CategoryTheory.sheafificationAdjunction.{u1, u2, u3} C _inst_1 J D _inst_2 _inst_3 _inst_4 (fun (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8)) P)
+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) 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_inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8)) P)
+Case conversion may be inaccurate. Consider using '#align category_theory.is_iso_sheafification_adjunction_counit CategoryTheory.isIso_sheafificationAdjunction_counitₓ'. -/
 instance isIso_sheafificationAdjunction_counit (P : Sheaf J D) :
     IsIso ((sheafificationAdjunction J D).counit.app P) :=
   isIso_of_fully_faithful (sheafToPresheaf J D) _
 #align category_theory.is_iso_sheafification_adjunction_counit CategoryTheory.isIso_sheafificationAdjunction_counit
 
+/- warning: category_theory.sheafification_reflective -> CategoryTheory.sheafification_reflective is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u2 u3, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (CategoryTheory.forget.{u1, max u2 u3, max u2 u3} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u2 u3, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u2 u3, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.Cover.preorder.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u2 u3, max u2 u3, u1, succ (max u2 u3)} D _inst_2 Type.{max u2 u3} CategoryTheory.types.{max u2 u3} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) 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+but is expected to have type
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {J : CategoryTheory.GrothendieckTopology.{u2, u3} C _inst_1} {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{max u2 u3, u1} D] [_inst_3 : CategoryTheory.ConcreteCategory.{max u2 u3, max u3 u2, u1} D _inst_2] [_inst_4 : CategoryTheory.Limits.PreservesLimits.{max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (CategoryTheory.forget.{u1, max u3 u2, max u3 u2} D _inst_2 _inst_3)] [_inst_5 : forall (P : CategoryTheory.Functor.{u2, max u3 u2, u3, u1} (Opposite.{succ u3} C) (CategoryTheory.Category.opposite.{u2, u3} C _inst_1) D _inst_2) (X : C) (S : CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X), CategoryTheory.Limits.HasMultiequalizer.{max u3 u2, u1, max u3 u2} D _inst_2 (CategoryTheory.GrothendieckTopology.Cover.index.{u1, u2, u3} C _inst_1 X J D _inst_2 S P)] [_inst_6 : forall (X : C), CategoryTheory.Limits.HasColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, u1} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (CategoryTheory.GrothendieckTopology.instPreorderCover.{u2, u3} C _inst_1 J X))) D _inst_2] [_inst_7 : forall (X : C), CategoryTheory.Limits.PreservesColimitsOfShape.{max u3 u2, max u3 u2, max u3 u2, max u3 u2, u1, max (succ u3) (succ u2)} D _inst_2 Type.{max u3 u2} CategoryTheory.types.{max u3 u2} (Opposite.{succ (max u3 u2)} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X)) (CategoryTheory.Category.opposite.{max u3 u2, max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) (Preorder.smallCategory.{max u3 u2} (CategoryTheory.GrothendieckTopology.Cover.{u2, u3} C _inst_1 J X) 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X) => _inst_5 P X S) (fun (X : C) => _inst_6 X) (fun (X : C) => _inst_7 X) _inst_8))
+Case conversion may be inaccurate. Consider using '#align category_theory.sheafification_reflective CategoryTheory.sheafification_reflectiveₓ'. -/
 instance sheafification_reflective : IsIso (sheafificationAdjunction J D).counit :=
   NatIso.isIso_of_isIso_app _
 #align category_theory.sheafification_reflective CategoryTheory.sheafification_reflective

70fd9563

bump to nightly-2023-03-23-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82

53b827ba

Diff

@@ -128,13 +128,13 @@ noncomputable def equiv {X : C} (P : Cᵒᵖ ⥤ D) (S : J.cover X) [HasMultiequ
 @[simp]
 theorem equiv_apply {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} [HasMultiequalizer (S.index P)]
     (x : multiequalizer (S.index P)) (I : S.arrow) :
-    equiv P S x I = multiequalizer.ι (S.index P) I x :=
+    equiv P S x I = Multiequalizer.ι (S.index P) I x :=
   rfl
 #align category_theory.meq.equiv_apply CategoryTheory.Meq.equiv_apply
 
 @[simp]
 theorem equiv_symm_eq_apply {X : C} {P : Cᵒᵖ ⥤ D} {S : J.cover X} [HasMultiequalizer (S.index P)]
-    (x : Meq P S) (I : S.arrow) : multiequalizer.ι (S.index P) I ((Meq.equiv P S).symm x) = x I :=
+    (x : Meq P S) (I : S.arrow) : Multiequalizer.ι (S.index P) I ((Meq.equiv P S).symm x) = x I :=
   by
   let z := (meq.equiv P S).symm x
   rw [← equiv_apply]

70fd9563

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

70fd9563

chore: classify porting notes referring to missing linters (#12098)

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

c5b5490c

Diff

@@ -36,7 +36,7 @@ variable [ConcreteCategory.{max v u} D]
 
 attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.instFunLike
 
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 /-- A concrete version of the multiequalizer, to be used below. -/
 def Meq {X : C} (P : Cᵒᵖ ⥤ D) (S : J.Cover X) :=
   { x : ∀ I : S.Arrow, P.obj (op I.Y) //

70fd9563

chore(CategoryTheory): move Full, Faithful, EssSurj, IsEquivalence and ReflectsIsomorphisms to the Functor namespace (#11985)

These notions on functors are now Functor.Full, Functor.Faithful, Functor.EssSurj, Functor.IsEquivalence, Functor.ReflectsIsomorphisms. Deprecated aliases are introduced for the previous names.

65b7affc

Diff

@@ -409,7 +409,7 @@ theorem exists_of_sep (P : Cᵒᵖ ⥤ D)
   exact s.condition IR
 #align category_theory.grothendieck_topology.plus.exists_of_sep CategoryTheory.GrothendieckTopology.Plus.exists_of_sep
 
-variable [ReflectsIsomorphisms (forget D)]
+variable [(forget D).ReflectsIsomorphisms]
 
 /-- If `P` is separated, then `P⁺` is a sheaf. -/
 theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)
@@ -596,7 +596,7 @@ variable (J)
 variable [ConcreteCategory.{max v u} D] [PreservesLimits (forget D)]
   [∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : J.Cover X), HasMultiequalizer (S.index P)]
   [∀ X : C, HasColimitsOfShape (J.Cover X)ᵒᵖ D]
-  [∀ X : C, PreservesColimitsOfShape (J.Cover X)ᵒᵖ (forget D)] [ReflectsIsomorphisms (forget D)]
+  [∀ X : C, PreservesColimitsOfShape (J.Cover X)ᵒᵖ (forget D)] [(forget D).ReflectsIsomorphisms]
 
 theorem GrothendieckTopology.sheafify_isSheaf (P : Cᵒᵖ ⥤ D) : Presheaf.IsSheaf J (J.sheafify P) :=
   GrothendieckTopology.Plus.isSheaf_plus_plus _ _

70fd9563

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -28,7 +28,6 @@ open CategoryTheory.Limits Opposite
 universe w v u
 
 variable {C : Type u} [Category.{v} C] {J : GrothendieckTopology C}
-
 variable {D : Type w} [Category.{max v u} D]
 
 section
@@ -146,9 +145,7 @@ variable [ConcreteCategory.{max v u} D]
 attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.instFunLike
 
 variable [PreservesLimits (forget D)]
-
 variable [∀ X : C, HasColimitsOfShape (J.Cover X)ᵒᵖ D]
-
 variable [∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : J.Cover X), HasMultiequalizer (S.index P)]
 
 noncomputable section
@@ -457,7 +454,6 @@ end
 end Plus
 
 variable (J)
-
 variable [∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : J.Cover X), HasMultiequalizer (S.index P)]
   [∀ X : C, HasColimitsOfShape (J.Cover X)ᵒᵖ D]
 
@@ -597,7 +593,6 @@ theorem sheafifyMap_sheafifyLift {P Q R : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (γ : Q
 end GrothendieckTopology
 
 variable (J)
-
 variable [ConcreteCategory.{max v u} D] [PreservesLimits (forget D)]
   [∀ (P : Cᵒᵖ ⥤ D) (X : C) (S : J.Cover X), HasMultiequalizer (S.index P)]
   [∀ X : C, HasColimitsOfShape (J.Cover X)ᵒᵖ D]

70fd9563

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -659,7 +659,7 @@ theorem Sheaf.Hom.mono_iff_presheaf_mono {F G : Sheaf J D} (f : F ⟶ G) : Mono
 set_option linter.uppercaseLean3 false in
 #align category_theory.Sheaf.hom.mono_iff_presheaf_mono CategoryTheory.Sheaf.Hom.mono_iff_presheaf_mono
 
--- porting note: added to ease the port of CategoryTheory.Sites.LeftExact
+-- Porting note: added to ease the port of CategoryTheory.Sites.LeftExact
 -- in mathlib, this was `by refl`, but here it would timeout
 @[simps! hom_app inv_app]
 noncomputable

70fd9563

chore: classify removed @[nolint has_nonempty_instance] porting notes (#10929)

Classifies by adding issue number (#10927) to porting notes claiming removed @[nolint has_nonempty_instance].

2599c3bb

Diff

@@ -37,7 +37,7 @@ variable [ConcreteCategory.{max v u} D]
 
 attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.instFunLike
 
--- porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 /-- A concrete version of the multiequalizer, to be used below. -/
 def Meq {X : C} (P : Cᵒᵖ ⥤ D) (S : J.Cover X) :=
   { x : ∀ I : S.Arrow, P.obj (op I.Y) //

70fd9563

chore(CategoryTheory/Limits/Concrete): generalize universe assumptions (#10418)

Generalizes universe assumptions for various statements on colimits in concrete categories. Also simplifies some proofs.

76c1f6e7

Diff

@@ -241,7 +241,7 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.Cover X} (x : Meq
     mk x = mk y ↔ ∃ (W : J.Cover X) (h1 : W ⟶ S) (h2 : W ⟶ T), x.refine h1 = y.refine h2 := by
   constructor
   · intro h
-    obtain ⟨W, h1, h2, hh⟩ := Concrete.colimit_exists_of_rep_eq _ _ _ h
+    obtain ⟨W, h1, h2, hh⟩ := Concrete.colimit_exists_of_rep_eq.{u} _ _ _ h
     use W.unop, h1.unop, h2.unop
     ext I
     apply_fun Multiequalizer.ι (W.unop.index P) I at hh

70fd9563

chore: reduce imports (#9830)

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

f4c4ca61

Diff

@@ -4,9 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 -/
 import Mathlib.CategoryTheory.Sites.Plus
-import Mathlib.CategoryTheory.Sites.Sheafification
 import Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory
-import Mathlib.CategoryTheory.ConcreteCategory.Elementwise
 
 #align_import category_theory.sites.sheafification from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"

70fd9563

refactor(*): abbreviation for non-dependent FunLike (#9833)

This follows up from #9785, which renamed FunLike to DFunLike, by introducing a new abbreviation FunLike F α β := DFunLike F α (fun _ => β), to make the non-dependent use of FunLike easier.

I searched for the pattern DFunLike.*fun and DFunLike.*λ in all files to replace expressions of the form DFunLike F α (fun _ => β) with FunLike F α β. I did this everywhere except for extends clauses for two reasons: it would conflict with #8386, and more importantly extends must directly refer to a structure with no unfolding of defs or abbrevs.

54792e9e

Diff

@@ -37,7 +37,7 @@ section
 
 variable [ConcreteCategory.{max v u} D]
 
-attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.instDFunLike
+attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.instFunLike
 
 -- porting note: removed @[nolint has_nonempty_instance]
 /-- A concrete version of the multiequalizer, to be used below. -/
@@ -52,7 +52,7 @@ namespace Meq
 
 variable [ConcreteCategory.{max v u} D]
 
-attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.instDFunLike
+attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.instFunLike
 
 instance {X} (P : Cᵒᵖ ⥤ D) (S : J.Cover X) :
     CoeFun (Meq P S) fun _ => ∀ I : S.Arrow, P.obj (op I.Y) :=
@@ -145,7 +145,7 @@ namespace Plus
 
 variable [ConcreteCategory.{max v u} D]
 
-attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.instDFunLike
+attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.instFunLike
 
 variable [PreservesLimits (forget D)]

70fd9563

chore(*): rename FunLike to DFunLike (#9785)

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

82656743

Diff

@@ -37,7 +37,7 @@ section
 
 variable [ConcreteCategory.{max v u} D]
 
-attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.funLike
+attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.instDFunLike
 
 -- porting note: removed @[nolint has_nonempty_instance]
 /-- A concrete version of the multiequalizer, to be used below. -/
@@ -52,7 +52,7 @@ namespace Meq
 
 variable [ConcreteCategory.{max v u} D]
 
-attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.funLike
+attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.instDFunLike
 
 instance {X} (P : Cᵒᵖ ⥤ D) (S : J.Cover X) :
     CoeFun (Meq P S) fun _ => ∀ I : S.Arrow, P.obj (op I.Y) :=
@@ -145,7 +145,7 @@ namespace Plus
 
 variable [ConcreteCategory.{max v u} D]
 
-attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.funLike
+attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.instDFunLike
 
 variable [PreservesLimits (forget D)]

70fd9563

refactor(CategoryTheory/Sites): sheafification as an abstract left adjoint (#9012)

We define a typeclass HasSheafify which says that presheaves on a site with values in some category can be sheafified, i.e. that the inclusion functor from sheaves to presheaves has a left exact left adjoint. We redefine presheafToSheaf as an arbitrary choice of such a left adjoint.

4a55c95f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
 -/
-import Mathlib.CategoryTheory.Adjunction.FullyFaithful
 import Mathlib.CategoryTheory.Sites.Plus
+import Mathlib.CategoryTheory.Sites.Sheafification
 import Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory
 import Mathlib.CategoryTheory.ConcreteCategory.Elementwise
 
@@ -525,7 +525,8 @@ noncomputable def toSheafification : 𝟭 _ ⟶ sheafification J D :=
 #align category_theory.grothendieck_topology.to_sheafification CategoryTheory.GrothendieckTopology.toSheafification
 
 @[simp]
-theorem toSheafification_app (P : Cᵒᵖ ⥤ D) : (J.toSheafification D).app P = J.toSheafify P :=
+theorem toSheafification_app (P : Cᵒᵖ ⥤ D) :
+    (J.toSheafification D).app P = J.toSheafify P :=
   rfl
 #align category_theory.grothendieck_topology.to_sheafification_app CategoryTheory.GrothendieckTopology.toSheafification_app
 
@@ -550,8 +551,7 @@ theorem isoSheafify_hom {P : Cᵒᵖ ⥤ D} (hP : Presheaf.IsSheaf J P) :
   rfl
 #align category_theory.grothendieck_topology.iso_sheafify_hom CategoryTheory.GrothendieckTopology.isoSheafify_hom
 
-/-- Given a sheaf `Q` and a morphism `P ⟶ Q`, construct a morphism from
-`J.sheafify P` to `Q`. -/
+/-- Given a sheaf `Q` and a morphism `P ⟶ Q`, construct a morphism from `J.sheafify P` to `Q`. -/
 noncomputable def sheafifyLift {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) (hQ : Presheaf.IsSheaf J Q) :
     J.sheafify P ⟶ Q :=
   J.plusLift (J.plusLift η hQ) hQ
@@ -613,26 +613,26 @@ variable (D)
 
 /-- The sheafification functor, as a functor taking values in `Sheaf`. -/
 @[simps]
-noncomputable def presheafToSheaf : (Cᵒᵖ ⥤ D) ⥤ Sheaf J D where
+noncomputable def plusPlusSheaf : (Cᵒᵖ ⥤ D) ⥤ Sheaf J D where
   obj P := ⟨J.sheafify P, J.sheafify_isSheaf P⟩
   map η := ⟨J.sheafifyMap η⟩
   map_id _ := Sheaf.Hom.ext _ _ <| J.sheafifyMap_id _
   map_comp _ _ := Sheaf.Hom.ext _ _ <| J.sheafifyMap_comp _ _
 set_option linter.uppercaseLean3 false in
-#align category_theory.presheaf_to_Sheaf CategoryTheory.presheafToSheaf
+#align category_theory.presheaf_to_Sheaf CategoryTheory.plusPlusSheaf
 
-instance presheafToSheaf_preservesZeroMorphisms [Preadditive D] :
-    (presheafToSheaf J D).PreservesZeroMorphisms where
+instance plusPlusSheaf_preservesZeroMorphisms [Preadditive D] :
+    (plusPlusSheaf J D).PreservesZeroMorphisms where
   map_zero F G := by
     ext : 3
     refine' colimit.hom_ext (fun j => _)
     erw [colimit.ι_map, comp_zero, J.plusMap_zero, J.diagramNatTrans_zero, zero_comp]
 set_option linter.uppercaseLean3 false in
-#align category_theory.presheaf_to_Sheaf_preserves_zero_morphisms CategoryTheory.presheafToSheaf_preservesZeroMorphisms
+#align category_theory.presheaf_to_Sheaf_preserves_zero_morphisms CategoryTheory.plusPlusSheaf_preservesZeroMorphisms
 
 /-- The sheafification functor is left adjoint to the forgetful functor. -/
 @[simps! unit_app counit_app_val]
-noncomputable def sheafificationAdjunction : presheafToSheaf J D ⊣ sheafToPresheaf J D :=
+noncomputable def plusPlusAdjunction : plusPlusSheaf J D ⊣ sheafToPresheaf J D :=
   Adjunction.mkOfHomEquiv
     { homEquiv := fun P Q =>
         { toFun := fun e => J.toSheafify P ≫ e.val
@@ -645,10 +645,10 @@ noncomputable def sheafificationAdjunction : presheafToSheaf J D ⊣ sheafToPres
       homEquiv_naturality_right := fun η γ => by
         dsimp
         rw [Category.assoc] }
-#align category_theory.sheafification_adjunction CategoryTheory.sheafificationAdjunction
+#align category_theory.sheafification_adjunction CategoryTheory.plusPlusAdjunction
 
 noncomputable instance sheafToPresheafIsRightAdjoint : IsRightAdjoint (sheafToPresheaf J D) :=
-  ⟨_, sheafificationAdjunction J D⟩
+  ⟨_, plusPlusAdjunction J D⟩
 set_option linter.uppercaseLean3 false in
 #align category_theory.Sheaf_to_presheaf_is_right_adjoint CategoryTheory.sheafToPresheafIsRightAdjoint
 
@@ -666,31 +666,7 @@ set_option linter.uppercaseLean3 false in
 @[simps! hom_app inv_app]
 noncomputable
 def GrothendieckTopology.sheafificationIsoPresheafToSheafCompSheafToPreasheaf :
-    J.sheafification D ≅ presheafToSheaf J D ⋙ sheafToPresheaf J D :=
+    J.sheafification D ≅ plusPlusSheaf J D ⋙ sheafToPresheaf J D :=
   NatIso.ofComponents fun P => Iso.refl _
 
-variable {J D}
-
-/-- A sheaf `P` is isomorphic to its own sheafification. -/
-@[simps]
-noncomputable def sheafificationIso (P : Sheaf J D) : P ≅ (presheafToSheaf J D).obj P.val where
-  hom := ⟨(J.isoSheafify P.2).hom⟩
-  inv := ⟨(J.isoSheafify P.2).inv⟩
-  hom_inv_id := by
-    ext1
-    apply (J.isoSheafify P.2).hom_inv_id
-  inv_hom_id := by
-    ext1
-    apply (J.isoSheafify P.2).inv_hom_id
-#align category_theory.sheafification_iso CategoryTheory.sheafificationIso
-
-instance isIso_sheafificationAdjunction_counit (P : Sheaf J D) :
-    IsIso ((sheafificationAdjunction J D).counit.app P) :=
-  isIso_of_fully_faithful (sheafToPresheaf J D) _
-#align category_theory.is_iso_sheafification_adjunction_counit CategoryTheory.isIso_sheafificationAdjunction_counit
-
-instance sheafification_reflective : IsIso (sheafificationAdjunction J D).counit :=
-  NatIso.isIso_of_isIso_app _
-#align category_theory.sheafification_reflective CategoryTheory.sheafification_reflective
-
 end CategoryTheory

70fd9563

chore: space after ← (#8178)

Co-authored-by: Moritz Firsching <firsching@google.com>

5fb9beab

Diff

@@ -196,7 +196,7 @@ theorem toPlus_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.Cover X) (x : Meq P S) (
   dsimp only [toPlus, plusObj]
   delta Cover.toMultiequalizer
   dsimp [mk]
-  erw [←comp_apply]
+  erw [← comp_apply]
   rw [ι_colimMap_assoc, colimit.ι_pre, comp_apply, comp_apply]
   dsimp only [Functor.op]
   let e : (J.pullback I.f).obj (unop (op S)) ⟶ ⊤ := homOfLE (OrderTop.le_top _)
@@ -206,7 +206,7 @@ theorem toPlus_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.Cover X) (x : Meq P S) (
   apply Concrete.multiequalizer_ext
   intro i
   dsimp [diagram]
-  rw [←comp_apply, ←comp_apply, ←comp_apply, Multiequalizer.lift_ι, Multiequalizer.lift_ι,
+  rw [← comp_apply, ← comp_apply, ← comp_apply, Multiequalizer.lift_ι, Multiequalizer.lift_ι,
     Multiequalizer.lift_ι]
   erw [Meq.equiv_symm_eq_apply]
   let RR : S.Relation :=
@@ -224,7 +224,7 @@ theorem toPlus_eq_mk {X : C} {P : Cᵒᵖ ⥤ D} (x : P.obj (op X)) :
   apply congr_arg
   apply (Meq.equiv P ⊤).injective
   ext i
-  rw [Meq.equiv_apply, Equiv.apply_symm_apply, ←comp_apply, Multiequalizer.lift_ι]
+  rw [Meq.equiv_apply, Equiv.apply_symm_apply, ← comp_apply, Multiequalizer.lift_ι]
   rfl
 #align category_theory.grothendieck_topology.plus.to_plus_eq_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mk

70fd9563

feat(CategoryTheory): description of products and pullbacks in concrete categories (#8507)

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

e9d46c6c

Diff

@@ -5,7 +5,7 @@ Authors: Adam Topaz
 -/
 import Mathlib.CategoryTheory.Adjunction.FullyFaithful
 import Mathlib.CategoryTheory.Sites.Plus
-import Mathlib.CategoryTheory.Limits.ConcreteCategory
+import Mathlib.CategoryTheory.Limits.Shapes.ConcreteCategory
 import Mathlib.CategoryTheory.ConcreteCategory.Elementwise
 
 #align_import category_theory.sites.sheafification from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"

70fd9563

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Adam Topaz. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Adam Topaz
-
-! This file was ported from Lean 3 source module category_theory.sites.sheafification
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Adjunction.FullyFaithful
 import Mathlib.CategoryTheory.Sites.Plus
 import Mathlib.CategoryTheory.Limits.ConcreteCategory
 import Mathlib.CategoryTheory.ConcreteCategory.Elementwise
 
+#align_import category_theory.sites.sheafification from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 
 # Sheafification

70fd9563

chore: clean up spacing around at and goals (#5387)

Changes are of the form

some_tactic at h⊢ -> some_tactic at h ⊢
some_tactic at h -> some_tactic at h

2a870323

Diff

@@ -249,7 +249,7 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.Cover X} (x : Meq
     obtain ⟨W, h1, h2, hh⟩ := Concrete.colimit_exists_of_rep_eq _ _ _ h
     use W.unop, h1.unop, h2.unop
     ext I
-    apply_fun Multiequalizer.ι (W.unop.index P) I  at hh
+    apply_fun Multiequalizer.ι (W.unop.index P) I at hh
     convert hh
     all_goals
       dsimp [diagram]
@@ -260,7 +260,7 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.Cover X} (x : Meq
     use op S, h1.op, h2.op
     apply Concrete.multiequalizer_ext
     intro i
-    apply_fun fun ee => ee i  at e
+    apply_fun fun ee => ee i at e
     convert e
     all_goals
       dsimp [diagram]
@@ -310,7 +310,7 @@ theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.Cover X) (x y : (J.plusObj P).obj
   let IS : S.Arrow := I.fromMiddle
   specialize hh IS
   let IW : (W IS).Arrow := I.toMiddle
-  apply_fun fun e => e IW  at hh
+  apply_fun fun e => e IW at hh
   convert hh using 1
   · let Rx : Sx.Relation :=
       ⟨I.Y, I.Y, I.Y, 𝟙 _, 𝟙 _, I.f, I.toMiddleHom ≫ I.fromMiddleHom, leOfHom ex _ I.hf,
@@ -333,7 +333,7 @@ theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
   obtain ⟨W, h1, h2, hh⟩ := h
   apply hsep X W
   intro I
-  apply_fun fun e => e I  at hh
+  apply_fun fun e => e I at hh
   exact hh
 #align category_theory.grothendieck_topology.plus.inj_of_sep CategoryTheory.GrothendieckTopology.Plus.inj_of_sep
 
@@ -433,8 +433,8 @@ theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)
   · intro x y h
     apply sep P S _ _
     intro I
-    apply_fun Meq.equiv _ _  at h
-    apply_fun fun e => e I  at h
+    apply_fun Meq.equiv _ _ at h
+    apply_fun fun e => e I at h
     convert h <;> erw [Meq.equiv_apply, ← comp_apply, Multiequalizer.lift_ι] <;> rfl
   · rintro (x : (multiequalizer (S.index _) : D))
     obtain ⟨t, ht⟩ := exists_of_sep P hsep X S (Meq.equiv _ _ x)

70fd9563

feat: change ConcreteCategory.hasCoeToFun to FunLike (#4693)

b7cba33a

Diff

@@ -40,7 +40,7 @@ section
 
 variable [ConcreteCategory.{max v u} D]
 
-attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.hasCoeToFun
+attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.funLike
 
 -- porting note: removed @[nolint has_nonempty_instance]
 /-- A concrete version of the multiequalizer, to be used below. -/
@@ -55,7 +55,7 @@ namespace Meq
 
 variable [ConcreteCategory.{max v u} D]
 
-attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.hasCoeToFun
+attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.funLike
 
 instance {X} (P : Cᵒᵖ ⥤ D) (S : J.Cover X) :
     CoeFun (Meq P S) fun _ => ∀ I : S.Arrow, P.obj (op I.Y) :=
@@ -148,7 +148,7 @@ namespace Plus
 
 variable [ConcreteCategory.{max v u} D]
 
-attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.hasCoeToFun
+attribute [local instance] ConcreteCategory.hasCoeToSort ConcreteCategory.funLike
 
 variable [PreservesLimits (forget D)]
 
@@ -166,14 +166,15 @@ def mk {X : C} {P : Cᵒᵖ ⥤ D} {S : J.Cover X} (x : Meq P S) : (J.plusObj P)
 theorem res_mk_eq_mk_pullback {Y X : C} {P : Cᵒᵖ ⥤ D} {S : J.Cover X} (x : Meq P S) (f : Y ⟶ X) :
     (J.plusObj P).map f.op (mk x) = mk (x.pullback f) := by
   dsimp [mk, plusObj]
-  simp only [← comp_apply, colimit.ι_pre, ι_colimMap_assoc]
-  simp_rw [comp_apply]
+  rw [← comp_apply (x := (Meq.equiv P S).symm x), ι_colimMap_assoc, colimit.ι_pre,
+    comp_apply (x := (Meq.equiv P S).symm x)]
   apply congr_arg
   apply (Meq.equiv P _).injective
   erw [Equiv.apply_symm_apply]
   ext i
-  simp only [diagramPullback_app, Meq.pullback_apply, Meq.equiv_apply, ← comp_apply]
-  erw [Multiequalizer.lift_ι, Meq.equiv_symm_eq_apply]
+  simp only [Functor.op_obj, unop_op, pullback_obj, diagram_obj, Functor.comp_obj,
+    diagramPullback_app, Meq.equiv_apply, Meq.pullback_apply]
+  erw [← comp_apply, Multiequalizer.lift_ι, Meq.equiv_symm_eq_apply]
   cases i; rfl
 #align category_theory.grothendieck_topology.plus.res_mk_eq_mk_pullback CategoryTheory.GrothendieckTopology.Plus.res_mk_eq_mk_pullback
 
@@ -183,7 +184,7 @@ theorem toPlus_mk {X : C} {P : Cᵒᵖ ⥤ D} (S : J.Cover X) (x : P.obj (op X))
   let e : S ⟶ ⊤ := homOfLE (OrderTop.le_top _)
   rw [← colimit.w _ e.op]
   delta Cover.toMultiequalizer
-  simp only [comp_apply]
+  erw [comp_apply, comp_apply]
   apply congr_arg
   dsimp [diagram]
   apply Concrete.multiequalizer_ext
@@ -198,22 +199,23 @@ theorem toPlus_apply {X : C} {P : Cᵒᵖ ⥤ D} (S : J.Cover X) (x : Meq P S) (
   dsimp only [toPlus, plusObj]
   delta Cover.toMultiequalizer
   dsimp [mk]
-  simp only [← comp_apply, colimit.ι_pre, ι_colimMap_assoc]
-  simp only [comp_apply]
+  erw [←comp_apply]
+  rw [ι_colimMap_assoc, colimit.ι_pre, comp_apply, comp_apply]
   dsimp only [Functor.op]
   let e : (J.pullback I.f).obj (unop (op S)) ⟶ ⊤ := homOfLE (OrderTop.le_top _)
   rw [← colimit.w _ e.op]
-  simp only [comp_apply]
+  erw [comp_apply]
   apply congr_arg
   apply Concrete.multiequalizer_ext
   intro i
   dsimp [diagram]
-  simp only [← comp_apply, Category.assoc, Multiequalizer.lift_ι, Category.comp_id,
-    Meq.equiv_symm_eq_apply]
+  rw [←comp_apply, ←comp_apply, ←comp_apply, Multiequalizer.lift_ι, Multiequalizer.lift_ι,
+    Multiequalizer.lift_ι]
+  erw [Meq.equiv_symm_eq_apply]
   let RR : S.Relation :=
     ⟨_, _, _, i.f, 𝟙 _, I.f, i.f ≫ I.f, I.hf, Sieve.downward_closed _ I.hf _, by simp⟩
   erw [x.condition RR]
-  simp
+  simp only [unop_op, pullback_obj, op_id, Functor.map_id, id_apply]
   rfl
 #align category_theory.grothendieck_topology.plus.to_plus_apply CategoryTheory.GrothendieckTopology.Plus.toPlus_apply
 
@@ -225,7 +227,7 @@ theorem toPlus_eq_mk {X : C} {P : Cᵒᵖ ⥤ D} (x : P.obj (op X)) :
   apply congr_arg
   apply (Meq.equiv P ⊤).injective
   ext i
-  simp
+  rw [Meq.equiv_apply, Equiv.apply_symm_apply, ←comp_apply, Multiequalizer.lift_ι]
   rfl
 #align category_theory.grothendieck_topology.plus.to_plus_eq_mk CategoryTheory.GrothendieckTopology.Plus.toPlus_eq_mk
 
@@ -251,7 +253,7 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.Cover X} (x : Meq
     convert hh
     all_goals
       dsimp [diagram]
-      simp only [← comp_apply, Multiequalizer.lift_ι, Category.comp_id, Meq.equiv_symm_eq_apply]
+      erw [← comp_apply, Multiequalizer.lift_ι, Meq.equiv_symm_eq_apply]
       cases I; rfl
   · rintro ⟨S, h1, h2, e⟩
     apply Concrete.colimit_rep_eq_of_exists
@@ -262,7 +264,8 @@ theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.Cover X} (x : Meq
     convert e
     all_goals
       dsimp [diagram]
-      simp only [← comp_apply, Multiequalizer.lift_ι, Meq.equiv_symm_eq_apply]
+      rw [← comp_apply, Multiequalizer.lift_ι]
+      erw [Meq.equiv_symm_eq_apply]
       cases i; rfl
 #align category_theory.grothendieck_topology.plus.eq_mk_iff_exists CategoryTheory.GrothendieckTopology.Plus.eq_mk_iff_exists
 
@@ -312,13 +315,11 @@ theorem sep {X : C} (P : Cᵒᵖ ⥤ D) (S : J.Cover X) (x y : (J.plusObj P).obj
   · let Rx : Sx.Relation :=
       ⟨I.Y, I.Y, I.Y, 𝟙 _, 𝟙 _, I.f, I.toMiddleHom ≫ I.fromMiddleHom, leOfHom ex _ I.hf,
         by simpa only [I.middle_spec] using leOfHom ex _ I.hf, by simp [I.middle_spec]⟩
-    have := x.condition Rx
-    simpa using this
+    simpa [id_apply] using x.condition Rx
   · let Ry : Sy.Relation :=
       ⟨I.Y, I.Y, I.Y, 𝟙 _, 𝟙 _, I.f, I.toMiddleHom ≫ I.fromMiddleHom, leOfHom ey _ I.hf,
         by simpa only [I.middle_spec] using leOfHom ey _ I.hf, by simp [I.middle_spec]⟩
-    have := y.condition Ry
-    simpa using this
+    simpa [id_apply] using y.condition Ry
 #align category_theory.grothendieck_topology.plus.sep CategoryTheory.GrothendieckTopology.Plus.sep
 
 theorem inj_of_sep (P : Cᵒᵖ ⥤ D)
@@ -434,7 +435,7 @@ theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)
     intro I
     apply_fun Meq.equiv _ _  at h
     apply_fun fun e => e I  at h
-    convert h <;> erw [Meq.equiv_apply, ← comp_apply, Multiequalizer.lift_ι]
+    convert h <;> erw [Meq.equiv_apply, ← comp_apply, Multiequalizer.lift_ι] <;> rfl
   · rintro (x : (multiequalizer (S.index _) : D))
     obtain ⟨t, ht⟩ := exists_of_sep P hsep X S (Meq.equiv _ _ x)
     use t
@@ -442,7 +443,8 @@ theorem isSheaf_of_sep (P : Cᵒᵖ ⥤ D)
     rw [← ht]
     ext i
     dsimp
-    rw [← comp_apply, Multiequalizer.lift_ι]
+    erw [← comp_apply]
+    rw [Multiequalizer.lift_ι]
     rfl
 #align category_theory.grothendieck_topology.plus.is_sheaf_of_sep CategoryTheory.GrothendieckTopology.Plus.isSheaf_of_sep

70fd9563

chore: formatting issues (#4947)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

5068808d

Diff

@@ -232,7 +232,7 @@ theorem toPlus_eq_mk {X : C} {P : Cᵒᵖ ⥤ D} (x : P.obj (op X)) :
 variable [∀ X : C, PreservesColimitsOfShape (J.Cover X)ᵒᵖ (forget D)]
 
 theorem exists_rep {X : C} {P : Cᵒᵖ ⥤ D} (x : (J.plusObj P).obj (op X)) :
-    ∃ (S : J.Cover X)(y : Meq P S), x = mk y := by
+    ∃ (S : J.Cover X) (y : Meq P S), x = mk y := by
   obtain ⟨S, y, h⟩ := Concrete.colimit_exists_rep (J.diagram P X) x
   use S.unop, Meq.equiv _ _ y
   rw [← h]
@@ -241,7 +241,7 @@ theorem exists_rep {X : C} {P : Cᵒᵖ ⥤ D} (x : (J.plusObj P).obj (op X)) :
 #align category_theory.grothendieck_topology.plus.exists_rep CategoryTheory.GrothendieckTopology.Plus.exists_rep
 
 theorem eq_mk_iff_exists {X : C} {P : Cᵒᵖ ⥤ D} {S T : J.Cover X} (x : Meq P S) (y : Meq P T) :
-    mk x = mk y ↔ ∃ (W : J.Cover X)(h1 : W ⟶ S)(h2 : W ⟶ T), x.refine h1 = y.refine h2 := by
+    mk x = mk y ↔ ∃ (W : J.Cover X) (h1 : W ⟶ S) (h2 : W ⟶ T), x.refine h1 = y.refine h2 := by
   constructor
   · intro h
     obtain ⟨W, h1, h2, hh⟩ := Concrete.colimit_exists_of_rep_eq _ _ _ h

70fd9563

chore: fix many typos (#4967)

These are all doc fixes

6f9e51c3

Diff

@@ -379,7 +379,7 @@ theorem exists_of_sep (P : Cᵒᵖ ⥤ D)
   choose Z e1 e2 he2 _ _ using fun I : B.Arrow => I.hf
   -- Construct a compatible system of local sections over this large cover, using the chosen
   -- representatives of our local sections.
-  -- The compatilibity here follows from the separatedness assumption.
+  -- The compatibility here follows from the separatedness assumption.
   let w : Meq P B := meqOfSep P hsep X S s T t ht
   -- The associated gluing will be the candidate section.
   use mk w

70fd9563

chore: review of automation in category theory (#4793)

Clean up of automation in the category theory library. Leaving out unnecessary proof steps, or fields done by aesop_cat, and making more use of available autoparameters.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

5b958613

Diff

@@ -668,7 +668,7 @@ set_option linter.uppercaseLean3 false in
 noncomputable
 def GrothendieckTopology.sheafificationIsoPresheafToSheafCompSheafToPreasheaf :
     J.sheafification D ≅ presheafToSheaf J D ⋙ sheafToPresheaf J D :=
-  NatIso.ofComponents (fun P => Iso.refl _) (by simp)
+  NatIso.ofComponents fun P => Iso.refl _
 
 variable {J D}

70fd9563

chore: reenable eta, bump to nightly 2023-05-16 (#3414)

Now that leanprover/lean4#2210 has been merged, this PR:

removes all the set_option synthInstance.etaExperiment true commands (and some etaExperiment% term elaborators)
removes many but not quite all set_option maxHeartbeats commands
makes various other changes required to cope with leanprover/lean4#2210.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Matthew Ballard <matt@mrb.email>

a6e1045f

Diff

@@ -513,7 +513,6 @@ theorem sheafification_obj (P : Cᵒᵖ ⥤ D) : (J.sheafification D).obj P = J.
   rfl
 #align category_theory.grothendieck_topology.sheafification_obj CategoryTheory.GrothendieckTopology.sheafification_obj
 
-set_option maxHeartbeats 400000 in
 @[simp]
 theorem sheafification_map {P Q : Cᵒᵖ ⥤ D} (η : P ⟶ Q) :
     (J.sheafification D).map η = J.sheafifyMap η :=

70fd9563

feat: port CategoryTheory.Sites.LeftExact (#3706)

e8b2eac0

Diff

@@ -663,6 +663,14 @@ theorem Sheaf.Hom.mono_iff_presheaf_mono {F G : Sheaf J D} (f : F ⟶ G) : Mono
 set_option linter.uppercaseLean3 false in
 #align category_theory.Sheaf.hom.mono_iff_presheaf_mono CategoryTheory.Sheaf.Hom.mono_iff_presheaf_mono
 
+-- porting note: added to ease the port of CategoryTheory.Sites.LeftExact
+-- in mathlib, this was `by refl`, but here it would timeout
+@[simps! hom_app inv_app]
+noncomputable
+def GrothendieckTopology.sheafificationIsoPresheafToSheafCompSheafToPreasheaf :
+    J.sheafification D ≅ presheafToSheaf J D ⋙ sheafToPresheaf J D :=
+  NatIso.ofComponents (fun P => Iso.refl _) (by simp)
+
 variable {J D}
 
 /-- A sheaf `P` is isomorphic to its own sheafification. -/

70fd9563

chore: tidy various files (#3606)

e3fe5faf

Diff

@@ -403,7 +403,6 @@ theorem exists_of_sep (P : Cᵒᵖ ⥤ D)
           exact hf)
   use e0, 𝟙 _
   ext IV
-  --dsimp only [Meq.refine_apply, Meq.pullback_apply, w]
   let IA : B.Arrow := ⟨_, (IV.f ≫ II.f) ≫ I.f,
     ⟨I.Y, _, _, I.hf, Sieve.downward_closed _ II.hf _, rfl⟩⟩
   let IB : S.Arrow := IA.fromMiddle

70fd9563

feat: port CategoryTheory.Sites.Sheafification (#3387)

Co-authored-by: Jeremy Tan Jie Rui <e0191785@u.nus.edu> Co-authored-by: Pol_tta <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: EmilieUthaiwat <emiliepathum@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Gabriel Ebner <gebner@gebner.org> Co-authored-by: Violeta Hernández <vi.hdz.p@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

c35e8093

`category_theory.sites.sheafification` ⟷ `Mathlib.CategoryTheory.Sites.ConcreteSheafification`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 3 + 322

category_theory.sites.sheafification ⟷ Mathlib.CategoryTheory.Sites.ConcreteSheafification

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 3 + 322

`category_theory.sites.sheafification` ⟷ `Mathlib.CategoryTheory.Sites.ConcreteSheafification`