category_theory.limits.concrete_category

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

c3019c79

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

cb3ceec8

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -124,7 +124,7 @@ def Concrete.multiequalizerEquivAux (I : MulticospanIndex C) :
       by
       have a := x.2 (walking_multicospan.hom.fst i)
       have b := x.2 (walking_multicospan.hom.snd i)
-      rw [← b] at a 
+      rw [← b] at a
       exact a⟩
   invFun x :=
     { val := fun j =>
@@ -208,8 +208,8 @@ theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColim
     intro a
     obtain ⟨b, hb⟩ := this (TX.hom a)
     refine' ⟨b, _⟩
-    apply_fun TX.inv at hb 
-    change (TX.hom ≫ TX.inv) (ff b) = (TX.hom ≫ TX.inv) _ at hb 
+    apply_fun TX.inv at hb
+    change (TX.hom ≫ TX.inv) (ff b) = (TX.hom ≫ TX.inv) _ at hb
     simpa only [TX.hom_inv_id] using hb
   have : TX.hom ∘ ff = fun a => G.ι.app a.1 a.2 :=
     by
@@ -285,9 +285,9 @@ theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsCol
   let hG := Types.colimitCoconeIsColimit.{v, v} (F ⋙ forget C)
   let T : E ≅ G := hE.unique_up_to_iso hG
   let TX : E.X ≅ G.X := (cocones.forget _).mapIso T
-  apply_fun TX.hom at h 
-  change (E.ι.app i ≫ TX.hom) x = (E.ι.app j ≫ TX.hom) y at h 
-  erw [T.hom.w, T.hom.w] at h 
+  apply_fun TX.hom at h
+  change (E.ι.app i ≫ TX.hom) x = (E.ι.app j ≫ TX.hom) y at h
+  erw [T.hom.w, T.hom.w] at h
   replace h := Quot.exact _ h
   suffices
     ∀ (a b : Σ j, F.obj j) (h : EqvGen (Limits.Types.Quot.Rel.{v, v} (F ⋙ forget C)) a b),

cb3ceec8

bump to nightly-2023-11-29-11

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

049e2cad

Diff

@@ -177,16 +177,16 @@ end Limits
 
 section Colimits
 
-#print CategoryTheory.Limits.cokernel_funext /-
+#print CategoryTheory.Limits.Concrete.cokernel_funext /-
 -- We don't mark this as an `@[ext]` lemma as we don't always want to work elementwise.
-theorem cokernel_funext {C : Type _} [Category C] [HasZeroMorphisms C] [ConcreteCategory C]
-    {M N K : C} {f : M ⟶ N} [HasCokernel f] {g h : cokernel f ⟶ K}
-    (w : ∀ n : N, g (cokernel.π f n) = h (cokernel.π f n)) : g = h :=
+theorem CategoryTheory.Limits.Concrete.cokernel_funext {C : Type _} [Category C]
+    [HasZeroMorphisms C] [ConcreteCategory C] {M N K : C} {f : M ⟶ N} [HasCokernel f]
+    {g h : cokernel f ⟶ K} (w : ∀ n : N, g (cokernel.π f n) = h (cokernel.π f n)) : g = h :=
   by
   apply coequalizer.hom_ext
   apply concrete_category.hom_ext _ _
   simpa using w
-#align category_theory.limits.cokernel_funext CategoryTheory.Limits.cokernel_funext
+#align category_theory.limits.cokernel_funext CategoryTheory.Limits.Concrete.cokernel_funext
 -/
 
 variable {C : Type u} [Category.{v} C] [ConcreteCategory.{v} C] {J : Type v} [SmallCategory J]

cb3ceec8

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,13 +3,13 @@ Copyright (c) 2017 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Adam Topaz
 -/
-import Mathbin.CategoryTheory.Limits.Preserves.Basic
-import Mathbin.CategoryTheory.Limits.Types
-import Mathbin.CategoryTheory.Limits.Shapes.WidePullbacks
-import Mathbin.CategoryTheory.Limits.Shapes.Multiequalizer
-import Mathbin.CategoryTheory.ConcreteCategory.Basic
-import Mathbin.CategoryTheory.Limits.Shapes.Kernels
-import Mathbin.Tactic.ApplyFun
+import CategoryTheory.Limits.Preserves.Basic
+import CategoryTheory.Limits.Types
+import CategoryTheory.Limits.Shapes.WidePullbacks
+import CategoryTheory.Limits.Shapes.Multiequalizer
+import CategoryTheory.ConcreteCategory.Basic
+import CategoryTheory.Limits.Shapes.Kernels
+import Tactic.ApplyFun
 
 #align_import category_theory.limits.concrete_category from "leanprover-community/mathlib"@"cb3ceec8485239a61ed51d944cb9a95b68c6bafc"

cb3ceec8

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2017 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Adam Topaz
-
-! This file was ported from Lean 3 source module category_theory.limits.concrete_category
-! leanprover-community/mathlib commit cb3ceec8485239a61ed51d944cb9a95b68c6bafc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Limits.Preserves.Basic
 import Mathbin.CategoryTheory.Limits.Types
@@ -16,6 +11,8 @@ import Mathbin.CategoryTheory.ConcreteCategory.Basic
 import Mathbin.CategoryTheory.Limits.Shapes.Kernels
 import Mathbin.Tactic.ApplyFun
 
+#align_import category_theory.limits.concrete_category from "leanprover-community/mathlib"@"cb3ceec8485239a61ed51d944cb9a95b68c6bafc"
+
 /-!
 # Facts about (co)limits of functors into concrete categories

cb3ceec8

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -37,6 +37,7 @@ section Limits
 variable {C : Type u} [Category.{v} C] [ConcreteCategory.{max w v} C] {J : Type w} [SmallCategory J]
   (F : J ⥤ C) [PreservesLimit F (forget C)]
 
+#print CategoryTheory.Limits.Concrete.to_product_injective_of_isLimit /-
 theorem Concrete.to_product_injective_of_isLimit {D : Cone F} (hD : IsLimit D) :
     Function.Injective fun (x : D.pt) (j : J) => D.π.app j x :=
   by
@@ -53,16 +54,21 @@ theorem Concrete.to_product_injective_of_isLimit {D : Cone F} (hD : IsLimit D) :
   suffices Function.Injective fun (x : G.X) j => G.π.app j x by exact this.comp h
   apply Subtype.ext
 #align category_theory.limits.concrete.to_product_injective_of_is_limit CategoryTheory.Limits.Concrete.to_product_injective_of_isLimit
+-/
 
+#print CategoryTheory.Limits.Concrete.isLimit_ext /-
 theorem Concrete.isLimit_ext {D : Cone F} (hD : IsLimit D) (x y : D.pt) :
     (∀ j, D.π.app j x = D.π.app j y) → x = y := fun h =>
   Concrete.to_product_injective_of_isLimit _ hD (funext h)
 #align category_theory.limits.concrete.is_limit_ext CategoryTheory.Limits.Concrete.isLimit_ext
+-/
 
+#print CategoryTheory.Limits.Concrete.limit_ext /-
 theorem Concrete.limit_ext [HasLimit F] (x y : limit F) :
     (∀ j, limit.π F j x = limit.π F j y) → x = y :=
   Concrete.isLimit_ext F (limit.isLimit _) _ _
 #align category_theory.limits.concrete.limit_ext CategoryTheory.Limits.Concrete.limit_ext
+-/
 
 section WidePullback
 
@@ -70,6 +76,7 @@ open WidePullback
 
 open WidePullbackShape
 
+#print CategoryTheory.Limits.Concrete.widePullback_ext /-
 theorem Concrete.widePullback_ext {B : C} {ι : Type w} {X : ι → C} (f : ∀ j : ι, X j ⟶ B)
     [HasWidePullback B X f] [PreservesLimit (wideCospan B X f) (forget C)]
     (x y : widePullback B X f) (h₀ : base f x = base f y) (h : ∀ j, π f j x = π f j y) : x = y :=
@@ -79,7 +86,9 @@ theorem Concrete.widePullback_ext {B : C} {ι : Type w} {X : ι → C} (f : ∀
   · exact h₀
   · apply h
 #align category_theory.limits.concrete.wide_pullback_ext CategoryTheory.Limits.Concrete.widePullback_ext
+-/
 
+#print CategoryTheory.Limits.Concrete.widePullback_ext' /-
 theorem Concrete.widePullback_ext' {B : C} {ι : Type w} [Nonempty ι] {X : ι → C}
     (f : ∀ j : ι, X j ⟶ B) [HasWidePullback.{w} B X f]
     [PreservesLimit (wideCospan B X f) (forget C)] (x y : widePullback B X f)
@@ -89,11 +98,13 @@ theorem Concrete.widePullback_ext' {B : C} {ι : Type w} [Nonempty ι] {X : ι 
   inhabit ι
   simp only [← π_arrow f (Inhabited.default _), comp_apply, h]
 #align category_theory.limits.concrete.wide_pullback_ext' CategoryTheory.Limits.Concrete.widePullback_ext'
+-/
 
 end WidePullback
 
 section Multiequalizer
 
+#print CategoryTheory.Limits.Concrete.multiequalizer_ext /-
 theorem Concrete.multiequalizer_ext {I : MulticospanIndex.{w} C} [HasMultiequalizer I]
     [PreservesLimit I.multicospan (forget C)] (x y : multiequalizer I)
     (h : ∀ t : I.L, Multiequalizer.ι I t x = Multiequalizer.ι I t y) : x = y :=
@@ -103,7 +114,9 @@ theorem Concrete.multiequalizer_ext {I : MulticospanIndex.{w} C} [HasMultiequali
   · apply h
   · rw [← limit.w I.multicospan (walking_multicospan.hom.fst b), comp_apply, comp_apply, h]
 #align category_theory.limits.concrete.multiequalizer_ext CategoryTheory.Limits.Concrete.multiequalizer_ext
+-/
 
+#print CategoryTheory.Limits.Concrete.multiequalizerEquivAux /-
 /-- An auxiliary equivalence to be used in `multiequalizer_equiv` below.-/
 def Concrete.multiequalizerEquivAux (I : MulticospanIndex C) :
     (I.multicospan ⋙ forget C).sections ≃
@@ -135,7 +148,9 @@ def Concrete.multiequalizerEquivAux (I : MulticospanIndex C) :
       rfl
   right_inv := by intro x; ext i; rfl
 #align category_theory.limits.concrete.multiequalizer_equiv_aux CategoryTheory.Limits.Concrete.multiequalizerEquivAux
+-/
 
+#print CategoryTheory.Limits.Concrete.multiequalizerEquiv /-
 /-- The equivalence between the noncomputable multiequalizer and
 and the concrete multiequalizer. -/
 noncomputable def Concrete.multiequalizerEquiv (I : MulticospanIndex.{w} C) [HasMultiequalizer I]
@@ -147,13 +162,16 @@ noncomputable def Concrete.multiequalizerEquiv (I : MulticospanIndex.{w} C) [Has
   let E := h2.conePointUniqueUpToIso (Types.limitConeIsLimit _)
   Equiv.trans E.toEquiv (Concrete.multiequalizerEquivAux I)
 #align category_theory.limits.concrete.multiequalizer_equiv CategoryTheory.Limits.Concrete.multiequalizerEquiv
+-/
 
+#print CategoryTheory.Limits.Concrete.multiequalizerEquiv_apply /-
 @[simp]
 theorem Concrete.multiequalizerEquiv_apply (I : MulticospanIndex.{w} C) [HasMultiequalizer I]
     [PreservesLimit I.multicospan (forget C)] (x : multiequalizer I) (i : I.L) :
     ((Concrete.multiequalizerEquiv I) x : ∀ i : I.L, I.left i) i = Multiequalizer.ι I i x :=
   rfl
 #align category_theory.limits.concrete.multiequalizer_equiv_apply CategoryTheory.Limits.Concrete.multiequalizerEquiv_apply
+-/
 
 end Multiequalizer
 
@@ -162,6 +180,7 @@ end Limits
 
 section Colimits
 
+#print CategoryTheory.Limits.cokernel_funext /-
 -- We don't mark this as an `@[ext]` lemma as we don't always want to work elementwise.
 theorem cokernel_funext {C : Type _} [Category C] [HasZeroMorphisms C] [ConcreteCategory C]
     {M N K : C} {f : M ⟶ N} [HasCokernel f] {g h : cokernel f ⟶ K}
@@ -171,10 +190,12 @@ theorem cokernel_funext {C : Type _} [Category C] [HasZeroMorphisms C] [Concrete
   apply concrete_category.hom_ext _ _
   simpa using w
 #align category_theory.limits.cokernel_funext CategoryTheory.Limits.cokernel_funext
+-/
 
 variable {C : Type u} [Category.{v} C] [ConcreteCategory.{v} C] {J : Type v} [SmallCategory J]
   (F : J ⥤ C) [PreservesColimit F (forget C)]
 
+#print CategoryTheory.Limits.Concrete.from_union_surjective_of_isColimit /-
 theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColimit D) :
     let ff : (Σ j : J, F.obj j) → D.pt := fun a => D.ι.app a.1 a.2
     Function.Surjective ff :=
@@ -202,19 +223,25 @@ theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColim
   rintro ⟨⟨j, a⟩⟩
   exact ⟨⟨j, a⟩, rfl⟩
 #align category_theory.limits.concrete.from_union_surjective_of_is_colimit CategoryTheory.Limits.Concrete.from_union_surjective_of_isColimit
+-/
 
+#print CategoryTheory.Limits.Concrete.isColimit_exists_rep /-
 theorem Concrete.isColimit_exists_rep {D : Cocone F} (hD : IsColimit D) (x : D.pt) :
     ∃ (j : J) (y : F.obj j), D.ι.app j y = x :=
   by
   obtain ⟨a, rfl⟩ := concrete.from_union_surjective_of_is_colimit F hD x
   exact ⟨a.1, a.2, rfl⟩
 #align category_theory.limits.concrete.is_colimit_exists_rep CategoryTheory.Limits.Concrete.isColimit_exists_rep
+-/
 
+#print CategoryTheory.Limits.Concrete.colimit_exists_rep /-
 theorem Concrete.colimit_exists_rep [HasColimit F] (x : colimit F) :
     ∃ (j : J) (y : F.obj j), colimit.ι F j y = x :=
   Concrete.isColimit_exists_rep F (colimit.isColimit _) x
 #align category_theory.limits.concrete.colimit_exists_rep CategoryTheory.Limits.Concrete.colimit_exists_rep
+-/
 
+#print CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_exists /-
 theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) (h : ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y) :
     D.ι.app i x = D.ι.app j y := by
@@ -236,17 +263,21 @@ theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsCol
   symm
   exact Quot.sound ⟨g, rfl⟩
 #align category_theory.limits.concrete.is_colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_exists
+-/
 
+#print CategoryTheory.Limits.Concrete.colimit_rep_eq_of_exists /-
 theorem Concrete.colimit_rep_eq_of_exists [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j)
     (h : ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y) :
     colimit.ι F i x = colimit.ι F j y :=
   Concrete.isColimit_rep_eq_of_exists F (colimit.isColimit _) x y h
 #align category_theory.limits.concrete.colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.colimit_rep_eq_of_exists
+-/
 
 section FilteredColimits
 
 variable [IsFiltered J]
 
+#print CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eq /-
 theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) (h : D.ι.app _ x = D.ι.app _ y) :
     ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y :=
@@ -288,23 +319,30 @@ theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsCol
     simp only [← comp_apply, ← F.map_comp]
     rw [is_filtered.coeq_condition]
 #align category_theory.limits.concrete.is_colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eq
+-/
 
+#print CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists /-
 theorem Concrete.isColimit_rep_eq_iff_exists {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) :
     D.ι.app i x = D.ι.app j y ↔ ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y :=
   ⟨Concrete.isColimit_exists_of_rep_eq _ hD _ _, Concrete.isColimit_rep_eq_of_exists _ hD _ _⟩
 #align category_theory.limits.concrete.is_colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists
+-/
 
+#print CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eq /-
 theorem Concrete.colimit_exists_of_rep_eq [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j)
     (h : colimit.ι F _ x = colimit.ι F _ y) :
     ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y :=
   Concrete.isColimit_exists_of_rep_eq F (colimit.isColimit _) x y h
 #align category_theory.limits.concrete.colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eq
+-/
 
+#print CategoryTheory.Limits.Concrete.colimit_rep_eq_iff_exists /-
 theorem Concrete.colimit_rep_eq_iff_exists [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j) :
     colimit.ι F i x = colimit.ι F j y ↔ ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y :=
   ⟨Concrete.colimit_exists_of_rep_eq _ _ _, Concrete.colimit_rep_eq_of_exists _ _ _⟩
 #align category_theory.limits.concrete.colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.colimit_rep_eq_iff_exists
+-/
 
 end FilteredColimits
 
@@ -314,6 +352,7 @@ open WidePushout
 
 open WidePushoutShape
 
+#print CategoryTheory.Limits.Concrete.widePushout_exists_rep /-
 theorem Concrete.widePushout_exists_rep {B : C} {α : Type _} {X : α → C} (f : ∀ j : α, B ⟶ X j)
     [HasWidePushout.{v} B X f] [PreservesColimit (wideSpan B X f) (forget C)]
     (x : widePushout B X f) : (∃ y : B, head f y = x) ∨ ∃ (i : α) (y : X i), ι f i y = x :=
@@ -323,7 +362,9 @@ theorem Concrete.widePushout_exists_rep {B : C} {α : Type _} {X : α → C} (f
   · right
     use j, y
 #align category_theory.limits.concrete.wide_pushout_exists_rep CategoryTheory.Limits.Concrete.widePushout_exists_rep
+-/
 
+#print CategoryTheory.Limits.Concrete.widePushout_exists_rep' /-
 theorem Concrete.widePushout_exists_rep' {B : C} {α : Type _} [Nonempty α] {X : α → C}
     (f : ∀ j : α, B ⟶ X j) [HasWidePushout.{v} B X f] [PreservesColimit (wideSpan B X f) (forget C)]
     (x : widePushout B X f) : ∃ (i : α) (y : X i), ι f i y = x :=
@@ -334,6 +375,7 @@ theorem Concrete.widePushout_exists_rep' {B : C} {α : Type _} [Nonempty α] {X
     simp only [← arrow_ι _ (Inhabited.default α), comp_apply]
   · use i, y
 #align category_theory.limits.concrete.wide_pushout_exists_rep' CategoryTheory.Limits.Concrete.widePushout_exists_rep'
+-/
 
 end WidePushout

cb3ceec8

bump to nightly-2023-06-13-03

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

c9322c77

Diff

@@ -70,7 +70,6 @@ open WidePullback
 
 open WidePullbackShape
 
-#print CategoryTheory.Limits.Concrete.widePullback_ext /-
 theorem Concrete.widePullback_ext {B : C} {ι : Type w} {X : ι → C} (f : ∀ j : ι, X j ⟶ B)
     [HasWidePullback B X f] [PreservesLimit (wideCospan B X f) (forget C)]
     (x y : widePullback B X f) (h₀ : base f x = base f y) (h : ∀ j, π f j x = π f j y) : x = y :=
@@ -80,9 +79,7 @@ theorem Concrete.widePullback_ext {B : C} {ι : Type w} {X : ι → C} (f : ∀
   · exact h₀
   · apply h
 #align category_theory.limits.concrete.wide_pullback_ext CategoryTheory.Limits.Concrete.widePullback_ext
--/
 
-#print CategoryTheory.Limits.Concrete.widePullback_ext' /-
 theorem Concrete.widePullback_ext' {B : C} {ι : Type w} [Nonempty ι] {X : ι → C}
     (f : ∀ j : ι, X j ⟶ B) [HasWidePullback.{w} B X f]
     [PreservesLimit (wideCospan B X f) (forget C)] (x y : widePullback B X f)
@@ -92,13 +89,11 @@ theorem Concrete.widePullback_ext' {B : C} {ι : Type w} [Nonempty ι] {X : ι 
   inhabit ι
   simp only [← π_arrow f (Inhabited.default _), comp_apply, h]
 #align category_theory.limits.concrete.wide_pullback_ext' CategoryTheory.Limits.Concrete.widePullback_ext'
--/
 
 end WidePullback
 
 section Multiequalizer
 
-#print CategoryTheory.Limits.Concrete.multiequalizer_ext /-
 theorem Concrete.multiequalizer_ext {I : MulticospanIndex.{w} C} [HasMultiequalizer I]
     [PreservesLimit I.multicospan (forget C)] (x y : multiequalizer I)
     (h : ∀ t : I.L, Multiequalizer.ι I t x = Multiequalizer.ι I t y) : x = y :=
@@ -108,7 +103,6 @@ theorem Concrete.multiequalizer_ext {I : MulticospanIndex.{w} C} [HasMultiequali
   · apply h
   · rw [← limit.w I.multicospan (walking_multicospan.hom.fst b), comp_apply, comp_apply, h]
 #align category_theory.limits.concrete.multiequalizer_ext CategoryTheory.Limits.Concrete.multiequalizer_ext
--/
 
 /-- An auxiliary equivalence to be used in `multiequalizer_equiv` below.-/
 def Concrete.multiequalizerEquivAux (I : MulticospanIndex C) :
@@ -142,7 +136,6 @@ def Concrete.multiequalizerEquivAux (I : MulticospanIndex C) :
   right_inv := by intro x; ext i; rfl
 #align category_theory.limits.concrete.multiequalizer_equiv_aux CategoryTheory.Limits.Concrete.multiequalizerEquivAux
 
-#print CategoryTheory.Limits.Concrete.multiequalizerEquiv /-
 /-- The equivalence between the noncomputable multiequalizer and
 and the concrete multiequalizer. -/
 noncomputable def Concrete.multiequalizerEquiv (I : MulticospanIndex.{w} C) [HasMultiequalizer I]
@@ -154,7 +147,6 @@ noncomputable def Concrete.multiequalizerEquiv (I : MulticospanIndex.{w} C) [Has
   let E := h2.conePointUniqueUpToIso (Types.limitConeIsLimit _)
   Equiv.trans E.toEquiv (Concrete.multiequalizerEquivAux I)
 #align category_theory.limits.concrete.multiequalizer_equiv CategoryTheory.Limits.Concrete.multiequalizerEquiv
--/
 
 @[simp]
 theorem Concrete.multiequalizerEquiv_apply (I : MulticospanIndex.{w} C) [HasMultiequalizer I]
@@ -322,7 +314,6 @@ open WidePushout
 
 open WidePushoutShape
 
-#print CategoryTheory.Limits.Concrete.widePushout_exists_rep /-
 theorem Concrete.widePushout_exists_rep {B : C} {α : Type _} {X : α → C} (f : ∀ j : α, B ⟶ X j)
     [HasWidePushout.{v} B X f] [PreservesColimit (wideSpan B X f) (forget C)]
     (x : widePushout B X f) : (∃ y : B, head f y = x) ∨ ∃ (i : α) (y : X i), ι f i y = x :=
@@ -332,9 +323,7 @@ theorem Concrete.widePushout_exists_rep {B : C} {α : Type _} {X : α → C} (f
   · right
     use j, y
 #align category_theory.limits.concrete.wide_pushout_exists_rep CategoryTheory.Limits.Concrete.widePushout_exists_rep
--/
 
-#print CategoryTheory.Limits.Concrete.widePushout_exists_rep' /-
 theorem Concrete.widePushout_exists_rep' {B : C} {α : Type _} [Nonempty α] {X : α → C}
     (f : ∀ j : α, B ⟶ X j) [HasWidePushout.{v} B X f] [PreservesColimit (wideSpan B X f) (forget C)]
     (x : widePushout B X f) : ∃ (i : α) (y : X i), ι f i y = x :=
@@ -345,7 +334,6 @@ theorem Concrete.widePushout_exists_rep' {B : C} {α : Type _} [Nonempty α] {X
     simp only [← arrow_ι _ (Inhabited.default α), comp_apply]
   · use i, y
 #align category_theory.limits.concrete.wide_pushout_exists_rep' CategoryTheory.Limits.Concrete.widePushout_exists_rep'
--/
 
 end WidePushout

cb3ceec8

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -198,7 +198,7 @@ theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColim
     intro a
     obtain ⟨b, hb⟩ := this (TX.hom a)
     refine' ⟨b, _⟩
-    apply_fun TX.inv  at hb 
+    apply_fun TX.inv at hb 
     change (TX.hom ≫ TX.inv) (ff b) = (TX.hom ≫ TX.inv) _ at hb 
     simpa only [TX.hom_inv_id] using hb
   have : TX.hom ∘ ff = fun a => G.ι.app a.1 a.2 :=
@@ -265,7 +265,7 @@ theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsCol
   let hG := Types.colimitCoconeIsColimit.{v, v} (F ⋙ forget C)
   let T : E ≅ G := hE.unique_up_to_iso hG
   let TX : E.X ≅ G.X := (cocones.forget _).mapIso T
-  apply_fun TX.hom  at h 
+  apply_fun TX.hom at h 
   change (E.ι.app i ≫ TX.hom) x = (E.ι.app j ≫ TX.hom) y at h 
   erw [T.hom.w, T.hom.w] at h 
   replace h := Quot.exact _ h

cb3ceec8

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -120,7 +120,7 @@ def Concrete.multiequalizerEquivAux (I : MulticospanIndex C) :
       by
       have a := x.2 (walking_multicospan.hom.fst i)
       have b := x.2 (walking_multicospan.hom.snd i)
-      rw [← b] at a
+      rw [← b] at a 
       exact a⟩
   invFun x :=
     { val := fun j =>
@@ -184,7 +184,7 @@ variable {C : Type u} [Category.{v} C] [ConcreteCategory.{v} C] {J : Type v} [Sm
   (F : J ⥤ C) [PreservesColimit F (forget C)]
 
 theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColimit D) :
-    let ff : (Σj : J, F.obj j) → D.pt := fun a => D.ι.app a.1 a.2
+    let ff : (Σ j : J, F.obj j) → D.pt := fun a => D.ι.app a.1 a.2
     Function.Surjective ff :=
   by
   intro ff
@@ -198,8 +198,8 @@ theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColim
     intro a
     obtain ⟨b, hb⟩ := this (TX.hom a)
     refine' ⟨b, _⟩
-    apply_fun TX.inv  at hb
-    change (TX.hom ≫ TX.inv) (ff b) = (TX.hom ≫ TX.inv) _ at hb
+    apply_fun TX.inv  at hb 
+    change (TX.hom ≫ TX.inv) (ff b) = (TX.hom ≫ TX.inv) _ at hb 
     simpa only [TX.hom_inv_id] using hb
   have : TX.hom ∘ ff = fun a => G.ι.app a.1 a.2 :=
     by
@@ -212,19 +212,19 @@ theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColim
 #align category_theory.limits.concrete.from_union_surjective_of_is_colimit CategoryTheory.Limits.Concrete.from_union_surjective_of_isColimit
 
 theorem Concrete.isColimit_exists_rep {D : Cocone F} (hD : IsColimit D) (x : D.pt) :
-    ∃ (j : J)(y : F.obj j), D.ι.app j y = x :=
+    ∃ (j : J) (y : F.obj j), D.ι.app j y = x :=
   by
   obtain ⟨a, rfl⟩ := concrete.from_union_surjective_of_is_colimit F hD x
   exact ⟨a.1, a.2, rfl⟩
 #align category_theory.limits.concrete.is_colimit_exists_rep CategoryTheory.Limits.Concrete.isColimit_exists_rep
 
 theorem Concrete.colimit_exists_rep [HasColimit F] (x : colimit F) :
-    ∃ (j : J)(y : F.obj j), colimit.ι F j y = x :=
+    ∃ (j : J) (y : F.obj j), colimit.ι F j y = x :=
   Concrete.isColimit_exists_rep F (colimit.isColimit _) x
 #align category_theory.limits.concrete.colimit_exists_rep CategoryTheory.Limits.Concrete.colimit_exists_rep
 
 theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsColimit D)
-    (x : F.obj i) (y : F.obj j) (h : ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y) :
+    (x : F.obj i) (y : F.obj j) (h : ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y) :
     D.ι.app i x = D.ι.app j y := by
   let E := (forget C).mapCocone D
   let hE : is_colimit E := is_colimit_of_preserves _ hD
@@ -246,7 +246,7 @@ theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsCol
 #align category_theory.limits.concrete.is_colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_exists
 
 theorem Concrete.colimit_rep_eq_of_exists [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j)
-    (h : ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y) :
+    (h : ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y) :
     colimit.ι F i x = colimit.ι F j y :=
   Concrete.isColimit_rep_eq_of_exists F (colimit.isColimit _) x y h
 #align category_theory.limits.concrete.colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.colimit_rep_eq_of_exists
@@ -257,7 +257,7 @@ variable [IsFiltered J]
 
 theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) (h : D.ι.app _ x = D.ι.app _ y) :
-    ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=
+    ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y :=
   by
   let E := (forget C).mapCocone D
   let hE : is_colimit E := is_colimit_of_preserves _ hD
@@ -265,13 +265,13 @@ theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsCol
   let hG := Types.colimitCoconeIsColimit.{v, v} (F ⋙ forget C)
   let T : E ≅ G := hE.unique_up_to_iso hG
   let TX : E.X ≅ G.X := (cocones.forget _).mapIso T
-  apply_fun TX.hom  at h
-  change (E.ι.app i ≫ TX.hom) x = (E.ι.app j ≫ TX.hom) y at h
-  erw [T.hom.w, T.hom.w] at h
+  apply_fun TX.hom  at h 
+  change (E.ι.app i ≫ TX.hom) x = (E.ι.app j ≫ TX.hom) y at h 
+  erw [T.hom.w, T.hom.w] at h 
   replace h := Quot.exact _ h
   suffices
-    ∀ (a b : Σj, F.obj j) (h : EqvGen (Limits.Types.Quot.Rel.{v, v} (F ⋙ forget C)) a b),
-      ∃ (k : _)(f : a.1 ⟶ k)(g : b.1 ⟶ k), F.map f a.2 = F.map g b.2
+    ∀ (a b : Σ j, F.obj j) (h : EqvGen (Limits.Types.Quot.Rel.{v, v} (F ⋙ forget C)) a b),
+      ∃ (k : _) (f : a.1 ⟶ k) (g : b.1 ⟶ k), F.map f a.2 = F.map g b.2
     by exact this ⟨i, x⟩ ⟨j, y⟩ h
   intro a b h
   induction h
@@ -299,18 +299,18 @@ theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsCol
 
 theorem Concrete.isColimit_rep_eq_iff_exists {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) :
-    D.ι.app i x = D.ι.app j y ↔ ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=
+    D.ι.app i x = D.ι.app j y ↔ ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y :=
   ⟨Concrete.isColimit_exists_of_rep_eq _ hD _ _, Concrete.isColimit_rep_eq_of_exists _ hD _ _⟩
 #align category_theory.limits.concrete.is_colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists
 
 theorem Concrete.colimit_exists_of_rep_eq [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j)
     (h : colimit.ι F _ x = colimit.ι F _ y) :
-    ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=
+    ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y :=
   Concrete.isColimit_exists_of_rep_eq F (colimit.isColimit _) x y h
 #align category_theory.limits.concrete.colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eq
 
 theorem Concrete.colimit_rep_eq_iff_exists [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j) :
-    colimit.ι F i x = colimit.ι F j y ↔ ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=
+    colimit.ι F i x = colimit.ι F j y ↔ ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y :=
   ⟨Concrete.colimit_exists_of_rep_eq _ _ _, Concrete.colimit_rep_eq_of_exists _ _ _⟩
 #align category_theory.limits.concrete.colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.colimit_rep_eq_iff_exists
 
@@ -325,7 +325,7 @@ open WidePushoutShape
 #print CategoryTheory.Limits.Concrete.widePushout_exists_rep /-
 theorem Concrete.widePushout_exists_rep {B : C} {α : Type _} {X : α → C} (f : ∀ j : α, B ⟶ X j)
     [HasWidePushout.{v} B X f] [PreservesColimit (wideSpan B X f) (forget C)]
-    (x : widePushout B X f) : (∃ y : B, head f y = x) ∨ ∃ (i : α)(y : X i), ι f i y = x :=
+    (x : widePushout B X f) : (∃ y : B, head f y = x) ∨ ∃ (i : α) (y : X i), ι f i y = x :=
   by
   obtain ⟨_ | j, y, rfl⟩ := concrete.colimit_exists_rep _ x
   · use y
@@ -337,7 +337,7 @@ theorem Concrete.widePushout_exists_rep {B : C} {α : Type _} {X : α → C} (f
 #print CategoryTheory.Limits.Concrete.widePushout_exists_rep' /-
 theorem Concrete.widePushout_exists_rep' {B : C} {α : Type _} [Nonempty α] {X : α → C}
     (f : ∀ j : α, B ⟶ X j) [HasWidePushout.{v} B X f] [PreservesColimit (wideSpan B X f) (forget C)]
-    (x : widePushout B X f) : ∃ (i : α)(y : X i), ι f i y = x :=
+    (x : widePushout B X f) : ∃ (i : α) (y : X i), ι f i y = x :=
   by
   rcases concrete.wide_pushout_exists_rep f x with (⟨y, rfl⟩ | ⟨i, y, rfl⟩)
   · inhabit α

cb3ceec8

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -37,9 +37,6 @@ section Limits
 variable {C : Type u} [Category.{v} C] [ConcreteCategory.{max w v} C] {J : Type w} [SmallCategory J]
   (F : J ⥤ C) [PreservesLimit F (forget C)]
 
-/- warning: category_theory.limits.concrete.to_product_injective_of_is_limit -> CategoryTheory.Limits.Concrete.to_product_injective_of_isLimit is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.to_product_injective_of_is_limit CategoryTheory.Limits.Concrete.to_product_injective_of_isLimitₓ'. -/
 theorem Concrete.to_product_injective_of_isLimit {D : Cone F} (hD : IsLimit D) :
     Function.Injective fun (x : D.pt) (j : J) => D.π.app j x :=
   by
@@ -57,17 +54,11 @@ theorem Concrete.to_product_injective_of_isLimit {D : Cone F} (hD : IsLimit D) :
   apply Subtype.ext
 #align category_theory.limits.concrete.to_product_injective_of_is_limit CategoryTheory.Limits.Concrete.to_product_injective_of_isLimit
 
-/- warning: category_theory.limits.concrete.is_limit_ext -> CategoryTheory.Limits.Concrete.isLimit_ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_limit_ext CategoryTheory.Limits.Concrete.isLimit_extₓ'. -/
 theorem Concrete.isLimit_ext {D : Cone F} (hD : IsLimit D) (x y : D.pt) :
     (∀ j, D.π.app j x = D.π.app j y) → x = y := fun h =>
   Concrete.to_product_injective_of_isLimit _ hD (funext h)
 #align category_theory.limits.concrete.is_limit_ext CategoryTheory.Limits.Concrete.isLimit_ext
 
-/- warning: category_theory.limits.concrete.limit_ext -> CategoryTheory.Limits.Concrete.limit_ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.limit_ext CategoryTheory.Limits.Concrete.limit_extₓ'. -/
 theorem Concrete.limit_ext [HasLimit F] (x y : limit F) :
     (∀ j, limit.π F j x = limit.π F j y) → x = y :=
   Concrete.isLimit_ext F (limit.isLimit _) _ _
@@ -119,9 +110,6 @@ theorem Concrete.multiequalizer_ext {I : MulticospanIndex.{w} C} [HasMultiequali
 #align category_theory.limits.concrete.multiequalizer_ext CategoryTheory.Limits.Concrete.multiequalizer_ext
 -/
 
-/- warning: category_theory.limits.concrete.multiequalizer_equiv_aux -> CategoryTheory.Limits.Concrete.multiequalizerEquivAux is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.multiequalizer_equiv_aux CategoryTheory.Limits.Concrete.multiequalizerEquivAuxₓ'. -/
 /-- An auxiliary equivalence to be used in `multiequalizer_equiv` below.-/
 def Concrete.multiequalizerEquivAux (I : MulticospanIndex C) :
     (I.multicospan ⋙ forget C).sections ≃
@@ -168,9 +156,6 @@ noncomputable def Concrete.multiequalizerEquiv (I : MulticospanIndex.{w} C) [Has
 #align category_theory.limits.concrete.multiequalizer_equiv CategoryTheory.Limits.Concrete.multiequalizerEquiv
 -/
 
-/- warning: category_theory.limits.concrete.multiequalizer_equiv_apply -> CategoryTheory.Limits.Concrete.multiequalizerEquiv_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.multiequalizer_equiv_apply CategoryTheory.Limits.Concrete.multiequalizerEquiv_applyₓ'. -/
 @[simp]
 theorem Concrete.multiequalizerEquiv_apply (I : MulticospanIndex.{w} C) [HasMultiequalizer I]
     [PreservesLimit I.multicospan (forget C)] (x : multiequalizer I) (i : I.L) :
@@ -185,9 +170,6 @@ end Limits
 
 section Colimits
 
-/- warning: category_theory.limits.cokernel_funext -> CategoryTheory.Limits.cokernel_funext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.cokernel_funext CategoryTheory.Limits.cokernel_funextₓ'. -/
 -- We don't mark this as an `@[ext]` lemma as we don't always want to work elementwise.
 theorem cokernel_funext {C : Type _} [Category C] [HasZeroMorphisms C] [ConcreteCategory C]
     {M N K : C} {f : M ⟶ N} [HasCokernel f] {g h : cokernel f ⟶ K}
@@ -201,9 +183,6 @@ theorem cokernel_funext {C : Type _} [Category C] [HasZeroMorphisms C] [Concrete
 variable {C : Type u} [Category.{v} C] [ConcreteCategory.{v} C] {J : Type v} [SmallCategory J]
   (F : J ⥤ C) [PreservesColimit F (forget C)]
 
-/- warning: category_theory.limits.concrete.from_union_surjective_of_is_colimit -> CategoryTheory.Limits.Concrete.from_union_surjective_of_isColimit is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.from_union_surjective_of_is_colimit CategoryTheory.Limits.Concrete.from_union_surjective_of_isColimitₓ'. -/
 theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColimit D) :
     let ff : (Σj : J, F.obj j) → D.pt := fun a => D.ι.app a.1 a.2
     Function.Surjective ff :=
@@ -232,9 +211,6 @@ theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColim
   exact ⟨⟨j, a⟩, rfl⟩
 #align category_theory.limits.concrete.from_union_surjective_of_is_colimit CategoryTheory.Limits.Concrete.from_union_surjective_of_isColimit
 
-/- warning: category_theory.limits.concrete.is_colimit_exists_rep -> CategoryTheory.Limits.Concrete.isColimit_exists_rep is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_colimit_exists_rep CategoryTheory.Limits.Concrete.isColimit_exists_repₓ'. -/
 theorem Concrete.isColimit_exists_rep {D : Cocone F} (hD : IsColimit D) (x : D.pt) :
     ∃ (j : J)(y : F.obj j), D.ι.app j y = x :=
   by
@@ -242,20 +218,11 @@ theorem Concrete.isColimit_exists_rep {D : Cocone F} (hD : IsColimit D) (x : D.p
   exact ⟨a.1, a.2, rfl⟩
 #align category_theory.limits.concrete.is_colimit_exists_rep CategoryTheory.Limits.Concrete.isColimit_exists_rep
 
-/- warning: category_theory.limits.concrete.colimit_exists_rep -> CategoryTheory.Limits.Concrete.colimit_exists_rep is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.colimit_exists_rep CategoryTheory.Limits.Concrete.colimit_exists_repₓ'. -/
 theorem Concrete.colimit_exists_rep [HasColimit F] (x : colimit F) :
     ∃ (j : J)(y : F.obj j), colimit.ι F j y = x :=
   Concrete.isColimit_exists_rep F (colimit.isColimit _) x
 #align category_theory.limits.concrete.colimit_exists_rep CategoryTheory.Limits.Concrete.colimit_exists_rep
 
-/- warning: category_theory.limits.concrete.is_colimit_rep_eq_of_exists -> CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_exists is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_existsₓ'. -/
 theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) (h : ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y) :
     D.ι.app i x = D.ι.app j y := by
@@ -278,9 +245,6 @@ theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsCol
   exact Quot.sound ⟨g, rfl⟩
 #align category_theory.limits.concrete.is_colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_exists
 
-/- warning: category_theory.limits.concrete.colimit_rep_eq_of_exists -> CategoryTheory.Limits.Concrete.colimit_rep_eq_of_exists is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.colimit_rep_eq_of_existsₓ'. -/
 theorem Concrete.colimit_rep_eq_of_exists [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j)
     (h : ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y) :
     colimit.ι F i x = colimit.ι F j y :=
@@ -291,9 +255,6 @@ section FilteredColimits
 
 variable [IsFiltered J]
 
-/- warning: category_theory.limits.concrete.is_colimit_exists_of_rep_eq -> CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eqₓ'. -/
 theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) (h : D.ι.app _ x = D.ι.app _ y) :
     ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=
@@ -336,27 +297,18 @@ theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsCol
     rw [is_filtered.coeq_condition]
 #align category_theory.limits.concrete.is_colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eq
 
-/- warning: category_theory.limits.concrete.is_colimit_rep_eq_iff_exists -> CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_existsₓ'. -/
 theorem Concrete.isColimit_rep_eq_iff_exists {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) :
     D.ι.app i x = D.ι.app j y ↔ ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=
   ⟨Concrete.isColimit_exists_of_rep_eq _ hD _ _, Concrete.isColimit_rep_eq_of_exists _ hD _ _⟩
 #align category_theory.limits.concrete.is_colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists
 
-/- warning: category_theory.limits.concrete.colimit_exists_of_rep_eq -> CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eqₓ'. -/
 theorem Concrete.colimit_exists_of_rep_eq [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j)
     (h : colimit.ι F _ x = colimit.ι F _ y) :
     ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=
   Concrete.isColimit_exists_of_rep_eq F (colimit.isColimit _) x y h
 #align category_theory.limits.concrete.colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eq
 
-/- warning: category_theory.limits.concrete.colimit_rep_eq_iff_exists -> CategoryTheory.Limits.Concrete.colimit_rep_eq_iff_exists is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.colimit_rep_eq_iff_existsₓ'. -/
 theorem Concrete.colimit_rep_eq_iff_exists [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j) :
     colimit.ι F i x = colimit.ι F j y ↔ ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=
   ⟨Concrete.colimit_exists_of_rep_eq _ _ _, Concrete.colimit_rep_eq_of_exists _ _ _⟩

cb3ceec8

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -141,24 +141,17 @@ def Concrete.multiequalizerEquivAux (I : MulticospanIndex C) :
         | walking_multicospan.right b => I.fst b (x.1 _)
       property := by
         rintro (a | b) (a' | b') (f | f | f)
-        · change (I.multicospan.map (𝟙 _)) _ = _
-          simp
+        · change (I.multicospan.map (𝟙 _)) _ = _; simp
         · rfl
-        · dsimp
-          erw [← x.2 b']
-          rfl
-        · change (I.multicospan.map (𝟙 _)) _ = _
-          simp }
+        · dsimp; erw [← x.2 b']; rfl
+        · change (I.multicospan.map (𝟙 _)) _ = _; simp }
   left_inv := by
     intro x; ext (a | b)
     · rfl
     · change _ = x.val _
       rw [← x.2 (walking_multicospan.hom.fst b)]
       rfl
-  right_inv := by
-    intro x
-    ext i
-    rfl
+  right_inv := by intro x; ext i; rfl
 #align category_theory.limits.concrete.multiequalizer_equiv_aux CategoryTheory.Limits.Concrete.multiequalizerEquivAux
 
 #print CategoryTheory.Limits.Concrete.multiequalizerEquiv /-
@@ -275,8 +268,7 @@ theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsCol
   apply_fun TX.hom
   swap;
   · suffices Function.Bijective TX.hom by exact this.1
-    rw [← is_iso_iff_bijective]
-    apply is_iso.of_iso
+    rw [← is_iso_iff_bijective]; apply is_iso.of_iso
   change (E.ι.app i ≫ TX.hom) x = (E.ι.app j ≫ TX.hom) y
   erw [T.hom.w, T.hom.w]
   obtain ⟨k, f, g, h⟩ := h

cb3ceec8

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -38,10 +38,7 @@ variable {C : Type u} [Category.{v} C] [ConcreteCategory.{max w v} C] {J : Type
   (F : J ⥤ C) [PreservesLimit F (forget C)]
 
 /- warning: category_theory.limits.concrete.to_product_injective_of_is_limit -> CategoryTheory.Limits.Concrete.to_product_injective_of_isLimit is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.to_product_injective_of_is_limit CategoryTheory.Limits.Concrete.to_product_injective_of_isLimitₓ'. -/
 theorem Concrete.to_product_injective_of_isLimit {D : Cone F} (hD : IsLimit D) :
     Function.Injective fun (x : D.pt) (j : J) => D.π.app j x :=
@@ -61,10 +58,7 @@ theorem Concrete.to_product_injective_of_isLimit {D : Cone F} (hD : IsLimit D) :
 #align category_theory.limits.concrete.to_product_injective_of_is_limit CategoryTheory.Limits.Concrete.to_product_injective_of_isLimit
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_limit_ext CategoryTheory.Limits.Concrete.isLimit_extₓ'. -/
 theorem Concrete.isLimit_ext {D : Cone F} (hD : IsLimit D) (x y : D.pt) :
     (∀ j, D.π.app j x = D.π.app j y) → x = y := fun h =>
@@ -72,10 +66,7 @@ theorem Concrete.isLimit_ext {D : Cone F} (hD : IsLimit D) (x y : D.pt) :
 #align category_theory.limits.concrete.is_limit_ext CategoryTheory.Limits.Concrete.isLimit_ext
 
 /- warning: category_theory.limits.concrete.limit_ext -> CategoryTheory.Limits.Concrete.limit_ext is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.limit_ext CategoryTheory.Limits.Concrete.limit_extₓ'. -/
 theorem Concrete.limit_ext [HasLimit F] (x y : limit F) :
     (∀ j, limit.π F j x = limit.π F j y) → x = y :=
@@ -129,10 +120,7 @@ theorem Concrete.multiequalizer_ext {I : MulticospanIndex.{w} C} [HasMultiequali
 -/
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.multiequalizer_equiv_aux CategoryTheory.Limits.Concrete.multiequalizerEquivAuxₓ'. -/
 /-- An auxiliary equivalence to be used in `multiequalizer_equiv` below.-/
 def Concrete.multiequalizerEquivAux (I : MulticospanIndex C) :
@@ -188,10 +176,7 @@ noncomputable def Concrete.multiequalizerEquiv (I : MulticospanIndex.{w} C) [Has
 -/
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.multiequalizer_equiv_apply CategoryTheory.Limits.Concrete.multiequalizerEquiv_applyₓ'. -/
 @[simp]
 theorem Concrete.multiequalizerEquiv_apply (I : MulticospanIndex.{w} C) [HasMultiequalizer I]
@@ -208,10 +193,7 @@ end Limits
 section Colimits
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.cokernel_funext CategoryTheory.Limits.cokernel_funextₓ'. -/
 -- We don't mark this as an `@[ext]` lemma as we don't always want to work elementwise.
 theorem cokernel_funext {C : Type _} [Category C] [HasZeroMorphisms C] [ConcreteCategory C]
@@ -227,10 +209,7 @@ variable {C : Type u} [Category.{v} C] [ConcreteCategory.{v} C] {J : Type v} [Sm
   (F : J ⥤ C) [PreservesColimit F (forget C)]
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.from_union_surjective_of_is_colimit CategoryTheory.Limits.Concrete.from_union_surjective_of_isColimitₓ'. -/
 theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColimit D) :
     let ff : (Σj : J, F.obj j) → D.pt := fun a => D.ι.app a.1 a.2
@@ -261,10 +240,7 @@ theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColim
 #align category_theory.limits.concrete.from_union_surjective_of_is_colimit CategoryTheory.Limits.Concrete.from_union_surjective_of_isColimit
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_colimit_exists_rep CategoryTheory.Limits.Concrete.isColimit_exists_repₓ'. -/
 theorem Concrete.isColimit_exists_rep {D : Cocone F} (hD : IsColimit D) (x : D.pt) :
     ∃ (j : J)(y : F.obj j), D.ι.app j y = x :=
@@ -285,10 +261,7 @@ theorem Concrete.colimit_exists_rep [HasColimit F] (x : colimit F) :
 #align category_theory.limits.concrete.colimit_exists_rep CategoryTheory.Limits.Concrete.colimit_exists_rep
 
 /- warning: category_theory.limits.concrete.is_colimit_rep_eq_of_exists -> CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_exists is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_existsₓ'. -/
 theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) (h : ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y) :
@@ -314,10 +287,7 @@ theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsCol
 #align category_theory.limits.concrete.is_colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_exists
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.colimit_rep_eq_of_existsₓ'. -/
 theorem Concrete.colimit_rep_eq_of_exists [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j)
     (h : ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y) :
@@ -330,10 +300,7 @@ section FilteredColimits
 variable [IsFiltered J]
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eqₓ'. -/
 theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) (h : D.ι.app _ x = D.ι.app _ y) :
@@ -378,10 +345,7 @@ theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsCol
 #align category_theory.limits.concrete.is_colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eq
 
 /- warning: category_theory.limits.concrete.is_colimit_rep_eq_iff_exists -> CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_existsₓ'. -/
 theorem Concrete.isColimit_rep_eq_iff_exists {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) :
@@ -390,10 +354,7 @@ theorem Concrete.isColimit_rep_eq_iff_exists {D : Cocone F} {i j : J} (hD : IsCo
 #align category_theory.limits.concrete.is_colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eqₓ'. -/
 theorem Concrete.colimit_exists_of_rep_eq [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j)
     (h : colimit.ι F _ x = colimit.ι F _ y) :
@@ -402,10 +363,7 @@ theorem Concrete.colimit_exists_of_rep_eq [HasColimit F] {i j : J} (x : F.obj i)
 #align category_theory.limits.concrete.colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eq
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.colimit_rep_eq_iff_existsₓ'. -/
 theorem Concrete.colimit_rep_eq_iff_exists [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j) :
     colimit.ι F i x = colimit.ι F j y ↔ ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=

cb3ceec8

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -191,7 +191,7 @@ noncomputable def Concrete.multiequalizerEquiv (I : MulticospanIndex.{w} C) [Has
 lean 3 declaration is
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(CategoryTheory.Limits.Concrete.multiequalizerEquiv.{u1, u2, u3} C _inst_1 _inst_2 I _inst_5 _inst_6) x) i) (Prefunctor.map.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.multiequalizer.{u2, u3, u1} C _inst_1 I _inst_5) (CategoryTheory.Limits.MulticospanIndex.left.{u1, u2, u3} C _inst_1 I i) (CategoryTheory.Limits.Multiequalizer.ι.{u2, u3, u1} C _inst_1 I _inst_5 i) x)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.multiequalizer_equiv_apply CategoryTheory.Limits.Concrete.multiequalizerEquiv_applyₓ'. -/
 @[simp]
 theorem Concrete.multiequalizerEquiv_apply (I : MulticospanIndex.{w} C) [HasMultiequalizer I]

cb3ceec8

bump to nightly-2023-05-12-14

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

fab1af65

Diff

@@ -41,7 +41,7 @@ variable {C : Type u} [Category.{v} C] [ConcreteCategory.{max w v} C] {J : Type
 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] [_inst_2 : CategoryTheory.ConcreteCategory.{max u1 u2, u2, u3} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesLimit.{u1, u1, u2, max u2 u1, u3, max (succ u2) (succ u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} J _inst_3 F (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)] {D : CategoryTheory.Limits.Cone.{u1, u2, u1, u3} J _inst_3 C _inst_1 F}, (CategoryTheory.Limits.IsLimit.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D) -> (Function.Injective.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.ConcreteCategory.Forget.{max u2 u1, u2, u3} C _inst_1 _inst_2)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D)) (forall (j : J), Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} J _inst_3 C _inst_1 F) j)) (fun (x : Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.ConcreteCategory.Forget.{max u2 u1, u2, u3} C _inst_1 _inst_2)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D)) (j : J) => Prefunctor.map.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} J _inst_3 C _inst_1 (Prefunctor.obj.{succ u2, max (succ u1) (succ u2), u3, max (max u1 u2) u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max (max u1 u3) u2} (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max (max u1 u3) u2} (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u2, u1, u3} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u2, max u1 u2, u3, max (max u1 u3) u2} C _inst_1 (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u2, u1, u3} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D))) j) (Prefunctor.obj.{succ u1, succ u2, u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} J _inst_3 C _inst_1 F) j) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} J _inst_3 C _inst_1 (Prefunctor.obj.{succ u2, max (succ u1) (succ u2), u3, max (max u1 u2) u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max (max u1 u3) u2} (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max (max u1 u3) u2} (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u2, u1, u3} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u2, max u1 u2, u3, max (max u1 u3) u2} C _inst_1 (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u2, u1, u3} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D) j) x))
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] [_inst_2 : CategoryTheory.ConcreteCategory.{max u1 u2, u2, u3} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesLimit.{u1, u1, u2, max u2 u1, u3, max (succ u2) (succ u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} J _inst_3 F (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)] {D : CategoryTheory.Limits.Cone.{u1, u2, u1, u3} J _inst_3 C _inst_1 F}, (CategoryTheory.Limits.IsLimit.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D) -> (Function.Injective.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D)) (forall (j : J), Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} J _inst_3 C _inst_1 F) j)) (fun (x : Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D)) (j : J) => Prefunctor.map.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} J _inst_3 C _inst_1 (Prefunctor.obj.{succ u2, max (succ u1) (succ u2), u3, max (max u1 u2) u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max (max u1 u3) u2} (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max (max u1 u3) u2} (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u2, u1, u3} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u2, max u1 u2, u3, max (max u1 u3) u2} C _inst_1 (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u2, u1, u3} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D))) j) (Prefunctor.obj.{succ u1, succ u2, u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} J _inst_3 C _inst_1 F) j) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} J _inst_3 C _inst_1 (Prefunctor.obj.{succ u2, max (succ u1) (succ u2), u3, max (max u1 u2) u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max (max u1 u3) u2} (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max (max u1 u3) u2} (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u2, u1, u3} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u2, max u1 u2, u3, max (max u1 u3) u2} C _inst_1 (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u2, u1, u3} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D) j) x))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.to_product_injective_of_is_limit CategoryTheory.Limits.Concrete.to_product_injective_of_isLimitₓ'. -/
 theorem Concrete.to_product_injective_of_isLimit {D : Cone F} (hD : IsLimit D) :
     Function.Injective fun (x : D.pt) (j : J) => D.π.app j x :=
@@ -64,7 +64,7 @@ theorem Concrete.to_product_injective_of_isLimit {D : Cone F} (hD : IsLimit D) :
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] [_inst_2 : CategoryTheory.ConcreteCategory.{max u1 u2, u2, u3} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesLimit.{u1, u1, u2, max u1 u2, u3, succ (max u1 u2)} C _inst_1 Type.{max u1 u2} CategoryTheory.types.{max u1 u2} J _inst_3 F (CategoryTheory.forget.{u3, max u1 u2, u2} C _inst_1 _inst_2)] {D : CategoryTheory.Limits.Cone.{u1, u2, u1, u3} J _inst_3 C _inst_1 F}, (CategoryTheory.Limits.IsLimit.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D) -> (forall (x : coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u3, max u1 u2, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.Cone.pt.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D)) (y : coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u3, max u1 u2, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.Cone.pt.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D)), (forall (j : J), Eq.{succ (max u1 u2)} (coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u3, max u1 u2, u2} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} J _inst_3 C _inst_1 F j)) (coeFn.{succ u2, succ (max u1 u2)} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} J _inst_3 C _inst_1 (CategoryTheory.Functor.obj.{u2, max u1 u2, u3, max u1 u2 u1 u3} C _inst_1 (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Limits.Cone.pt.{u1, u2, u1, u3} J _inst_3 C 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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] [_inst_2 : CategoryTheory.ConcreteCategory.{max u1 u2, u2, u3} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesLimit.{u1, u1, u2, max u2 u1, u3, max (succ u2) (succ u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} J _inst_3 F (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)] {D : CategoryTheory.Limits.Cone.{u1, u2, u1, u3} J _inst_3 C _inst_1 F}, (CategoryTheory.Limits.IsLimit.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D) -> (forall (x : Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} 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_inst_2)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D)), (forall (j : J), Eq.{max (succ u2) (succ u1)} (Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} J _inst_3 C _inst_1 F) j)) (Prefunctor.map.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) 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u1, u3} J _inst_3 C _inst_1 F D))) j) (Prefunctor.obj.{succ u1, succ u2, u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} J _inst_3 C _inst_1 F) j) (CategoryTheory.NatTrans.app.{u1, u2, u1, u3} J _inst_3 C _inst_1 (Prefunctor.obj.{succ u2, max (succ u1) (succ u2), u3, max (max u1 u2) u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max (max u1 u3) u2} (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max (max u1 u3) u2} (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u2, u1, u3} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u2, max u1 u2, u3, max (max u1 u3) u2} C _inst_1 (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u2, u1, u3} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D) j) x) (Prefunctor.map.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} J _inst_3 C _inst_1 (Prefunctor.obj.{succ u2, max (succ u1) (succ u2), u3, max (max u1 u2) u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max (max u1 u3) u2} (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max (max u1 u3) u2} (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) 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(CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u2, max (max u1 u3) u2} (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{max u1 u2, max (max u1 u3) u2} (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u2, u1, u3} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u2, max u1 u2, u3, max (max u1 u3) u2} C _inst_1 (CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u2, u1, u3} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u2, u1, u3} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D)) F (CategoryTheory.Limits.Cone.π.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D) j) y)) -> (Eq.{max (succ u2) (succ u1)} (Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.Cone.pt.{u1, u2, u1, u3} J _inst_3 C _inst_1 F D)) x y))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_limit_ext CategoryTheory.Limits.Concrete.isLimit_extₓ'. -/
 theorem Concrete.isLimit_ext {D : Cone F} (hD : IsLimit D) (x y : D.pt) :
     (∀ j, D.π.app j x = D.π.app j y) → x = y := fun h =>
@@ -75,7 +75,7 @@ theorem Concrete.isLimit_ext {D : Cone F} (hD : IsLimit D) (x y : D.pt) :
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] [_inst_2 : CategoryTheory.ConcreteCategory.{max u1 u2, u2, u3} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesLimit.{u1, u1, u2, max u1 u2, u3, succ (max u1 u2)} C _inst_1 Type.{max u1 u2} CategoryTheory.types.{max u1 u2} J _inst_3 F (CategoryTheory.forget.{u3, max u1 u2, u2} C _inst_1 _inst_2)] [_inst_5 : CategoryTheory.Limits.HasLimit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F] (x : coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u3, max u1 u2, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5)) (y : coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u3, max u1 u2, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5)), (forall (j : J), Eq.{succ (max u1 u2)} (coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u3, max u1 u2, u2} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} J _inst_3 C _inst_1 F j)) (coeFn.{succ u2, succ (max u1 u2)} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} J _inst_3 C _inst_1 F j)) (fun (f : Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} J _inst_3 C _inst_1 F j)) => (coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u3, max u1 u2, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5)) -> (coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u3, max u1 u2, u2} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} J _inst_3 C _inst_1 F j))) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u3, u2, max u1 u2} C _inst_1 _inst_2 (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} J _inst_3 C _inst_1 F j)) (CategoryTheory.Limits.limit.π.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5 j) x) (coeFn.{succ u2, succ (max u1 u2)} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} J _inst_3 C _inst_1 F j)) (fun (f : Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} J _inst_3 C _inst_1 F j)) => (coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u3, max u1 u2, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5)) -> (coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u3, max u1 u2, u2} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} J _inst_3 C _inst_1 F j))) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u3, u2, max u1 u2} C _inst_1 _inst_2 (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5) (CategoryTheory.Functor.obj.{u1, u2, u1, u3} J _inst_3 C _inst_1 F j)) (CategoryTheory.Limits.limit.π.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5 j) y)) -> (Eq.{succ (max u1 u2)} (coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u3, max u1 u2, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5)) x y)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] [_inst_2 : CategoryTheory.ConcreteCategory.{max u1 u2, u2, u3} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesLimit.{u1, u1, u2, max u2 u1, u3, max (succ u2) (succ u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} J _inst_3 F (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)] [_inst_5 : CategoryTheory.Limits.HasLimit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F] (x : Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.ConcreteCategory.Forget.{max u2 u1, u2, u3} C _inst_1 _inst_2)) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5)) (y : Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.ConcreteCategory.Forget.{max u2 u1, u2, u3} C _inst_1 _inst_2)) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5)), (forall (j : J), Eq.{max (succ u2) (succ u1)} (Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} J _inst_3 C _inst_1 F) j)) (Prefunctor.map.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5) (Prefunctor.obj.{succ u1, succ u2, u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} J _inst_3 C _inst_1 F) j) (CategoryTheory.Limits.limit.π.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5 j) x) (Prefunctor.map.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5) (Prefunctor.obj.{succ u1, succ u2, u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} J _inst_3 C _inst_1 F) j) (CategoryTheory.Limits.limit.π.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5 j) y)) -> (Eq.{max (succ u2) (succ u1)} (Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.ConcreteCategory.Forget.{max u2 u1, u2, u3} C _inst_1 _inst_2)) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5)) x y)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] [_inst_2 : CategoryTheory.ConcreteCategory.{max u1 u2, u2, u3} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u2, u1, u3} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesLimit.{u1, u1, u2, max u2 u1, u3, max (succ u2) (succ u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} J _inst_3 F (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)] [_inst_5 : CategoryTheory.Limits.HasLimit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F] (x : Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5)) (y : Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5)), (forall (j : J), Eq.{max (succ u2) (succ u1)} (Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u2, u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} J _inst_3 C _inst_1 F) j)) (Prefunctor.map.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5) (Prefunctor.obj.{succ u1, succ u2, u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} J _inst_3 C _inst_1 F) j) (CategoryTheory.Limits.limit.π.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5 j) x) (Prefunctor.map.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5) (Prefunctor.obj.{succ u1, succ u2, u1, u3} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u1, u3} J _inst_3 C _inst_1 F) j) (CategoryTheory.Limits.limit.π.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5 j) y)) -> (Eq.{max (succ u2) (succ u1)} (Prefunctor.obj.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.limit.{u1, u1, u2, u3} J _inst_3 C _inst_1 F _inst_5)) x y)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.limit_ext CategoryTheory.Limits.Concrete.limit_extₓ'. -/
 theorem Concrete.limit_ext [HasLimit F] (x y : limit F) :
     (∀ j, limit.π F j x = limit.π F j y) → x = y :=
@@ -132,7 +132,7 @@ theorem Concrete.multiequalizer_ext {I : MulticospanIndex.{w} C} [HasMultiequali
 lean 3 declaration is
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] [_inst_2 : CategoryTheory.ConcreteCategory.{max u1 u2, u2, u3} C _inst_1] (I : CategoryTheory.Limits.MulticospanIndex.{u4, u2, u3} C _inst_1), Equiv.{succ (max u4 u1 u2), max 1 (succ u4) (succ (max u1 u2))} (coeSort.{succ (max u4 u1 u2), succ (succ (max u4 u1 u2))} (Set.{max u4 u1 u2} (forall (j : CategoryTheory.Limits.WalkingMulticospan.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)), CategoryTheory.Functor.obj.{u4, max u1 u2, u4, succ (max u1 u2)} (CategoryTheory.Limits.WalkingMulticospan.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)) (CategoryTheory.Limits.WalkingMulticospan.CategoryTheory.smallCategory.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)) Type.{max u1 u2} CategoryTheory.types.{max u1 u2} (CategoryTheory.Functor.comp.{u4, u2, max u1 u2, u4, u3, succ (max u1 u2)} (CategoryTheory.Limits.WalkingMulticospan.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)) (CategoryTheory.Limits.WalkingMulticospan.CategoryTheory.smallCategory.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)) C _inst_1 Type.{max u1 u2} CategoryTheory.types.{max u1 u2} (CategoryTheory.Limits.MulticospanIndex.multicospan.{u2, u3, u4} C _inst_1 I) (CategoryTheory.forget.{u3, max u1 u2, u2} C _inst_1 _inst_2)) j)) Type.{max u4 u1 u2} (Set.hasCoeToSort.{max u4 u1 u2} (forall (j : CategoryTheory.Limits.WalkingMulticospan.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)), CategoryTheory.Functor.obj.{u4, max u1 u2, u4, succ (max u1 u2)} (CategoryTheory.Limits.WalkingMulticospan.{u4} 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u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)) (CategoryTheory.Limits.WalkingMulticospan.CategoryTheory.smallCategory.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)) C _inst_1 Type.{max u1 u2} CategoryTheory.types.{max u1 u2} (CategoryTheory.Limits.MulticospanIndex.multicospan.{u2, u3, u4} C _inst_1 I) (CategoryTheory.forget.{u3, max u1 u2, u2} C _inst_1 _inst_2)) j)) (CategoryTheory.Functor.sections.{u4, max u1 u2, u4} (CategoryTheory.Limits.WalkingMulticospan.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)) (CategoryTheory.Limits.WalkingMulticospan.CategoryTheory.smallCategory.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)) (CategoryTheory.Functor.comp.{u4, u2, max u1 u2, u4, u3, succ (max u1 u2)} (CategoryTheory.Limits.WalkingMulticospan.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)) (CategoryTheory.Limits.WalkingMulticospan.CategoryTheory.smallCategory.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)) C _inst_1 Type.{max u1 u2} CategoryTheory.types.{max u1 u2} (CategoryTheory.Limits.MulticospanIndex.multicospan.{u2, u3, u4} C _inst_1 I) (CategoryTheory.forget.{u3, max u1 u2, u2} C _inst_1 _inst_2)))) (Subtype.{max (succ u4) (succ (max u1 u2))} (forall (i : CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I), coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u3, max u1 u2, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.MulticospanIndex.left.{u4, u2, u3} C _inst_1 I i)) (fun (x : forall (i : CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I), coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u3, max u1 u2, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.MulticospanIndex.left.{u4, u2, u3} C _inst_1 I i)) => forall (i : CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I), Eq.{succ (max u1 u2)} (coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u3, max u1 u2, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.MulticospanIndex.right.{u4, u2, u3} C _inst_1 I i)) (coeFn.{succ u2, succ (max u1 u2)} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Limits.MulticospanIndex.left.{u4, u2, u3} C _inst_1 I (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I i)) (CategoryTheory.Limits.MulticospanIndex.right.{u4, u2, u3} C _inst_1 I i)) (fun (f : Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Limits.MulticospanIndex.left.{u4, u2, u3} C _inst_1 I (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I i)) (CategoryTheory.Limits.MulticospanIndex.right.{u4, u2, u3} C _inst_1 I i)) => (coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u3, max u1 u2, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.MulticospanIndex.left.{u4, u2, u3} C _inst_1 I (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I i))) -> (coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u3, max u1 u2, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.MulticospanIndex.right.{u4, u2, u3} C _inst_1 I i))) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u3, u2, max u1 u2} C _inst_1 _inst_2 (CategoryTheory.Limits.MulticospanIndex.left.{u4, u2, u3} C _inst_1 I (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I i)) (CategoryTheory.Limits.MulticospanIndex.right.{u4, u2, u3} C _inst_1 I i)) (CategoryTheory.Limits.MulticospanIndex.fst.{u4, u2, u3} C _inst_1 I i) (x (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I i))) (coeFn.{succ u2, succ (max u1 u2)} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Limits.MulticospanIndex.left.{u4, u2, u3} C _inst_1 I (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I i)) (CategoryTheory.Limits.MulticospanIndex.right.{u4, u2, u3} C _inst_1 I i)) (fun (f : Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Limits.MulticospanIndex.left.{u4, u2, u3} C _inst_1 I (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I i)) (CategoryTheory.Limits.MulticospanIndex.right.{u4, u2, u3} C _inst_1 I i)) => (coeSort.{succ u3, succ (succ (max u1 u2))} C Type.{max u1 u2} 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 but is expected to have type
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(CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)))) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u4, max u2 u1, u4, succ (max u2 u1)} (CategoryTheory.Limits.WalkingMulticospan.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)) (CategoryTheory.Limits.WalkingMulticospan.instSmallCategoryWalkingMulticospan.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)) Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.Functor.comp.{u4, u2, max u2 u1, u4, u3, max (succ u2) (succ u1)} (CategoryTheory.Limits.WalkingMulticospan.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)) (CategoryTheory.Limits.WalkingMulticospan.instSmallCategoryWalkingMulticospan.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)) C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.Limits.MulticospanIndex.multicospan.{u2, u3, u4} C _inst_1 I) (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2))) j) (CategoryTheory.Functor.sections.{u4, max u2 u1, u4} (CategoryTheory.Limits.WalkingMulticospan.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I)) (CategoryTheory.Limits.WalkingMulticospan.instSmallCategoryWalkingMulticospan.{u4} (CategoryTheory.Limits.MulticospanIndex.L.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.R.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.fstTo.{u4, u2, u3} C _inst_1 I) (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, 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_inst_2)) (CategoryTheory.Limits.MulticospanIndex.left.{u4, u2, u3} C _inst_1 I (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I i)) (CategoryTheory.Limits.MulticospanIndex.right.{u4, u2, u3} C _inst_1 I i) (CategoryTheory.Limits.MulticospanIndex.snd.{u4, u2, u3} C _inst_1 I i) (x (CategoryTheory.Limits.MulticospanIndex.sndTo.{u4, u2, u3} C _inst_1 I i)))))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.multiequalizer_equiv_aux CategoryTheory.Limits.Concrete.multiequalizerEquivAuxₓ'. -/
 /-- An auxiliary equivalence to be used in `multiequalizer_equiv` below.-/
 def Concrete.multiequalizerEquivAux (I : MulticospanIndex C) :
@@ -191,7 +191,7 @@ noncomputable def Concrete.multiequalizerEquiv (I : MulticospanIndex.{w} C) [Has
 lean 3 declaration is
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(CategoryTheory.Limits.Concrete.multiequalizerEquiv.{u1, u2, u3} C _inst_1 _inst_2 I _inst_5 _inst_6) x) i) (Prefunctor.map.{succ u2, succ (max u2 u1), u3, succ (max u2 u1)} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{max u2 u1} (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} (CategoryTheory.Category.toCategoryStruct.{max u2 u1, succ (max u2 u1)} Type.{max u2 u1} CategoryTheory.types.{max u2 u1})) (CategoryTheory.Functor.toPrefunctor.{u2, max u2 u1, u3, succ (max u2 u1)} C _inst_1 Type.{max u2 u1} CategoryTheory.types.{max u2 u1} (CategoryTheory.forget.{u3, max u2 u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.multiequalizer.{u2, u3, u1} C _inst_1 I _inst_5) (CategoryTheory.Limits.MulticospanIndex.left.{u1, u2, u3} C _inst_1 I i) (CategoryTheory.Limits.Multiequalizer.ι.{u2, u3, u1} C _inst_1 I _inst_5 i) x)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.multiequalizer_equiv_apply CategoryTheory.Limits.Concrete.multiequalizerEquiv_applyₓ'. -/
 @[simp]
 theorem Concrete.multiequalizerEquiv_apply (I : MulticospanIndex.{w} C) [HasMultiequalizer I]
@@ -211,7 +211,7 @@ section Colimits
 lean 3 declaration is
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u2, u1} C _inst_1] [_inst_3 : CategoryTheory.ConcreteCategory.{u3, u2, u1} C _inst_1] {M : C} {N : C} {K : C} {f : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) M N} [_inst_4 : CategoryTheory.Limits.HasCokernel.{u2, u1} C _inst_1 _inst_2 M N f] {g : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4) K} {h : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4) K}, (forall (n : coeSort.{succ u1, succ (succ u3)} C Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, u3, u2} C _inst_1 _inst_3) N), Eq.{succ u3} (coeSort.{succ u1, succ (succ u3)} C Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, u3, u2} C _inst_1 _inst_3) K) (coeFn.{succ u2, succ u3} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4) K) (fun (f_1 : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4) K) => (coeSort.{succ u1, succ (succ u3)} C Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, u3, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4)) -> (coeSort.{succ u1, succ (succ u3)} C Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, u3, u2} C _inst_1 _inst_3) K)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u1, u2, u3} C _inst_1 _inst_3 (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4) K) g (coeFn.{succ u2, succ u3} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) N (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4)) (fun (f_1 : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) N (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4)) => (coeSort.{succ u1, succ (succ u3)} C Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, u3, u2} C _inst_1 _inst_3) N) -> (coeSort.{succ u1, succ (succ u3)} C Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, u3, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4))) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u1, u2, u3} C _inst_1 _inst_3 N (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4)) (CategoryTheory.Limits.cokernel.π.{u2, u1} C _inst_1 _inst_2 M N f _inst_4) n)) (coeFn.{succ u2, succ u3} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4) K) (fun (f_1 : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4) K) => (coeSort.{succ u1, succ (succ u3)} C Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, u3, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4)) -> (coeSort.{succ u1, succ (succ u3)} C Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, u3, u2} C _inst_1 _inst_3) K)) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u1, u2, u3} C _inst_1 _inst_3 (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4) K) h (coeFn.{succ u2, succ u3} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) N (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4)) (fun (f_1 : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) N (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4)) => (coeSort.{succ u1, succ (succ u3)} C Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, u3, u2} C _inst_1 _inst_3) N) -> (coeSort.{succ u1, succ (succ u3)} C Type.{u3} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u1, u3, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4))) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u1, u2, u3} C _inst_1 _inst_3 N (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4)) (CategoryTheory.Limits.cokernel.π.{u2, u1} C _inst_1 _inst_2 M N f _inst_4) n))) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Limits.cokernel.{u2, u1} C _inst_1 _inst_2 M N f _inst_4) K) g h)
 but is expected to have type
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u2, u3} C _inst_1] [_inst_3 : CategoryTheory.ConcreteCategory.{u1, u2, u3} C _inst_1] {M : C} {N : C} {K : C} {f : Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) M N} [_inst_4 : CategoryTheory.Limits.HasCokernel.{u2, u3} C _inst_1 _inst_2 M N f] {g : Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Limits.cokernel.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) K} {h : Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Limits.cokernel.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) K}, (forall (n : Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.ConcreteCategory.Forget.{u1, u2, u3} C _inst_1 _inst_3)) N), Eq.{succ u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_1 _inst_3)) K) (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Limits.cokernel.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) K g (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_1 _inst_3)) N (CategoryTheory.Limits.cokernel.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) (CategoryTheory.Limits.cokernel.π.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) n)) (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Limits.cokernel.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) K h (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_1 _inst_3)) N (CategoryTheory.Limits.cokernel.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) (CategoryTheory.Limits.cokernel.π.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) n))) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Limits.cokernel.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) K) g h)
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u2, u3} C _inst_1] [_inst_3 : CategoryTheory.ConcreteCategory.{u1, u2, u3} C _inst_1] {M : C} {N : C} {K : C} {f : Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) M N} [_inst_4 : CategoryTheory.Limits.HasCokernel.{u2, u3} C _inst_1 _inst_2 M N f] {g : Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Limits.cokernel.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) K} {h : Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Limits.cokernel.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) K}, (forall (n : Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_1 _inst_3)) N), Eq.{succ u1} (Prefunctor.obj.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_1 _inst_3)) K) (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Limits.cokernel.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) K g (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_1 _inst_3)) N (CategoryTheory.Limits.cokernel.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) (CategoryTheory.Limits.cokernel.π.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) n)) (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Limits.cokernel.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) K h (Prefunctor.map.{succ u2, succ u1, u3, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u3, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u3, u1, u2} C _inst_1 _inst_3)) N (CategoryTheory.Limits.cokernel.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) (CategoryTheory.Limits.cokernel.π.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) n))) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (CategoryTheory.Limits.cokernel.{u2, u3} C _inst_1 _inst_2 M N f _inst_4) K) g h)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.cokernel_funext CategoryTheory.Limits.cokernel_funextₓ'. -/
 -- We don't mark this as an `@[ext]` lemma as we don't always want to work elementwise.
 theorem cokernel_funext {C : Type _} [Category C] [HasZeroMorphisms C] [ConcreteCategory C]
@@ -230,7 +230,7 @@ variable {C : Type u} [Category.{v} C] [ConcreteCategory.{v} C] {J : Type v} [Sm
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] {D : CategoryTheory.Limits.Cocone.{u1, u1, u1, u2} J _inst_3 C _inst_1 F}, (CategoryTheory.Limits.IsColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) -> (let ff : (Sigma.{u1, u1} J (fun (j : J) => coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j))) -> (coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) := fun (a : Sigma.{u1, u1} J (fun (j : J) => coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j))) => coeFn.{succ u1, succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F (Sigma.fst.{u1, u1} J (fun (j : J) => coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j)) a)) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) (Sigma.fst.{u1, u1} J (fun (j : J) => coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j)) a))) (fun (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F (Sigma.fst.{u1, u1} J (fun (j : J) => coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j)) a)) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 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Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j)) a)) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) (Sigma.fst.{u1, u1} J (fun (j : J) => coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j)) a))) (CategoryTheory.NatTrans.app.{u1, u1, u1, u2} J _inst_3 C _inst_1 F (CategoryTheory.Functor.obj.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) (CategoryTheory.Limits.Cocone.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) (Sigma.fst.{u1, u1} J (fun (j : J) => coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j)) a)) (Sigma.snd.{u1, u1} J (fun (j : J) => coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j)) a); Function.Surjective.{succ u1, succ u1} (Sigma.{u1, u1} J (fun (j : J) => coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j))) (coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) ff)
 but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] {D : CategoryTheory.Limits.Cocone.{u1, u1, u1, u2} J _inst_3 C _inst_1 F}, (CategoryTheory.Limits.IsColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) -> (let ff : (Sigma.{u1, u1} J (fun (j : J) => Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) 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(CategoryTheory.ConcreteCategory.Forget.{u1, u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) := fun (a : Sigma.{u1, u1} J (fun (j : J) => Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.ConcreteCategory.Forget.{u1, u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j))) => Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) (Sigma.fst.{u1, u1} J (fun (j : J) => Prefunctor.obj.{succ u1, succ u1, 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(CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D))) (Sigma.fst.{u1, u1} J (fun (j : J) => Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.ConcreteCategory.Forget.{u1, u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j)) a)) (CategoryTheory.NatTrans.app.{u1, u1, u1, u2} J _inst_3 C _inst_1 F (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) (CategoryTheory.Limits.Cocone.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) (Sigma.fst.{u1, u1} J (fun (j : J) => Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.ConcreteCategory.Forget.{u1, u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j)) a)) (Sigma.snd.{u1, u1} J (fun (j : J) => Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.ConcreteCategory.Forget.{u1, u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j)) a); Function.Surjective.{succ u1, succ u1} (Sigma.{u1, u1} J (fun (j : J) => Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.ConcreteCategory.Forget.{u1, u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j))) (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.ConcreteCategory.Forget.{u1, u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) ff)
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] {D : CategoryTheory.Limits.Cocone.{u1, u1, u1, u2} J _inst_3 C _inst_1 F}, (CategoryTheory.Limits.IsColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) -> (let ff : (Sigma.{u1, u1} J (fun (j : J) => Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j))) -> (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) := fun (a : Sigma.{u1, u1} J (fun (j : J) => Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j))) => Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) (Sigma.fst.{u1, u1} J (fun (j : J) => Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j)) a)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D))) (Sigma.fst.{u1, u1} J (fun (j : J) => Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j)) a)) (CategoryTheory.NatTrans.app.{u1, u1, u1, u2} J _inst_3 C _inst_1 F (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) (CategoryTheory.Limits.Cocone.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) (Sigma.fst.{u1, u1} J (fun (j : J) => Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j)) a)) (Sigma.snd.{u1, u1} J (fun (j : J) => Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j)) a); Function.Surjective.{succ u1, succ u1} (Sigma.{u1, u1} J (fun (j : J) => Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j))) (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) ff)
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.from_union_surjective_of_is_colimit CategoryTheory.Limits.Concrete.from_union_surjective_of_isColimitₓ'. -/
 theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColimit D) :
     let ff : (Σj : J, F.obj j) → D.pt := fun a => D.ι.app a.1 a.2
@@ -264,7 +264,7 @@ theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColim
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] {D : CategoryTheory.Limits.Cocone.{u1, u1, u1, u2} J _inst_3 C _inst_1 F}, (CategoryTheory.Limits.IsColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) -> (forall (x : coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)), Exists.{succ u1} J (fun (j : J) => Exists.{succ u1} (coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j)) (fun (y : coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j)) => Eq.{succ u1} (coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) j)) (coeFn.{succ u1, succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) j)) (fun (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) j)) => (coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j)) -> (coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) j))) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u2, u1, u1} C _inst_1 _inst_2 (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) j)) (CategoryTheory.NatTrans.app.{u1, u1, u1, u2} J _inst_3 C _inst_1 F (CategoryTheory.Functor.obj.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) (CategoryTheory.Limits.Cocone.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) j) y) x)))
 but is expected to have type
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(CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j)) => Eq.{succ u1} (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C 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_inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D))) j) (CategoryTheory.NatTrans.app.{u1, u1, u1, u2} J _inst_3 C _inst_1 F (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) (CategoryTheory.Limits.Cocone.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) j) y) x)))
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] {D : CategoryTheory.Limits.Cocone.{u1, u1, u1, u2} J _inst_3 C _inst_1 F}, (CategoryTheory.Limits.IsColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) -> (forall (x : Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)), Exists.{succ u1} J (fun (j : J) => Exists.{succ u1} (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j)) (fun (y : Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j)) => Eq.{succ u1} (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D))) j)) (Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D))) j) (CategoryTheory.NatTrans.app.{u1, u1, u1, u2} J _inst_3 C _inst_1 F (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) (CategoryTheory.Limits.Cocone.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) j) y) x)))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_colimit_exists_rep CategoryTheory.Limits.Concrete.isColimit_exists_repₓ'. -/
 theorem Concrete.isColimit_exists_rep {D : Cocone F} (hD : IsColimit D) (x : D.pt) :
     ∃ (j : J)(y : F.obj j), D.ι.app j y = x :=
@@ -277,7 +277,7 @@ theorem Concrete.isColimit_exists_rep {D : Cocone F} (hD : IsColimit D) (x : D.p
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] [_inst_5 : CategoryTheory.Limits.HasColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F] (x : coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_5)), Exists.{succ u1} J (fun (j : J) => Exists.{succ u1} (coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j)) (fun (y : coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j)) => Eq.{succ u1} (coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_5)) (coeFn.{succ u1, succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_5)) (fun (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_5)) => (coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j)) -> (coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_5))) (CategoryTheory.ConcreteCategory.hasCoeToFun.{u2, u1, u1} C _inst_1 _inst_2 (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_5)) (CategoryTheory.Limits.colimit.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_5 j) y) x))
 but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] [_inst_5 : CategoryTheory.Limits.HasColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F] (x : Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.ConcreteCategory.Forget.{u1, u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_5)), Exists.{succ u1} J (fun (j : J) => Exists.{succ u1} (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.ConcreteCategory.Forget.{u1, u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j)) (fun (y : Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.ConcreteCategory.Forget.{u1, u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j)) => Eq.{succ u1} (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_5)) (Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_5) (CategoryTheory.Limits.colimit.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_5 j) y) x))
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] [_inst_5 : CategoryTheory.Limits.HasColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F] (x : Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_5)), Exists.{succ u1} J (fun (j : J) => Exists.{succ u1} (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j)) (fun (y : Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j)) => Eq.{succ u1} (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_5)) (Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_5) (CategoryTheory.Limits.colimit.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_5 j) y) x))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.colimit_exists_rep CategoryTheory.Limits.Concrete.colimit_exists_repₓ'. -/
 theorem Concrete.colimit_exists_rep [HasColimit F] (x : colimit F) :
     ∃ (j : J)(y : F.obj j), colimit.ι F j y = x :=
@@ -288,7 +288,7 @@ theorem Concrete.colimit_exists_rep [HasColimit F] (x : colimit F) :
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] {D : CategoryTheory.Limits.Cocone.{u1, u1, u1, u2} J _inst_3 C _inst_1 F} {i : J} {j : J}, (CategoryTheory.Limits.IsColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) -> (forall (x : coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F i)) (y : coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) 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 but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] {D : CategoryTheory.Limits.Cocone.{u1, u1, u1, u2} J _inst_3 C _inst_1 F} {i : J} {j : J}, (CategoryTheory.Limits.IsColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) -> (forall (x : Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) 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(CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j k g) y))))) -> (Eq.{succ u1} (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J 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u1, u1, u2} J _inst_3 C _inst_1 F D)) (CategoryTheory.Limits.Cocone.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) i) x) (Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) 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u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) (CategoryTheory.Limits.Cocone.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) j) y)))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_existsₓ'. -/
 theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) (h : ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y) :
@@ -317,7 +317,7 @@ theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsCol
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] [_inst_5 : CategoryTheory.Limits.HasColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F] {i : J} {j : J} (x : coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F i)) (y : coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j)), (Exists.{succ u1} J (fun (k : J) => 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.colimit_rep_eq_of_existsₓ'. -/
 theorem Concrete.colimit_rep_eq_of_exists [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j)
     (h : ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y) :
@@ -333,7 +333,7 @@ variable [IsFiltered J]
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] [_inst_5 : CategoryTheory.IsFiltered.{u1, u1} J _inst_3] {D : CategoryTheory.Limits.Cocone.{u1, u1, u1, u2} J _inst_3 C _inst_1 F} {i : J} {j : J}, (CategoryTheory.Limits.IsColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) -> (forall (x : coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F i)) (y : coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, 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(CategoryTheory.ConcreteCategory.hasCoeToFun.{u2, u1, u1} C _inst_1 _inst_2 (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F k)) (CategoryTheory.Functor.map.{u1, u1, u1, u2} J _inst_3 C _inst_1 F j k g) y))))))
 but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] [_inst_5 : CategoryTheory.IsFiltered.{u1, u1} J _inst_3] {D : CategoryTheory.Limits.Cocone.{u1, u1, u1, u2} J _inst_3 C _inst_1 F} {i : J} {j : J}, (CategoryTheory.Limits.IsColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) -> (forall (x : Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.ConcreteCategory.Forget.{u1, u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) i)) (y : Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.ConcreteCategory.Forget.{u1, u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j)), (Eq.{succ u1} (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, 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(CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) i) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D))) i) (CategoryTheory.NatTrans.app.{u1, u1, u1, u2} J _inst_3 C _inst_1 F (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) (CategoryTheory.Limits.Cocone.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) i) x) (Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D))) j) (CategoryTheory.NatTrans.app.{u1, u1, u1, u2} J _inst_3 C _inst_1 F (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) (CategoryTheory.Limits.Cocone.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) j) y)) -> (Exists.{succ u1} J (fun (k : J) => Exists.{succ u1} (Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) i k) (fun (f : Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) i k) => Exists.{succ u1} (Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) j k) (fun (g : Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) j k) => Eq.{succ u1} (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) k)) (Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) i) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) k) (Prefunctor.map.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) i k f) x) (Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) k) (Prefunctor.map.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j k g) y))))))
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] [_inst_5 : CategoryTheory.IsFiltered.{u1, u1} J _inst_3] {D : CategoryTheory.Limits.Cocone.{u1, u1, u1, u2} J _inst_3 C _inst_1 F} {i : J} {j : J}, (CategoryTheory.Limits.IsColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) -> (forall (x : Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) i)) (y : Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} 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_inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D))) j) (CategoryTheory.NatTrans.app.{u1, u1, u1, u2} J _inst_3 C _inst_1 F (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) (CategoryTheory.Limits.Cocone.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) j) y)) -> (Exists.{succ u1} J (fun (k : J) => Exists.{succ u1} (Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) i k) (fun (f : Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) i k) => Exists.{succ u1} (Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) j k) (fun (g : Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) j k) => Eq.{succ u1} (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) k)) (Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) 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u2} J _inst_3 C _inst_1 F) k) (Prefunctor.map.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j k g) y))))))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eqₓ'. -/
 theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) (h : D.ι.app _ x = D.ι.app _ y) :
@@ -381,7 +381,7 @@ theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsCol
 lean 3 declaration is
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 but is expected to have type
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+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] [_inst_5 : CategoryTheory.IsFiltered.{u1, u1} J _inst_3] {D : CategoryTheory.Limits.Cocone.{u1, u1, u1, u2} J _inst_3 C _inst_1 F} {i : J} {j : J}, (CategoryTheory.Limits.IsColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D) -> (forall (x : Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} 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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_existsₓ'. -/
 theorem Concrete.isColimit_rep_eq_iff_exists {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) :
@@ -393,7 +393,7 @@ theorem Concrete.isColimit_rep_eq_iff_exists {D : Cocone F} {i j : J} (hD : IsCo
 lean 3 declaration is
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 but is expected to have type
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+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] [_inst_5 : CategoryTheory.IsFiltered.{u1, u1} J _inst_3] [_inst_6 : CategoryTheory.Limits.HasColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F] {i : J} {j : J} (x : Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, 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(CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) i k f) x) (Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j) 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 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eqₓ'. -/
 theorem Concrete.colimit_exists_of_rep_eq [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j)
     (h : colimit.ι F _ x = colimit.ι F _ y) :
@@ -405,7 +405,7 @@ theorem Concrete.colimit_exists_of_rep_eq [HasColimit F] {i j : J} (x : F.obj i)
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] [_inst_5 : CategoryTheory.IsFiltered.{u1, u1} J _inst_3] [_inst_6 : CategoryTheory.Limits.HasColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F] {i : J} {j : J} (x : coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J _inst_3 C _inst_1 F i)) (y : coeSort.{succ u2, succ (succ u1)} C Type.{u1} (CategoryTheory.ConcreteCategory.hasCoeToSort.{u2, u1, u1} C _inst_1 _inst_2) (CategoryTheory.Functor.obj.{u1, u1, u1, u2} J 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 but is expected to have type
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(Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) k) (Prefunctor.map.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j k g) y)))))
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.ConcreteCategory.{u1, u1, u2} C _inst_1] {J : Type.{u1}} [_inst_3 : CategoryTheory.SmallCategory.{u1} J] (F : CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) [_inst_4 : CategoryTheory.Limits.PreservesColimit.{u1, u1, u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} J _inst_3 F (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)] [_inst_5 : CategoryTheory.IsFiltered.{u1, u1} J _inst_3] [_inst_6 : CategoryTheory.Limits.HasColimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F] {i : J} {j : J} (x : Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, 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(CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) i) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_6) (CategoryTheory.Limits.colimit.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_6 i) x) (Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_6) (CategoryTheory.Limits.colimit.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_6 j) y)) (Exists.{succ u1} J (fun (k : J) => Exists.{succ u1} (Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) i k) (fun (f : Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) i k) => Exists.{succ u1} (Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) j k) (fun (g : Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) j k) => Eq.{succ u1} (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) k)) (Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) i) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) k) (Prefunctor.map.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) i k f) x) (Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) k) (Prefunctor.map.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j k g) y)))))
 Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.colimit_rep_eq_iff_existsₓ'. -/
 theorem Concrete.colimit_rep_eq_iff_exists [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j) :
     colimit.ι F i x = colimit.ι F j y ↔ ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=

cb3ceec8

bump to nightly-2023-03-26-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

ca5de00c

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Adam Topaz
 
 ! This file was ported from Lean 3 source module category_theory.limits.concrete_category
-! leanprover-community/mathlib commit c3019c79074b0619edb4b27553a91b2e82242395
+! leanprover-community/mathlib commit cb3ceec8485239a61ed51d944cb9a95b68c6bafc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -18,6 +18,9 @@ import Mathbin.Tactic.ApplyFun
 
 /-!
 # Facts about (co)limits of functors into concrete categories
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 -/

c3019c79

bump to nightly-2023-03-24-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/b19481deb571022990f1baa9cbf9172e6757a479

5b87f9bb

Diff

@@ -34,6 +34,12 @@ section Limits
 variable {C : Type u} [Category.{v} C] [ConcreteCategory.{max w v} C] {J : Type w} [SmallCategory J]
   (F : J ⥤ C) [PreservesLimit F (forget C)]
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.to_product_injective_of_is_limit CategoryTheory.Limits.Concrete.to_product_injective_of_isLimitₓ'. -/
 theorem Concrete.to_product_injective_of_isLimit {D : Cone F} (hD : IsLimit D) :
     Function.Injective fun (x : D.pt) (j : J) => D.π.app j x :=
   by
@@ -51,11 +57,23 @@ theorem Concrete.to_product_injective_of_isLimit {D : Cone F} (hD : IsLimit D) :
   apply Subtype.ext
 #align category_theory.limits.concrete.to_product_injective_of_is_limit CategoryTheory.Limits.Concrete.to_product_injective_of_isLimit
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_limit_ext CategoryTheory.Limits.Concrete.isLimit_extₓ'. -/
 theorem Concrete.isLimit_ext {D : Cone F} (hD : IsLimit D) (x y : D.pt) :
     (∀ j, D.π.app j x = D.π.app j y) → x = y := fun h =>
   Concrete.to_product_injective_of_isLimit _ hD (funext h)
 #align category_theory.limits.concrete.is_limit_ext CategoryTheory.Limits.Concrete.isLimit_ext
 
+/- warning: category_theory.limits.concrete.limit_ext -> CategoryTheory.Limits.Concrete.limit_ext is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.limit_ext CategoryTheory.Limits.Concrete.limit_extₓ'. -/
 theorem Concrete.limit_ext [HasLimit F] (x y : limit F) :
     (∀ j, limit.π F j x = limit.π F j y) → x = y :=
   Concrete.isLimit_ext F (limit.isLimit _) _ _
@@ -67,6 +85,7 @@ open WidePullback
 
 open WidePullbackShape
 
+#print CategoryTheory.Limits.Concrete.widePullback_ext /-
 theorem Concrete.widePullback_ext {B : C} {ι : Type w} {X : ι → C} (f : ∀ j : ι, X j ⟶ B)
     [HasWidePullback B X f] [PreservesLimit (wideCospan B X f) (forget C)]
     (x y : widePullback B X f) (h₀ : base f x = base f y) (h : ∀ j, π f j x = π f j y) : x = y :=
@@ -76,7 +95,9 @@ theorem Concrete.widePullback_ext {B : C} {ι : Type w} {X : ι → C} (f : ∀
   · exact h₀
   · apply h
 #align category_theory.limits.concrete.wide_pullback_ext CategoryTheory.Limits.Concrete.widePullback_ext
+-/
 
+#print CategoryTheory.Limits.Concrete.widePullback_ext' /-
 theorem Concrete.widePullback_ext' {B : C} {ι : Type w} [Nonempty ι] {X : ι → C}
     (f : ∀ j : ι, X j ⟶ B) [HasWidePullback.{w} B X f]
     [PreservesLimit (wideCospan B X f) (forget C)] (x y : widePullback B X f)
@@ -86,11 +107,13 @@ theorem Concrete.widePullback_ext' {B : C} {ι : Type w} [Nonempty ι] {X : ι 
   inhabit ι
   simp only [← π_arrow f (Inhabited.default _), comp_apply, h]
 #align category_theory.limits.concrete.wide_pullback_ext' CategoryTheory.Limits.Concrete.widePullback_ext'
+-/
 
 end WidePullback
 
 section Multiequalizer
 
+#print CategoryTheory.Limits.Concrete.multiequalizer_ext /-
 theorem Concrete.multiequalizer_ext {I : MulticospanIndex.{w} C} [HasMultiequalizer I]
     [PreservesLimit I.multicospan (forget C)] (x y : multiequalizer I)
     (h : ∀ t : I.L, Multiequalizer.ι I t x = Multiequalizer.ι I t y) : x = y :=
@@ -100,7 +123,14 @@ theorem Concrete.multiequalizer_ext {I : MulticospanIndex.{w} C} [HasMultiequali
   · apply h
   · rw [← limit.w I.multicospan (walking_multicospan.hom.fst b), comp_apply, comp_apply, h]
 #align category_theory.limits.concrete.multiequalizer_ext CategoryTheory.Limits.Concrete.multiequalizer_ext
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.multiequalizer_equiv_aux CategoryTheory.Limits.Concrete.multiequalizerEquivAuxₓ'. -/
 /-- An auxiliary equivalence to be used in `multiequalizer_equiv` below.-/
 def Concrete.multiequalizerEquivAux (I : MulticospanIndex C) :
     (I.multicospan ⋙ forget C).sections ≃
@@ -140,6 +170,7 @@ def Concrete.multiequalizerEquivAux (I : MulticospanIndex C) :
     rfl
 #align category_theory.limits.concrete.multiequalizer_equiv_aux CategoryTheory.Limits.Concrete.multiequalizerEquivAux
 
+#print CategoryTheory.Limits.Concrete.multiequalizerEquiv /-
 /-- The equivalence between the noncomputable multiequalizer and
 and the concrete multiequalizer. -/
 noncomputable def Concrete.multiequalizerEquiv (I : MulticospanIndex.{w} C) [HasMultiequalizer I]
@@ -151,7 +182,14 @@ noncomputable def Concrete.multiequalizerEquiv (I : MulticospanIndex.{w} C) [Has
   let E := h2.conePointUniqueUpToIso (Types.limitConeIsLimit _)
   Equiv.trans E.toEquiv (Concrete.multiequalizerEquivAux I)
 #align category_theory.limits.concrete.multiequalizer_equiv CategoryTheory.Limits.Concrete.multiequalizerEquiv
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.multiequalizer_equiv_apply CategoryTheory.Limits.Concrete.multiequalizerEquiv_applyₓ'. -/
 @[simp]
 theorem Concrete.multiequalizerEquiv_apply (I : MulticospanIndex.{w} C) [HasMultiequalizer I]
     [PreservesLimit I.multicospan (forget C)] (x : multiequalizer I) (i : I.L) :
@@ -166,6 +204,12 @@ end Limits
 
 section Colimits
 
+/- warning: category_theory.limits.cokernel_funext -> CategoryTheory.Limits.cokernel_funext is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.cokernel_funext CategoryTheory.Limits.cokernel_funextₓ'. -/
 -- We don't mark this as an `@[ext]` lemma as we don't always want to work elementwise.
 theorem cokernel_funext {C : Type _} [Category C] [HasZeroMorphisms C] [ConcreteCategory C]
     {M N K : C} {f : M ⟶ N} [HasCokernel f] {g h : cokernel f ⟶ K}
@@ -179,6 +223,12 @@ theorem cokernel_funext {C : Type _} [Category C] [HasZeroMorphisms C] [Concrete
 variable {C : Type u} [Category.{v} C] [ConcreteCategory.{v} C] {J : Type v} [SmallCategory J]
   (F : J ⥤ C) [PreservesColimit F (forget C)]
 
+/- warning: category_theory.limits.concrete.from_union_surjective_of_is_colimit -> CategoryTheory.Limits.Concrete.from_union_surjective_of_isColimit is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u1 u2} (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.category.{u1, u1, u1, u2} J _inst_3 C _inst_1) (CategoryTheory.Functor.const.{u1, u1, u1, u2} J _inst_3 C _inst_1)) 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(CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.ConcreteCategory.Forget.{u1, u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.Cocone.pt.{u1, u1, u1, u2} J _inst_3 C _inst_1 F D)) ff)
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.from_union_surjective_of_is_colimit CategoryTheory.Limits.Concrete.from_union_surjective_of_isColimitₓ'. -/
 theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColimit D) :
     let ff : (Σj : J, F.obj j) → D.pt := fun a => D.ι.app a.1 a.2
     Function.Surjective ff :=
@@ -207,6 +257,12 @@ theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColim
   exact ⟨⟨j, a⟩, rfl⟩
 #align category_theory.limits.concrete.from_union_surjective_of_is_colimit CategoryTheory.Limits.Concrete.from_union_surjective_of_isColimit
 
+/- warning: category_theory.limits.concrete.is_colimit_exists_rep -> CategoryTheory.Limits.Concrete.isColimit_exists_rep is a dubious translation:
+lean 3 declaration is
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y) x)))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_colimit_exists_rep CategoryTheory.Limits.Concrete.isColimit_exists_repₓ'. -/
 theorem Concrete.isColimit_exists_rep {D : Cocone F} (hD : IsColimit D) (x : D.pt) :
     ∃ (j : J)(y : F.obj j), D.ι.app j y = x :=
   by
@@ -214,11 +270,23 @@ theorem Concrete.isColimit_exists_rep {D : Cocone F} (hD : IsColimit D) (x : D.p
   exact ⟨a.1, a.2, rfl⟩
 #align category_theory.limits.concrete.is_colimit_exists_rep CategoryTheory.Limits.Concrete.isColimit_exists_rep
 
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 theorem Concrete.colimit_exists_rep [HasColimit F] (x : colimit F) :
     ∃ (j : J)(y : F.obj j), colimit.ι F j y = x :=
   Concrete.isColimit_exists_rep F (colimit.isColimit _) x
 #align category_theory.limits.concrete.colimit_exists_rep CategoryTheory.Limits.Concrete.colimit_exists_rep
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_existsₓ'. -/
 theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) (h : ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y) :
     D.ι.app i x = D.ι.app j y := by
@@ -242,6 +310,12 @@ theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsCol
   exact Quot.sound ⟨g, rfl⟩
 #align category_theory.limits.concrete.is_colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_exists
 
+/- warning: category_theory.limits.concrete.colimit_rep_eq_of_exists -> CategoryTheory.Limits.Concrete.colimit_rep_eq_of_exists is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.colimit_rep_eq_of_existsₓ'. -/
 theorem Concrete.colimit_rep_eq_of_exists [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j)
     (h : ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y) :
     colimit.ι F i x = colimit.ι F j y :=
@@ -252,6 +326,12 @@ section FilteredColimits
 
 variable [IsFiltered J]
 
+/- warning: category_theory.limits.concrete.is_colimit_exists_of_rep_eq -> CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eqₓ'. -/
 theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) (h : D.ι.app _ x = D.ι.app _ y) :
     ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=
@@ -294,18 +374,36 @@ theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsCol
     rw [is_filtered.coeq_condition]
 #align category_theory.limits.concrete.is_colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eq
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.is_colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_existsₓ'. -/
 theorem Concrete.isColimit_rep_eq_iff_exists {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) :
     D.ι.app i x = D.ι.app j y ↔ ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=
   ⟨Concrete.isColimit_exists_of_rep_eq _ hD _ _, Concrete.isColimit_rep_eq_of_exists _ hD _ _⟩
 #align category_theory.limits.concrete.is_colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eqₓ'. -/
 theorem Concrete.colimit_exists_of_rep_eq [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j)
     (h : colimit.ι F _ x = colimit.ι F _ y) :
     ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=
   Concrete.isColimit_exists_of_rep_eq F (colimit.isColimit _) x y h
 #align category_theory.limits.concrete.colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eq
 
+/- warning: category_theory.limits.concrete.colimit_rep_eq_iff_exists -> CategoryTheory.Limits.Concrete.colimit_rep_eq_iff_exists is a dubious translation:
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+but is expected to have type
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u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.ConcreteCategory.Forget.{u1, u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) i)) (y : Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.ConcreteCategory.Forget.{u1, u1, u2} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j)), Iff (Eq.{succ u1} (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_6)) (Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) i) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_6) (CategoryTheory.Limits.colimit.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_6 i) x) (Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j) (CategoryTheory.Limits.colimit.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_6) (CategoryTheory.Limits.colimit.ι.{u1, u1, u1, u2} J _inst_3 C _inst_1 F _inst_6 j) y)) (Exists.{succ u1} J (fun (k : J) => Exists.{succ u1} (Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) i k) (fun (f : Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) i k) => Exists.{succ u1} (Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) j k) (fun (g : Quiver.Hom.{succ u1, u1} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) j k) => Eq.{succ u1} (Prefunctor.obj.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) k)) (Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) i) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) k) (Prefunctor.map.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) i k f) x) (Prefunctor.map.{succ u1, succ u1, u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} C _inst_1 Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.forget.{u2, u1, u1} C _inst_1 _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j) (Prefunctor.obj.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) k) (Prefunctor.map.{succ u1, succ u1, u1, u2} J (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} J (CategoryTheory.Category.toCategoryStruct.{u1, u1} J _inst_3)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, u2} J _inst_3 C _inst_1 F) j k g) y)))))
+Case conversion may be inaccurate. Consider using '#align category_theory.limits.concrete.colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.colimit_rep_eq_iff_existsₓ'. -/
 theorem Concrete.colimit_rep_eq_iff_exists [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j) :
     colimit.ι F i x = colimit.ι F j y ↔ ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=
   ⟨Concrete.colimit_exists_of_rep_eq _ _ _, Concrete.colimit_rep_eq_of_exists _ _ _⟩
@@ -319,6 +417,7 @@ open WidePushout
 
 open WidePushoutShape
 
+#print CategoryTheory.Limits.Concrete.widePushout_exists_rep /-
 theorem Concrete.widePushout_exists_rep {B : C} {α : Type _} {X : α → C} (f : ∀ j : α, B ⟶ X j)
     [HasWidePushout.{v} B X f] [PreservesColimit (wideSpan B X f) (forget C)]
     (x : widePushout B X f) : (∃ y : B, head f y = x) ∨ ∃ (i : α)(y : X i), ι f i y = x :=
@@ -328,7 +427,9 @@ theorem Concrete.widePushout_exists_rep {B : C} {α : Type _} {X : α → C} (f
   · right
     use j, y
 #align category_theory.limits.concrete.wide_pushout_exists_rep CategoryTheory.Limits.Concrete.widePushout_exists_rep
+-/
 
+#print CategoryTheory.Limits.Concrete.widePushout_exists_rep' /-
 theorem Concrete.widePushout_exists_rep' {B : C} {α : Type _} [Nonempty α] {X : α → C}
     (f : ∀ j : α, B ⟶ X j) [HasWidePushout.{v} B X f] [PreservesColimit (wideSpan B X f) (forget C)]
     (x : widePushout B X f) : ∃ (i : α)(y : X i), ι f i y = x :=
@@ -339,6 +440,7 @@ theorem Concrete.widePushout_exists_rep' {B : C} {α : Type _} [Nonempty α] {X
     simp only [← arrow_ι _ (Inhabited.default α), comp_apply]
   · use i, y
 #align category_theory.limits.concrete.wide_pushout_exists_rep' CategoryTheory.Limits.Concrete.widePushout_exists_rep'
+-/
 
 end WidePushout

c3019c79

bump to nightly-2023-03-23-20

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

53b827ba

Diff

@@ -93,7 +93,7 @@ section Multiequalizer
 
 theorem Concrete.multiequalizer_ext {I : MulticospanIndex.{w} C} [HasMultiequalizer I]
     [PreservesLimit I.multicospan (forget C)] (x y : multiequalizer I)
-    (h : ∀ t : I.L, multiequalizer.ι I t x = multiequalizer.ι I t y) : x = y :=
+    (h : ∀ t : I.L, Multiequalizer.ι I t x = Multiequalizer.ι I t y) : x = y :=
   by
   apply concrete.limit_ext
   rintro (a | b)
@@ -155,7 +155,7 @@ noncomputable def Concrete.multiequalizerEquiv (I : MulticospanIndex.{w} C) [Has
 @[simp]
 theorem Concrete.multiequalizerEquiv_apply (I : MulticospanIndex.{w} C) [HasMultiequalizer I]
     [PreservesLimit I.multicospan (forget C)] (x : multiequalizer I) (i : I.L) :
-    ((Concrete.multiequalizerEquiv I) x : ∀ i : I.L, I.left i) i = multiequalizer.ι I i x :=
+    ((Concrete.multiequalizerEquiv I) x : ∀ i : I.L, I.left i) i = Multiequalizer.ι I i x :=
   rfl
 #align category_theory.limits.concrete.multiequalizer_equiv_apply CategoryTheory.Limits.Concrete.multiequalizerEquiv_apply

c3019c79

bump to nightly-2023-02-28-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

1fb1623f

Diff

@@ -35,7 +35,7 @@ variable {C : Type u} [Category.{v} C] [ConcreteCategory.{max w v} C] {J : Type
   (F : J ⥤ C) [PreservesLimit F (forget C)]
 
 theorem Concrete.to_product_injective_of_isLimit {D : Cone F} (hD : IsLimit D) :
-    Function.Injective fun (x : D.x) (j : J) => D.π.app j x :=
+    Function.Injective fun (x : D.pt) (j : J) => D.π.app j x :=
   by
   let E := (forget C).mapCone D
   let hE : is_limit E := is_limit_of_preserves _ hD
@@ -51,7 +51,7 @@ theorem Concrete.to_product_injective_of_isLimit {D : Cone F} (hD : IsLimit D) :
   apply Subtype.ext
 #align category_theory.limits.concrete.to_product_injective_of_is_limit CategoryTheory.Limits.Concrete.to_product_injective_of_isLimit
 
-theorem Concrete.isLimit_ext {D : Cone F} (hD : IsLimit D) (x y : D.x) :
+theorem Concrete.isLimit_ext {D : Cone F} (hD : IsLimit D) (x y : D.pt) :
     (∀ j, D.π.app j x = D.π.app j y) → x = y := fun h =>
   Concrete.to_product_injective_of_isLimit _ hD (funext h)
 #align category_theory.limits.concrete.is_limit_ext CategoryTheory.Limits.Concrete.isLimit_ext
@@ -180,7 +180,7 @@ variable {C : Type u} [Category.{v} C] [ConcreteCategory.{v} C] {J : Type v} [Sm
   (F : J ⥤ C) [PreservesColimit F (forget C)]
 
 theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColimit D) :
-    let ff : (Σj : J, F.obj j) → D.x := fun a => D.ι.app a.1 a.2
+    let ff : (Σj : J, F.obj j) → D.pt := fun a => D.ι.app a.1 a.2
     Function.Surjective ff :=
   by
   intro ff
@@ -207,7 +207,7 @@ theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColim
   exact ⟨⟨j, a⟩, rfl⟩
 #align category_theory.limits.concrete.from_union_surjective_of_is_colimit CategoryTheory.Limits.Concrete.from_union_surjective_of_isColimit
 
-theorem Concrete.isColimit_exists_rep {D : Cocone F} (hD : IsColimit D) (x : D.x) :
+theorem Concrete.isColimit_exists_rep {D : Cocone F} (hD : IsColimit D) (x : D.pt) :
     ∃ (j : J)(y : F.obj j), D.ι.app j y = x :=
   by
   obtain ⟨a, rfl⟩ := concrete.from_union_surjective_of_is_colimit F hD x

c3019c79

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

c3019c79

feat: existence of a limit in a concrete category implies smallness (#11625)

In this PR, it is shown that if a functor G : J ⥤ C to a concrete category has a limit and that forget C is corepresentable, then G ⋙ forget C).sections is small. As the corepresentability property holds in many concrete categories (e.g. groups, abelian groups) and that we already know since #11420 that limits exist under the smallness assumption in such categories, then this lemma may be used in future PR in order to show that usual forgetful functors preserve all limits (regardless of universe assumptions). This shall be convenient in the development of sheaves of modules.

In this PR, universes assumptions have also been generalized in the file Limits.Yoneda. In order to do this, a small refactor of the file Limits.Types was necessary. This introduces bijections like compCoyonedaSectionsEquiv (F : J ⥤ C) (X : C) : (F ⋙ coyoneda.obj (op X)).sections ≃ ((const J).obj X ⟶ F) with general universe parameters. In order to reduce imports in Limits.Yoneda, part of the file Limits.Types was moved to a new file Limits.TypesFiltered.

Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>

3cb545c7

Diff

@@ -5,7 +5,8 @@ Authors: Scott Morrison, Adam Topaz
 -/
 import Mathlib.CategoryTheory.ConcreteCategory.Basic
 import Mathlib.CategoryTheory.Limits.Preserves.Basic
-import Mathlib.CategoryTheory.Limits.Types
+import Mathlib.CategoryTheory.Limits.TypesFiltered
+import Mathlib.CategoryTheory.Limits.Yoneda
 import Mathlib.Tactic.ApplyFun
 
 #align_import category_theory.limits.concrete_category from "leanprover-community/mathlib"@"c3019c79074b0619edb4b27553a91b2e82242395"
@@ -25,6 +26,15 @@ attribute [local instance] ConcreteCategory.instFunLike ConcreteCategory.hasCoeT
 
 section Limits
 
+/-- If a functor `G : J ⥤ C` to a concrete category has a limit and that `forget C`
+is corepresentable, then `G ⋙ forget C).sections` is small. -/
+lemma Concrete.small_sections_of_hasLimit
+    {C : Type u} [Category.{v} C] [ConcreteCategory.{v} C]
+    [(forget C).Corepresentable] {J : Type w} [Category.{t} J] (G : J ⥤ C) [HasLimit G] :
+    Small.{v} (G ⋙ forget C).sections := by
+  rw [← Types.hasLimit_iff_small_sections]
+  infer_instance
+
 variable {C : Type u} [Category.{v} C] [ConcreteCategory.{max w v} C] {J : Type w} [SmallCategory J]
   (F : J ⥤ C) [PreservesLimit F (forget C)]

c3019c79

refactor: generalize universes for colimits in Type (#11148)

This is a smaller version of #7020. Before this PR, for limits, we gave instances for small indexing categories, but for colimits, we gave instances for TypeMax. This PR changes so that we give instances for small indexing categories in both cases. This is more general and also more uniform.

Co-authored-by: Joël Riou <rioujoel@gmail.com>

d73713b9

Diff

@@ -114,7 +114,7 @@ theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsCol
     ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y := by
   let E := (forget C).mapCocone D
   let hE : IsColimit E := isColimitOfPreserves _ hD
-  exact (Types.FilteredColimit.isColimit_eq_iff.{w, t, r} (F ⋙ forget C) hE).mp h
+  exact (Types.FilteredColimit.isColimit_eq_iff (F ⋙ forget C) hE).mp h
 #align category_theory.limits.concrete.is_colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eq
 
 theorem Concrete.isColimit_rep_eq_iff_exists {D : Cocone F} {i j : J} (hD : IsColimit D)

c3019c79

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

@@ -15,7 +15,7 @@ import Mathlib.Tactic.ApplyFun
 -/
 
 
-universe w v u
+universe t w v u r
 
 open CategoryTheory
 
@@ -58,33 +58,19 @@ end Limits
 
 section Colimits
 
-variable {C : Type u} [Category.{v} C] [ConcreteCategory.{v} C] {J : Type v} [SmallCategory J]
+section
+
+variable {C : Type u} [Category.{v} C] [ConcreteCategory.{t} C] {J : Type w} [Category.{r} J]
   (F : J ⥤ C) [PreservesColimit F (forget C)]
 
 theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColimit D) :
     let ff : (Σj : J, F.obj j) → D.pt := fun a => D.ι.app a.1 a.2
     Function.Surjective ff := by
-  intro ff
-  let E := (forget C).mapCocone D
-  let hE : IsColimit E := isColimitOfPreserves _ hD
-  let G := Types.colimitCocone.{v, v} (F ⋙ forget C)
-  let hG := Types.colimitCoconeIsColimit.{v, v} (F ⋙ forget C)
-  let T : E ≅ G := hE.uniqueUpToIso hG
-  let TX : E.pt ≅ G.pt := (Cocones.forget _).mapIso T
-  suffices Function.Surjective (TX.hom ∘ ff) by
-    intro a
-    obtain ⟨b, hb⟩ := this (TX.hom a)
-    refine' ⟨b, _⟩
-    apply_fun TX.inv at hb
-    change (TX.hom ≫ TX.inv) (ff b) = (TX.hom ≫ TX.inv) _ at hb
-    simpa only [TX.hom_inv_id] using hb
-  have : TX.hom ∘ ff = fun a => G.ι.app a.1 a.2 := by
-    ext a
-    change (E.ι.app a.1 ≫ hE.desc G) a.2 = _
-    rw [hE.fac]
-  rw [this]
-  rintro ⟨⟨j, a⟩⟩
-  exact ⟨⟨j, a⟩, rfl⟩
+  intro ff x
+  let E : Cocone (F ⋙ forget C) := (forget C).mapCocone D
+  let hE : IsColimit E := isColimitOfPreserves (forget C) hD
+  obtain ⟨j, y, hy⟩ := Types.jointly_surjective_of_isColimit hE x
+  exact ⟨⟨j, y⟩, hy⟩
 #align category_theory.limits.concrete.from_union_surjective_of_is_colimit CategoryTheory.Limits.Concrete.from_union_surjective_of_isColimit
 
 theorem Concrete.isColimit_exists_rep {D : Cocone F} (hD : IsColimit D) (x : D.pt) :
@@ -98,92 +84,55 @@ theorem Concrete.colimit_exists_rep [HasColimit F] (x : ↑(colimit F)) :
   Concrete.isColimit_exists_rep F (colimit.isColimit _) x
 #align category_theory.limits.concrete.colimit_exists_rep CategoryTheory.Limits.Concrete.colimit_exists_rep
 
-theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsColimit D)
-    (x : F.obj i) (y : F.obj j) (h : ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y) :
+theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (x : F.obj i) (y : F.obj j)
+    (h : ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y) :
     D.ι.app i x = D.ι.app j y := by
   let E := (forget C).mapCocone D
-  let hE : IsColimit E := isColimitOfPreserves _ hD
-  let G := Types.colimitCocone.{v, v} (F ⋙ forget C)
-  let hG := Types.colimitCoconeIsColimit.{v, v} (F ⋙ forget C)
-  let T : E ≅ G := hE.uniqueUpToIso hG
-  let TX : E.pt ≅ G.pt := (Cocones.forget _).mapIso T
-  apply_fun TX.hom using injective_of_mono TX.hom
-  change (E.ι.app i ≫ TX.hom) x = (E.ι.app j ≫ TX.hom) y
-  erw [T.hom.w, T.hom.w]
-  obtain ⟨k, f, g, h⟩ := h
-  have : G.ι.app i x = (G.ι.app k (F.map f x) : G.pt) := Quot.sound ⟨f, rfl⟩
-  rw [this, h]
-  symm
-  exact Quot.sound ⟨g, rfl⟩
+  obtain ⟨k, f, g, (hfg : (F ⋙ forget C).map f x = F.map g y)⟩ := h
+  let h1 : (F ⋙ forget C).map f ≫ E.ι.app k = E.ι.app i := E.ι.naturality f
+  let h2 : (F ⋙ forget C).map g ≫ E.ι.app k = E.ι.app j := E.ι.naturality g
+  show E.ι.app i x = E.ι.app j y
+  rw [← h1, types_comp_apply, hfg]
+  exact congrFun h2 y
 #align category_theory.limits.concrete.is_colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_exists
 
 theorem Concrete.colimit_rep_eq_of_exists [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j)
     (h : ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y) :
     colimit.ι F i x = colimit.ι F j y :=
-  Concrete.isColimit_rep_eq_of_exists F (colimit.isColimit _) x y h
+  Concrete.isColimit_rep_eq_of_exists F x y h
 #align category_theory.limits.concrete.colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.colimit_rep_eq_of_exists
 
+end
+
 section FilteredColimits
 
-variable [IsFiltered J]
+variable {C : Type u} [Category.{v} C] [ConcreteCategory.{max t w} C] {J : Type w} [Category.{r} J]
+  (F : J ⥤ C) [PreservesColimit F (forget C)] [IsFiltered J]
 
 theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) (h : D.ι.app _ x = D.ι.app _ y) :
     ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y := by
   let E := (forget C).mapCocone D
   let hE : IsColimit E := isColimitOfPreserves _ hD
-  let G := Types.colimitCocone.{v, v} (F ⋙ forget C)
-  let hG := Types.colimitCoconeIsColimit.{v, v} (F ⋙ forget C)
-  let T : E ≅ G := hE.uniqueUpToIso hG
-  let TX : E.pt ≅ G.pt := (Cocones.forget _).mapIso T
-  apply_fun TX.hom at h
-  change (E.ι.app i ≫ TX.hom) x = (E.ι.app j ≫ TX.hom) y at h
-  erw [T.hom.w, T.hom.w] at h
-  replace h := Quot.exact _ h
-  suffices
-    ∀ (a b : Σj, F.obj j) (_ : EqvGen (Limits.Types.Quot.Rel.{v, v} (F ⋙ forget C)) a b),
-      ∃ (k : _) (f : a.1 ⟶ k) (g : b.1 ⟶ k), F.map f a.2 = F.map g b.2
-    by exact this ⟨i, x⟩ ⟨j, y⟩ h
-  intro a b h
-  induction h with
-  | rel x y hh =>
-    obtain ⟨e, he⟩ := hh
-    use y.1, e, 𝟙 _
-    simpa using he.symm
-  | refl x =>
-    exact ⟨x.1, 𝟙 _, 𝟙 _, rfl⟩
-  | symm x y _ hh =>
-    obtain ⟨k, f, g, hh⟩ := hh
-    exact ⟨k, g, f, hh.symm⟩
-  | trans x y z _ _ hh1 hh2 =>
-    obtain ⟨k1, f1, g1, h1⟩ := hh1
-    obtain ⟨k2, f2, g2, h2⟩ := hh2
-    let k0 : J := IsFiltered.max k1 k2
-    let e1 : k1 ⟶ k0 := IsFiltered.leftToMax _ _
-    let e2 : k2 ⟶ k0 := IsFiltered.rightToMax _ _
-    let k : J := IsFiltered.coeq (g1 ≫ e1) (f2 ≫ e2)
-    let e : k0 ⟶ k := IsFiltered.coeqHom _ _
-    use k, f1 ≫ e1 ≫ e, g2 ≫ e2 ≫ e
-    simp only [F.map_comp, comp_apply, h1, ← h2]
-    simp only [← comp_apply, ← F.map_comp]
-    rw [IsFiltered.coeq_condition]
+  exact (Types.FilteredColimit.isColimit_eq_iff.{w, t, r} (F ⋙ forget C) hE).mp h
 #align category_theory.limits.concrete.is_colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.isColimit_exists_of_rep_eq
 
 theorem Concrete.isColimit_rep_eq_iff_exists {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) :
     D.ι.app i x = D.ι.app j y ↔ ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y :=
-  ⟨Concrete.isColimit_exists_of_rep_eq _ hD _ _, Concrete.isColimit_rep_eq_of_exists _ hD _ _⟩
+  ⟨Concrete.isColimit_exists_of_rep_eq.{t} _ hD _ _,
+   Concrete.isColimit_rep_eq_of_exists _ _ _⟩
 #align category_theory.limits.concrete.is_colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists
 
 theorem Concrete.colimit_exists_of_rep_eq [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j)
     (h : colimit.ι F _ x = colimit.ι F _ y) :
     ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y :=
-  Concrete.isColimit_exists_of_rep_eq F (colimit.isColimit _) x y h
+  Concrete.isColimit_exists_of_rep_eq.{t} F (colimit.isColimit _) x y h
 #align category_theory.limits.concrete.colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eq
 
 theorem Concrete.colimit_rep_eq_iff_exists [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j) :
     colimit.ι F i x = colimit.ι F j y ↔ ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y :=
-  ⟨Concrete.colimit_exists_of_rep_eq _ _ _, Concrete.colimit_rep_eq_of_exists _ _ _⟩
+  ⟨Concrete.colimit_exists_of_rep_eq.{t} _ _ _, Concrete.colimit_rep_eq_of_exists _ _ _⟩
 #align category_theory.limits.concrete.colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.colimit_rep_eq_iff_exists
 
 end FilteredColimits

c3019c79

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

@@ -21,7 +21,7 @@ open CategoryTheory
 
 namespace CategoryTheory.Limits
 
-attribute [local instance] ConcreteCategory.instDFunLike ConcreteCategory.hasCoeToSort
+attribute [local instance] ConcreteCategory.instFunLike ConcreteCategory.hasCoeToSort
 
 section Limits

c3019c79

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

@@ -21,7 +21,7 @@ open CategoryTheory
 
 namespace CategoryTheory.Limits
 
-attribute [local instance] ConcreteCategory.funLike ConcreteCategory.hasCoeToSort
+attribute [local instance] ConcreteCategory.instDFunLike ConcreteCategory.hasCoeToSort
 
 section Limits

c3019c79

style: use cases x with | ... instead of cases x; case => ... (#9321)

This converts usages of the pattern

cases h
case inl h' => ...
case inr h' => ...

which derive from mathported code, to the "structured cases" syntax:

cases h with
| inl h' => ...
| inr h' => ...

The case where the subgoals are handled with · instead of case is more contentious (and much more numerous) so I left those alone. This pattern also appears with cases', induction, induction', and rcases. Furthermore, there is a similar transformation for by_cases:

by_cases h : cond
case pos => ...
case neg => ...

is replaced by:

if h : cond then
  ...
else
  ...

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

e04a464d

Diff

@@ -145,17 +145,17 @@ theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsCol
       ∃ (k : _) (f : a.1 ⟶ k) (g : b.1 ⟶ k), F.map f a.2 = F.map g b.2
     by exact this ⟨i, x⟩ ⟨j, y⟩ h
   intro a b h
-  induction h
-  case rel x y hh =>
+  induction h with
+  | rel x y hh =>
     obtain ⟨e, he⟩ := hh
     use y.1, e, 𝟙 _
     simpa using he.symm
-  case refl x =>
+  | refl x =>
     exact ⟨x.1, 𝟙 _, 𝟙 _, rfl⟩
-  case symm x y _ hh =>
+  | symm x y _ hh =>
     obtain ⟨k, f, g, hh⟩ := hh
     exact ⟨k, g, f, hh.symm⟩
-  case trans x y z _ _ hh1 hh2 =>
+  | trans x y z _ _ hh1 hh2 =>
     obtain ⟨k1, f1, g1, h1⟩ := hh1
     obtain ⟨k2, f2, g2, h2⟩ := hh2
     let k0 : J := IsFiltered.max k1 k2

c3019c79

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

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

e9d46c6c

Diff

@@ -3,12 +3,9 @@ Copyright (c) 2017 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Adam Topaz
 -/
+import Mathlib.CategoryTheory.ConcreteCategory.Basic
 import Mathlib.CategoryTheory.Limits.Preserves.Basic
 import Mathlib.CategoryTheory.Limits.Types
-import Mathlib.CategoryTheory.Limits.Shapes.WidePullbacks
-import Mathlib.CategoryTheory.Limits.Shapes.Multiequalizer
-import Mathlib.CategoryTheory.ConcreteCategory.Basic
-import Mathlib.CategoryTheory.Limits.Shapes.Kernels
 import Mathlib.Tactic.ApplyFun
 
 #align_import category_theory.limits.concrete_category from "leanprover-community/mathlib"@"c3019c79074b0619edb4b27553a91b2e82242395"
@@ -57,112 +54,10 @@ theorem Concrete.limit_ext [HasLimit F] (x y : ↑(limit F)) :
   Concrete.isLimit_ext F (limit.isLimit _) _ _
 #align category_theory.limits.concrete.limit_ext CategoryTheory.Limits.Concrete.limit_ext
 
-section WidePullback
-
-open WidePullback
-
-open WidePullbackShape
-
-theorem Concrete.widePullback_ext {B : C} {ι : Type w} {X : ι → C} (f : ∀ j : ι, X j ⟶ B)
-    [HasWidePullback B X f] [PreservesLimit (wideCospan B X f) (forget C)]
-    (x y : ↑(widePullback B X f)) (h₀ : base f x = base f y) (h : ∀ j, π f j x = π f j y) :
-    x = y := by
-  apply Concrete.limit_ext
-  rintro (_ | j)
-  · exact h₀
-  · apply h
-#align category_theory.limits.concrete.wide_pullback_ext CategoryTheory.Limits.Concrete.widePullback_ext
-
-theorem Concrete.widePullback_ext' {B : C} {ι : Type w} [Nonempty ι] {X : ι → C}
-    (f : ∀ j : ι, X j ⟶ B) [HasWidePullback.{w} B X f]
-    [PreservesLimit (wideCospan B X f) (forget C)] (x y : ↑(widePullback B X f))
-    (h : ∀ j, π f j x = π f j y) : x = y := by
-  apply Concrete.widePullback_ext _ _ _ _ h
-  inhabit ι
-  simp only [← π_arrow f default, comp_apply, h]
-#align category_theory.limits.concrete.wide_pullback_ext' CategoryTheory.Limits.Concrete.widePullback_ext'
-
-end WidePullback
-
-section Multiequalizer
-
-theorem Concrete.multiequalizer_ext {I : MulticospanIndex.{w} C} [HasMultiequalizer I]
-    [PreservesLimit I.multicospan (forget C)] (x y : ↑(multiequalizer I))
-    (h : ∀ t : I.L, Multiequalizer.ι I t x = Multiequalizer.ι I t y) : x = y := by
-  apply Concrete.limit_ext
-  rintro (a | b)
-  · apply h
-  · rw [← limit.w I.multicospan (WalkingMulticospan.Hom.fst b), comp_apply, comp_apply]
-    simp [h]
-#align category_theory.limits.concrete.multiequalizer_ext CategoryTheory.Limits.Concrete.multiequalizer_ext
-
-/-- An auxiliary equivalence to be used in `multiequalizerEquiv` below.-/
-def Concrete.multiequalizerEquivAux (I : MulticospanIndex C) :
-    (I.multicospan ⋙ forget C).sections ≃
-    { x : ∀ i : I.L, I.left i // ∀ i : I.R, I.fst i (x _) = I.snd i (x _) } where
-  toFun x :=
-    ⟨fun i => x.1 (WalkingMulticospan.left _), fun i => by
-      have a := x.2 (WalkingMulticospan.Hom.fst i)
-      have b := x.2 (WalkingMulticospan.Hom.snd i)
-      rw [← b] at a
-      exact a⟩
-  invFun x :=
-    { val := fun j =>
-        match j with
-        | WalkingMulticospan.left a => x.1 _
-        | WalkingMulticospan.right b => I.fst b (x.1 _)
-      property := by
-        rintro (a | b) (a' | b') (f | f | f)
-        · simp
-        · rfl
-        · dsimp
-          exact (x.2 b').symm
-        · simp }
-  left_inv := by
-    intro x; ext (a | b)
-    · rfl
-    · rw [← x.2 (WalkingMulticospan.Hom.fst b)]
-      rfl
-  right_inv := by
-    intro x
-    ext i
-    rfl
-#align category_theory.limits.concrete.multiequalizer_equiv_aux CategoryTheory.Limits.Concrete.multiequalizerEquivAux
-
-/-- The equivalence between the noncomputable multiequalizer and
-the concrete multiequalizer. -/
-noncomputable def Concrete.multiequalizerEquiv (I : MulticospanIndex.{w} C) [HasMultiequalizer I]
-    [PreservesLimit I.multicospan (forget C)] :
-    (multiequalizer I : C) ≃
-      { x : ∀ i : I.L, I.left i // ∀ i : I.R, I.fst i (x _) = I.snd i (x _) } := by
-  let h1 := limit.isLimit I.multicospan
-  let h2 := isLimitOfPreserves (forget C) h1
-  let E := h2.conePointUniqueUpToIso (Types.limitConeIsLimit.{w, v} _)
-  exact Equiv.trans E.toEquiv (Concrete.multiequalizerEquivAux.{w, v} I)
-#align category_theory.limits.concrete.multiequalizer_equiv CategoryTheory.Limits.Concrete.multiequalizerEquiv
-
-@[simp]
-theorem Concrete.multiequalizerEquiv_apply (I : MulticospanIndex.{w} C) [HasMultiequalizer I]
-    [PreservesLimit I.multicospan (forget C)] (x : ↑(multiequalizer I)) (i : I.L) :
-    ((Concrete.multiequalizerEquiv I) x : ∀ i : I.L, I.left i) i = Multiequalizer.ι I i x :=
-  rfl
-#align category_theory.limits.concrete.multiequalizer_equiv_apply CategoryTheory.Limits.Concrete.multiequalizerEquiv_apply
-
-end Multiequalizer
-
--- TODO: Add analogous lemmas about products and equalizers.
 end Limits
 
 section Colimits
 
--- We don't mark this as an `@[ext]` lemma as we don't always want to work elementwise.
-theorem cokernel_funext {C : Type*} [Category C] [HasZeroMorphisms C] [ConcreteCategory C]
-    {M N K : C} {f : M ⟶ N} [HasCokernel f] {g h : cokernel f ⟶ K}
-    (w : ∀ n : N, g (cokernel.π f n) = h (cokernel.π f n)) : g = h := by
-  ext x
-  simpa using w x
-#align category_theory.limits.cokernel_funext CategoryTheory.Limits.cokernel_funext
-
 variable {C : Type u} [Category.{v} C] [ConcreteCategory.{v} C] {J : Type v} [SmallCategory J]
   (F : J ⥤ C) [PreservesColimit F (forget C)]
 
@@ -293,37 +188,6 @@ theorem Concrete.colimit_rep_eq_iff_exists [HasColimit F] {i j : J} (x : F.obj i
 
 end FilteredColimits
 
-section WidePushout
-
-open WidePushout
-
-open WidePushoutShape
-
-theorem Concrete.widePushout_exists_rep {B : C} {α : Type _} {X : α → C} (f : ∀ j : α, B ⟶ X j)
-    [HasWidePushout.{v} B X f] [PreservesColimit (wideSpan B X f) (forget C)]
-    (x : ↑(widePushout B X f)) : (∃ y : B, head f y = x) ∨ ∃ (i : α) (y : X i), ι f i y = x := by
-  obtain ⟨_ | j, y, rfl⟩ := Concrete.colimit_exists_rep _ x
-  · left
-    use y
-    rfl
-  · right
-    use j, y
-    rfl
-#align category_theory.limits.concrete.wide_pushout_exists_rep CategoryTheory.Limits.Concrete.widePushout_exists_rep
-
-theorem Concrete.widePushout_exists_rep' {B : C} {α : Type _} [Nonempty α] {X : α → C}
-    (f : ∀ j : α, B ⟶ X j) [HasWidePushout.{v} B X f] [PreservesColimit (wideSpan B X f) (forget C)]
-    (x : ↑(widePushout B X f)) : ∃ (i : α) (y : X i), ι f i y = x := by
-  rcases Concrete.widePushout_exists_rep f x with (⟨y, rfl⟩ | ⟨i, y, rfl⟩)
-  · inhabit α
-    use default, f _ y
-    simp only [← arrow_ι _ default, comp_apply]
-  · use i, y
-#align category_theory.limits.concrete.wide_pushout_exists_rep' CategoryTheory.Limits.Concrete.widePushout_exists_rep'
-
-end WidePushout
-
--- TODO: Add analogous lemmas about coproducts and coequalizers.
 end Colimits
 
 end CategoryTheory.Limits

c3019c79

feat: some improvements to apply_fun (#6732)

Re-enabling applying an order equiv to the target
using withMainContext so that locals are treated properly
enabling some commented out tests

57230798

Diff

@@ -180,8 +180,7 @@ theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColim
     intro a
     obtain ⟨b, hb⟩ := this (TX.hom a)
     refine' ⟨b, _⟩
-    -- porting note: `apply_fun TX.inv at hb` does not work here
-    replace hb := congr_arg TX.inv hb
+    apply_fun TX.inv at hb
     change (TX.hom ≫ TX.inv) (ff b) = (TX.hom ≫ TX.inv) _ at hb
     simpa only [TX.hom_inv_id] using hb
   have : TX.hom ∘ ff = fun a => G.ι.app a.1 a.2 := by
@@ -213,10 +212,7 @@ theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsCol
   let hG := Types.colimitCoconeIsColimit.{v, v} (F ⋙ forget C)
   let T : E ≅ G := hE.uniqueUpToIso hG
   let TX : E.pt ≅ G.pt := (Cocones.forget _).mapIso T
-  -- porting note: `apply_fun TX.hom` does not work here
-  apply (show Function.Bijective TX.hom by
-    rw [← isIso_iff_bijective]
-    apply IsIso.of_iso).1
+  apply_fun TX.hom using injective_of_mono TX.hom
   change (E.ι.app i ≫ TX.hom) x = (E.ι.app j ≫ TX.hom) y
   erw [T.hom.w, T.hom.w]
   obtain ⟨k, f, g, h⟩ := h
@@ -245,8 +241,7 @@ theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsCol
   let hG := Types.colimitCoconeIsColimit.{v, v} (F ⋙ forget C)
   let T : E ≅ G := hE.uniqueUpToIso hG
   let TX : E.pt ≅ G.pt := (Cocones.forget _).mapIso T
-  -- porting note: `apply_fun TX.hom at h` does not work here
-  replace h := congr_arg TX.hom h
+  apply_fun TX.hom at h
   change (E.ι.app i ≫ TX.hom) x = (E.ι.app j ≫ TX.hom) y at h
   erw [T.hom.w, T.hom.w] at h
   replace h := Quot.exact _ h

c3019c79

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -156,7 +156,7 @@ end Limits
 section Colimits
 
 -- We don't mark this as an `@[ext]` lemma as we don't always want to work elementwise.
-theorem cokernel_funext {C : Type _} [Category C] [HasZeroMorphisms C] [ConcreteCategory C]
+theorem cokernel_funext {C : Type*} [Category C] [HasZeroMorphisms C] [ConcreteCategory C]
     {M N K : C} {f : M ⟶ N} [HasCokernel f] {g h : cokernel f ⟶ K}
     (w : ∀ n : N, g (cokernel.π f n) = h (cokernel.π f n)) : g = h := by
   ext x

c3019c79

chore: fix grammar mistakes (#6121)

a16538af

Diff

@@ -130,7 +130,7 @@ def Concrete.multiequalizerEquivAux (I : MulticospanIndex C) :
 #align category_theory.limits.concrete.multiequalizer_equiv_aux CategoryTheory.Limits.Concrete.multiequalizerEquivAux
 
 /-- The equivalence between the noncomputable multiequalizer and
-and the concrete multiequalizer. -/
+the concrete multiequalizer. -/
 noncomputable def Concrete.multiequalizerEquiv (I : MulticospanIndex.{w} C) [HasMultiequalizer I]
     [PreservesLimit I.multicospan (forget C)] :
     (multiequalizer I : C) ≃

c3019c79

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

@@ -2,11 +2,6 @@
 Copyright (c) 2017 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Adam Topaz
-
-! This file was ported from Lean 3 source module category_theory.limits.concrete_category
-! leanprover-community/mathlib commit c3019c79074b0619edb4b27553a91b2e82242395
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Limits.Preserves.Basic
 import Mathlib.CategoryTheory.Limits.Types
@@ -16,6 +11,8 @@ import Mathlib.CategoryTheory.ConcreteCategory.Basic
 import Mathlib.CategoryTheory.Limits.Shapes.Kernels
 import Mathlib.Tactic.ApplyFun
 
+#align_import category_theory.limits.concrete_category from "leanprover-community/mathlib"@"c3019c79074b0619edb4b27553a91b2e82242395"
+
 /-!
 # Facts about (co)limits of functors into concrete categories
 -/

c3019c79

feat: more consistent use of ext, and updating porting notes. (#5242)

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

dbae2f17

Diff

@@ -162,9 +162,8 @@ section Colimits
 theorem cokernel_funext {C : Type _} [Category C] [HasZeroMorphisms C] [ConcreteCategory C]
     {M N K : C} {f : M ⟶ N} [HasCokernel f] {g h : cokernel f ⟶ K}
     (w : ∀ n : N, g (cokernel.π f n) = h (cokernel.π f n)) : g = h := by
-  apply coequalizer.hom_ext
-  apply ConcreteCategory.hom_ext _ _
-  simpa using w
+  ext x
+  simpa using w x
 #align category_theory.limits.cokernel_funext CategoryTheory.Limits.cokernel_funext
 
 variable {C : Type u} [Category.{v} C] [ConcreteCategory.{v} C] {J : Type v} [SmallCategory J]

c3019c79

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

b7cba33a

Diff

@@ -27,7 +27,7 @@ open CategoryTheory
 
 namespace CategoryTheory.Limits
 
-attribute [local instance] ConcreteCategory.hasCoeToFun ConcreteCategory.hasCoeToSort
+attribute [local instance] ConcreteCategory.funLike ConcreteCategory.hasCoeToSort
 
 section Limits
 
@@ -95,7 +95,8 @@ theorem Concrete.multiequalizer_ext {I : MulticospanIndex.{w} C} [HasMultiequali
   apply Concrete.limit_ext
   rintro (a | b)
   · apply h
-  · rw [← limit.w I.multicospan (WalkingMulticospan.Hom.fst b), comp_apply, comp_apply, h]
+  · rw [← limit.w I.multicospan (WalkingMulticospan.Hom.fst b), comp_apply, comp_apply]
+    simp [h]
 #align category_theory.limits.concrete.multiequalizer_ext CategoryTheory.Limits.Concrete.multiequalizer_ext
 
 /-- An auxiliary equivalence to be used in `multiequalizerEquiv` below.-/
@@ -115,18 +116,15 @@ def Concrete.multiequalizerEquivAux (I : MulticospanIndex C) :
         | WalkingMulticospan.right b => I.fst b (x.1 _)
       property := by
         rintro (a | b) (a' | b') (f | f | f)
-        · change (I.multicospan.map (𝟙 _)) _ = _
-          simp
+        · simp
         · rfl
         · dsimp
-          erw [← x.2 b']
-        · change (I.multicospan.map (𝟙 _)) _ = _
-          simp }
+          exact (x.2 b').symm
+        · simp }
   left_inv := by
     intro x; ext (a | b)
     · rfl
-    · change _ = x.val _
-      rw [← x.2 (WalkingMulticospan.Hom.fst b)]
+    · rw [← x.2 (WalkingMulticospan.Hom.fst b)]
       rfl
   right_inv := by
     intro x
@@ -316,8 +314,10 @@ theorem Concrete.widePushout_exists_rep {B : C} {α : Type _} {X : α → C} (f
   obtain ⟨_ | j, y, rfl⟩ := Concrete.colimit_exists_rep _ x
   · left
     use y
+    rfl
   · right
     use j, y
+    rfl
 #align category_theory.limits.concrete.wide_pushout_exists_rep CategoryTheory.Limits.Concrete.widePushout_exists_rep
 
 theorem Concrete.widePushout_exists_rep' {B : C} {α : Type _} [Nonempty α] {X : α → C}

c3019c79

chore: formatting issues (#4947)

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

5068808d

Diff

@@ -200,18 +200,18 @@ theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColim
 #align category_theory.limits.concrete.from_union_surjective_of_is_colimit CategoryTheory.Limits.Concrete.from_union_surjective_of_isColimit
 
 theorem Concrete.isColimit_exists_rep {D : Cocone F} (hD : IsColimit D) (x : D.pt) :
-    ∃ (j : J)(y : F.obj j), D.ι.app j y = x := by
+    ∃ (j : J) (y : F.obj j), D.ι.app j y = x := by
   obtain ⟨a, rfl⟩ := Concrete.from_union_surjective_of_isColimit F hD x
   exact ⟨a.1, a.2, rfl⟩
 #align category_theory.limits.concrete.is_colimit_exists_rep CategoryTheory.Limits.Concrete.isColimit_exists_rep
 
 theorem Concrete.colimit_exists_rep [HasColimit F] (x : ↑(colimit F)) :
-    ∃ (j : J)(y : F.obj j), colimit.ι F j y = x :=
+    ∃ (j : J) (y : F.obj j), colimit.ι F j y = x :=
   Concrete.isColimit_exists_rep F (colimit.isColimit _) x
 #align category_theory.limits.concrete.colimit_exists_rep CategoryTheory.Limits.Concrete.colimit_exists_rep
 
 theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsColimit D)
-    (x : F.obj i) (y : F.obj j) (h : ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y) :
+    (x : F.obj i) (y : F.obj j) (h : ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y) :
     D.ι.app i x = D.ι.app j y := by
   let E := (forget C).mapCocone D
   let hE : IsColimit E := isColimitOfPreserves _ hD
@@ -233,7 +233,7 @@ theorem Concrete.isColimit_rep_eq_of_exists {D : Cocone F} {i j : J} (hD : IsCol
 #align category_theory.limits.concrete.is_colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_of_exists
 
 theorem Concrete.colimit_rep_eq_of_exists [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j)
-    (h : ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y) :
+    (h : ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y) :
     colimit.ι F i x = colimit.ι F j y :=
   Concrete.isColimit_rep_eq_of_exists F (colimit.isColimit _) x y h
 #align category_theory.limits.concrete.colimit_rep_eq_of_exists CategoryTheory.Limits.Concrete.colimit_rep_eq_of_exists
@@ -244,7 +244,7 @@ variable [IsFiltered J]
 
 theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) (h : D.ι.app _ x = D.ι.app _ y) :
-    ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y := by
+    ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y := by
   let E := (forget C).mapCocone D
   let hE : IsColimit E := isColimitOfPreserves _ hD
   let G := Types.colimitCocone.{v, v} (F ⋙ forget C)
@@ -258,7 +258,7 @@ theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsCol
   replace h := Quot.exact _ h
   suffices
     ∀ (a b : Σj, F.obj j) (_ : EqvGen (Limits.Types.Quot.Rel.{v, v} (F ⋙ forget C)) a b),
-      ∃ (k : _)(f : a.1 ⟶ k)(g : b.1 ⟶ k), F.map f a.2 = F.map g b.2
+      ∃ (k : _) (f : a.1 ⟶ k) (g : b.1 ⟶ k), F.map f a.2 = F.map g b.2
     by exact this ⟨i, x⟩ ⟨j, y⟩ h
   intro a b h
   induction h
@@ -287,18 +287,18 @@ theorem Concrete.isColimit_exists_of_rep_eq {D : Cocone F} {i j : J} (hD : IsCol
 
 theorem Concrete.isColimit_rep_eq_iff_exists {D : Cocone F} {i j : J} (hD : IsColimit D)
     (x : F.obj i) (y : F.obj j) :
-    D.ι.app i x = D.ι.app j y ↔ ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=
+    D.ι.app i x = D.ι.app j y ↔ ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y :=
   ⟨Concrete.isColimit_exists_of_rep_eq _ hD _ _, Concrete.isColimit_rep_eq_of_exists _ hD _ _⟩
 #align category_theory.limits.concrete.is_colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.isColimit_rep_eq_iff_exists
 
 theorem Concrete.colimit_exists_of_rep_eq [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j)
     (h : colimit.ι F _ x = colimit.ι F _ y) :
-    ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=
+    ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y :=
   Concrete.isColimit_exists_of_rep_eq F (colimit.isColimit _) x y h
 #align category_theory.limits.concrete.colimit_exists_of_rep_eq CategoryTheory.Limits.Concrete.colimit_exists_of_rep_eq
 
 theorem Concrete.colimit_rep_eq_iff_exists [HasColimit F] {i j : J} (x : F.obj i) (y : F.obj j) :
-    colimit.ι F i x = colimit.ι F j y ↔ ∃ (k : _)(f : i ⟶ k)(g : j ⟶ k), F.map f x = F.map g y :=
+    colimit.ι F i x = colimit.ι F j y ↔ ∃ (k : _) (f : i ⟶ k) (g : j ⟶ k), F.map f x = F.map g y :=
   ⟨Concrete.colimit_exists_of_rep_eq _ _ _, Concrete.colimit_rep_eq_of_exists _ _ _⟩
 #align category_theory.limits.concrete.colimit_rep_eq_iff_exists CategoryTheory.Limits.Concrete.colimit_rep_eq_iff_exists
 
@@ -312,7 +312,7 @@ open WidePushoutShape
 
 theorem Concrete.widePushout_exists_rep {B : C} {α : Type _} {X : α → C} (f : ∀ j : α, B ⟶ X j)
     [HasWidePushout.{v} B X f] [PreservesColimit (wideSpan B X f) (forget C)]
-    (x : ↑(widePushout B X f)) : (∃ y : B, head f y = x) ∨ ∃ (i : α)(y : X i), ι f i y = x := by
+    (x : ↑(widePushout B X f)) : (∃ y : B, head f y = x) ∨ ∃ (i : α) (y : X i), ι f i y = x := by
   obtain ⟨_ | j, y, rfl⟩ := Concrete.colimit_exists_rep _ x
   · left
     use y
@@ -322,7 +322,7 @@ theorem Concrete.widePushout_exists_rep {B : C} {α : Type _} {X : α → C} (f
 
 theorem Concrete.widePushout_exists_rep' {B : C} {α : Type _} [Nonempty α] {X : α → C}
     (f : ∀ j : α, B ⟶ X j) [HasWidePushout.{v} B X f] [PreservesColimit (wideSpan B X f) (forget C)]
-    (x : ↑(widePushout B X f)) : ∃ (i : α)(y : X i), ι f i y = x := by
+    (x : ↑(widePushout B X f)) : ∃ (i : α) (y : X i), ι f i y = x := by
   rcases Concrete.widePushout_exists_rep f x with (⟨y, rfl⟩ | ⟨i, y, rfl⟩)
   · inhabit α
     use default, f _ y

c3019c79

chore: bye-bye, solo bys! (#3825)

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

14167e48

Diff

@@ -101,11 +101,9 @@ theorem Concrete.multiequalizer_ext {I : MulticospanIndex.{w} C} [HasMultiequali
 /-- An auxiliary equivalence to be used in `multiequalizerEquiv` below.-/
 def Concrete.multiequalizerEquivAux (I : MulticospanIndex C) :
     (I.multicospan ⋙ forget C).sections ≃
-      { x : ∀ i : I.L, I.left i // ∀ i : I.R, I.fst i (x _) = I.snd i (x _) }
-    where
+    { x : ∀ i : I.L, I.left i // ∀ i : I.R, I.fst i (x _) = I.snd i (x _) } where
   toFun x :=
-    ⟨fun i => x.1 (WalkingMulticospan.left _), fun i =>
-      by
+    ⟨fun i => x.1 (WalkingMulticospan.left _), fun i => by
       have a := x.2 (WalkingMulticospan.Hom.fst i)
       have b := x.2 (WalkingMulticospan.Hom.snd i)
       rw [← b] at a
@@ -192,8 +190,7 @@ theorem Concrete.from_union_surjective_of_isColimit {D : Cocone F} (hD : IsColim
     replace hb := congr_arg TX.inv hb
     change (TX.hom ≫ TX.inv) (ff b) = (TX.hom ≫ TX.inv) _ at hb
     simpa only [TX.hom_inv_id] using hb
-  have : TX.hom ∘ ff = fun a => G.ι.app a.1 a.2 :=
-    by
+  have : TX.hom ∘ ff = fun a => G.ι.app a.1 a.2 := by
     ext a
     change (E.ι.app a.1 ≫ hE.desc G) a.2 = _
     rw [hE.fac]

c3019c79

feat: port CategoryTheory.Limits.ConcreteCategory (#3023)

Co-authored-by: adamtopaz <github@adamtopaz.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Adam Topaz <adamtopaz@users.noreply.github.com> Co-authored-by: Moritz Firsching <firsching@google.com>

507eaf9e

`category_theory.limits.concrete_category` ⟷ `Mathlib.CategoryTheory.Limits.ConcreteCategory`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 2 + 250

category_theory.limits.concrete_category ⟷ Mathlib.CategoryTheory.Limits.ConcreteCategory

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 2 + 250

`category_theory.limits.concrete_category` ⟷ `Mathlib.CategoryTheory.Limits.ConcreteCategory`