algebraic_geometry.presheafed_space ⟷ Mathlib.Geometry.RingedSpace.PresheafedSpace

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

@@ -296,7 +296,7 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.Hom _* X.2 ≅ Y.2) : X ≅ Y
     erw [← α.hom.naturality]
     have := nat_trans.congr_app α.inv_hom_id (op x)
     cases x
-    rw [nat_trans.comp_app] at this 
+    rw [nat_trans.comp_app] at this
     convert this
     · dsimp; simp
     · simp
@@ -314,15 +314,15 @@ def sheafIsoOfIso (H : X ≅ Y) : Y.2 ≅ H.Hom.base _* X.2
   hom_inv_id' := by
     ext U
     have := congr_app H.inv_hom_id U
-    simp only [comp_c_app, id_c_app, eq_to_hom_map, eq_to_hom_trans] at this 
-    generalize_proofs h at this 
+    simp only [comp_c_app, id_c_app, eq_to_hom_map, eq_to_hom_trans] at this
+    generalize_proofs h at this
     simpa using congr_arg (fun f => f ≫ eq_to_hom h.symm) this
   inv_hom_id' := by
     ext U
     simp only [presheaf.pushforward_to_of_iso_app, nat_trans.comp_app, category.assoc,
       nat_trans.id_app, H.hom.c.naturality]
     have := congr_app H.hom_inv_id ((opens.map H.hom.base).op.obj U)
-    generalize_proofs h at this 
+    generalize_proofs h at this
     simpa using congr_arg (fun f => f ≫ X.presheaf.map (eq_to_hom h.symm)) this
 #align algebraic_geometry.PresheafedSpace.sheaf_iso_of_iso AlgebraicGeometry.PresheafedSpace.sheafIsoOfIso
 -/
@@ -397,17 +397,17 @@ instance ofRestrict_mono {U : TopCat} (X : PresheafedSpace C) (f : U ⟶ X.1) (h
         _)
     have := PresheafedSpace.congr_app Eq (op (hf.is_open_map.functor.obj V))
     simp only [PresheafedSpace.comp_c_app, PresheafedSpace.of_restrict_c_app, category.assoc,
-      cancel_epi] at this 
+      cancel_epi] at this
     have h : _ ≫ _ = _ ≫ _ ≫ _ :=
       congr_arg (fun f => (X.restrict hf).Presheaf.map (eq_to_hom hV).op ≫ f) this
-    erw [g₁.c.naturality, g₂.c.naturality_assoc] at h 
+    erw [g₁.c.naturality, g₂.c.naturality_assoc] at h
     simp only [presheaf.pushforward_obj_map, eq_to_hom_op, category.assoc, eq_to_hom_map,
-      eq_to_hom_trans] at h 
-    rw [← is_iso.comp_inv_eq] at h 
+      eq_to_hom_trans] at h
+    rw [← is_iso.comp_inv_eq] at h
     simpa using h
   · have := congr_arg PresheafedSpace.hom.base Eq
-    simp only [PresheafedSpace.comp_base, PresheafedSpace.of_restrict_base] at this 
-    rw [cancel_mono] at this 
+    simp only [PresheafedSpace.comp_base, PresheafedSpace.of_restrict_base] at this
+    rw [cancel_mono] at this
     exact this
 #align algebraic_geometry.PresheafedSpace.of_restrict_mono AlgebraicGeometry.PresheafedSpace.ofRestrict_mono
 -/

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

@@ -3,8 +3,8 @@ Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.Topology.Sheaves.Presheaf
-import Mathbin.CategoryTheory.Adjunction.FullyFaithful
+import Topology.Sheaves.Presheaf
+import CategoryTheory.Adjunction.FullyFaithful
 
 #align_import algebraic_geometry.presheafed_space from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module algebraic_geometry.presheafed_space
-! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Sheaves.Presheaf
 import Mathbin.CategoryTheory.Adjunction.FullyFaithful
 
+#align_import algebraic_geometry.presheafed_space from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
+
 /-!
 # Presheafed spaces
 

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

@@ -43,11 +43,13 @@ attribute [local tidy] tactic.op_induction' tactic.auto_cases_opens
 
 namespace AlgebraicGeometry
 
+#print AlgebraicGeometry.PresheafedSpace /-
 /-- A `PresheafedSpace C` is a topological space equipped with a presheaf of `C`s. -/
 structure PresheafedSpace where
   carrier : TopCat.{w}
   Presheaf : carrier.Presheaf C
 #align algebraic_geometry.PresheafedSpace AlgebraicGeometry.PresheafedSpace
+-/
 
 variable {C}
 
@@ -55,24 +57,29 @@ namespace PresheafedSpace
 
 attribute [protected] presheaf
 
+#print AlgebraicGeometry.PresheafedSpace.coeCarrier /-
 instance coeCarrier : Coe (PresheafedSpace.{w, v, u} C) TopCat.{w} where coe X := X.carrier
 #align algebraic_geometry.PresheafedSpace.coe_carrier AlgebraicGeometry.PresheafedSpace.coeCarrier
+-/
 
 @[simp]
 theorem as_coe (X : PresheafedSpace.{w, v, u} C) : X.carrier = (X : TopCat.{w}) :=
   rfl
 #align algebraic_geometry.PresheafedSpace.as_coe AlgebraicGeometry.PresheafedSpace.as_coe
 
+#print AlgebraicGeometry.PresheafedSpace.mk_coe /-
 @[simp]
 theorem mk_coe (carrier) (presheaf) :
     (({     carrier
             Presheaf } : PresheafedSpace.{v} C) : TopCat.{v}) = carrier :=
   rfl
 #align algebraic_geometry.PresheafedSpace.mk_coe AlgebraicGeometry.PresheafedSpace.mk_coe
+-/
 
 instance (X : PresheafedSpace.{v} C) : TopologicalSpace X :=
   X.carrier.str
 
+#print AlgebraicGeometry.PresheafedSpace.const /-
 /-- The constant presheaf on `X` with value `Z`. -/
 def const (X : TopCat) (Z : C) : PresheafedSpace C
     where
@@ -81,10 +88,12 @@ def const (X : TopCat) (Z : C) : PresheafedSpace C
     { obj := fun U => Z
       map := fun U V f => 𝟙 Z }
 #align algebraic_geometry.PresheafedSpace.const AlgebraicGeometry.PresheafedSpace.const
+-/
 
 instance [Inhabited C] : Inhabited (PresheafedSpace C) :=
   ⟨const (TopCat.of PEmpty) default⟩
 
+#print AlgebraicGeometry.PresheafedSpace.Hom /-
 /-- A morphism between presheafed spaces `X` and `Y` consists of a continuous map
     `f` between the underlying topological spaces, and a (notice contravariant!) map
     from the presheaf on `Y` to the pushforward of the presheaf on `X` via `f`. -/
@@ -92,7 +101,9 @@ structure Hom (X Y : PresheafedSpace.{w, v, u} C) where
   base : (X : TopCat.{w}) ⟶ (Y : TopCat.{w})
   c : Y.Presheaf ⟶ base _* X.Presheaf
 #align algebraic_geometry.PresheafedSpace.hom AlgebraicGeometry.PresheafedSpace.Hom
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.Hom.ext /-
 @[ext]
 theorem AlgebraicGeometry.PresheafedSpace.Hom.ext {X Y : PresheafedSpace C} (α β : Hom X Y)
     (w : α.base = β.base) (h : α.c ≫ whiskerRight (eqToHom (by rw [w])) _ = β.c) : α = β :=
@@ -101,34 +112,45 @@ theorem AlgebraicGeometry.PresheafedSpace.Hom.ext {X Y : PresheafedSpace C} (α
   dsimp [presheaf.pushforward_obj] at *
   tidy
 #align algebraic_geometry.PresheafedSpace.ext AlgebraicGeometry.PresheafedSpace.Hom.ext
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.hext /-
 -- TODO including `injections` would make tidy work earlier.
 theorem hext {X Y : PresheafedSpace C} (α β : Hom X Y) (w : α.base = β.base) (h : HEq α.c β.c) :
     α = β := by cases α; cases β; congr; exacts [w, h]
 #align algebraic_geometry.PresheafedSpace.hext AlgebraicGeometry.PresheafedSpace.hext
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.id /-
 /-- The identity morphism of a `PresheafedSpace`. -/
 def id (X : PresheafedSpace.{w, v, u} C) : Hom X X
     where
   base := 𝟙 (X : TopCat.{w})
   c := eqToHom (Presheaf.Pushforward.id_eq X.Presheaf).symm
 #align algebraic_geometry.PresheafedSpace.id AlgebraicGeometry.PresheafedSpace.id
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.homInhabited /-
 instance homInhabited (X : PresheafedSpace C) : Inhabited (Hom X X) :=
   ⟨id X⟩
 #align algebraic_geometry.PresheafedSpace.hom_inhabited AlgebraicGeometry.PresheafedSpace.homInhabited
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.comp /-
 /-- Composition of morphisms of `PresheafedSpace`s. -/
 def comp {X Y Z : PresheafedSpace C} (α : Hom X Y) (β : Hom Y Z) : Hom X Z
     where
   base := α.base ≫ β.base
   c := β.c ≫ (Presheaf.pushforward _ β.base).map α.c
 #align algebraic_geometry.PresheafedSpace.comp AlgebraicGeometry.PresheafedSpace.comp
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.comp_c /-
 theorem comp_c {X Y Z : PresheafedSpace C} (α : Hom X Y) (β : Hom Y Z) :
     (comp α β).c = β.c ≫ (Presheaf.pushforward _ β.base).map α.c :=
   rfl
 #align algebraic_geometry.PresheafedSpace.comp_c AlgebraicGeometry.PresheafedSpace.comp_c
+-/
 
 variable (C)
 
@@ -136,6 +158,7 @@ section
 
 attribute [local simp] id comp
 
+#print AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces /-
 /- The proofs below can be done by `tidy`, but it is too slow,
    and we don't have a tactic caching mechanism. -/
 /-- The category of PresheafedSpaces. Morphisms are pairs, a continuous map and a presheaf map
@@ -169,6 +192,7 @@ instance categoryOfPresheafedSpaces : Category (PresheafedSpace.{v, v, u} C)
     congr
     rfl
 #align algebraic_geometry.PresheafedSpace.category_of_PresheafedSpaces AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces
+-/
 
 end
 
@@ -176,28 +200,36 @@ variable {C}
 
 attribute [local simp] eq_to_hom_map
 
+#print AlgebraicGeometry.PresheafedSpace.id_base /-
 @[simp]
 theorem id_base (X : PresheafedSpace.{v, v, u} C) : (𝟙 X : X ⟶ X).base = 𝟙 (X : TopCat.{v}) :=
   rfl
 #align algebraic_geometry.PresheafedSpace.id_base AlgebraicGeometry.PresheafedSpace.id_base
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.id_c /-
 theorem id_c (X : PresheafedSpace.{v, v, u} C) :
     (𝟙 X : X ⟶ X).c = eqToHom (Presheaf.Pushforward.id_eq X.Presheaf).symm :=
   rfl
 #align algebraic_geometry.PresheafedSpace.id_c AlgebraicGeometry.PresheafedSpace.id_c
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.id_c_app /-
 @[simp]
 theorem id_c_app (X : PresheafedSpace.{v, v, u} C) (U) :
     (𝟙 X : X ⟶ X).c.app U =
       X.Presheaf.map (eqToHom (by induction U using Opposite.rec'; cases U; rfl)) :=
   by induction U using Opposite.rec'; cases U; simp only [id_c]; dsimp; simp
 #align algebraic_geometry.PresheafedSpace.id_c_app AlgebraicGeometry.PresheafedSpace.id_c_app
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.comp_base /-
 @[simp]
 theorem comp_base {X Y Z : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) (g : Y ⟶ Z) :
     (f ≫ g).base = f.base ≫ g.base :=
   rfl
 #align algebraic_geometry.PresheafedSpace.comp_base AlgebraicGeometry.PresheafedSpace.comp_base
+-/
 
 instance (X Y : PresheafedSpace.{v, v, u} C) : CoeFun (X ⟶ Y) fun _ => X → Y :=
   ⟨fun f => f.base⟩
@@ -206,6 +238,7 @@ theorem coe_to_fun_eq {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) : (f : X
   rfl
 #align algebraic_geometry.PresheafedSpace.coe_to_fun_eq AlgebraicGeometry.PresheafedSpace.coe_to_fun_eq
 
+#print AlgebraicGeometry.PresheafedSpace.comp_c_app /-
 -- The `reassoc` attribute was added despite the LHS not being a composition of two homs,
 -- for the reasons explained in the docstring.
 /-- Sometimes rewriting with `comp_c_app` doesn't work because of dependent type issues.
@@ -216,15 +249,19 @@ theorem comp_c_app {X Y Z : PresheafedSpace.{v, v, u} C} (α : X ⟶ Y) (β : Y
     (α ≫ β).c.app U = β.c.app U ≫ α.c.app (op ((Opens.map β.base).obj (unop U))) :=
   rfl
 #align algebraic_geometry.PresheafedSpace.comp_c_app AlgebraicGeometry.PresheafedSpace.comp_c_app
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.congr_app /-
 theorem congr_app {X Y : PresheafedSpace.{v, v, u} C} {α β : X ⟶ Y} (h : α = β) (U) :
     α.c.app U = β.c.app U ≫ X.Presheaf.map (eqToHom (by subst h)) := by subst h; dsimp; simp
 #align algebraic_geometry.PresheafedSpace.congr_app AlgebraicGeometry.PresheafedSpace.congr_app
+-/
 
 section
 
 variable (C)
 
+#print AlgebraicGeometry.PresheafedSpace.forget /-
 /-- The forgetful functor from `PresheafedSpace` to `Top`. -/
 @[simps]
 def forget : PresheafedSpace.{v, v, u} C ⥤ TopCat
@@ -232,6 +269,7 @@ def forget : PresheafedSpace.{v, v, u} C ⥤ TopCat
   obj X := (X : TopCat.{v})
   map X Y f := f.base
 #align algebraic_geometry.PresheafedSpace.forget AlgebraicGeometry.PresheafedSpace.forget
+-/
 
 end
 
@@ -239,6 +277,7 @@ section Iso
 
 variable {X Y : PresheafedSpace.{v, v, u} C}
 
+#print AlgebraicGeometry.PresheafedSpace.isoOfComponents /-
 /-- An isomorphism of PresheafedSpaces is a homeomorphism of the underlying space, and a
 natural transformation between the sheaves.
 -/
@@ -266,7 +305,9 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.Hom _* X.2 ≅ Y.2) : X ≅ Y
     · simp
     · simp
 #align algebraic_geometry.PresheafedSpace.iso_of_components AlgebraicGeometry.PresheafedSpace.isoOfComponents
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.sheafIsoOfIso /-
 /-- Isomorphic PresheafedSpaces have natural isomorphic presheaves. -/
 @[simps]
 def sheafIsoOfIso (H : X ≅ Y) : Y.2 ≅ H.Hom.base _* X.2
@@ -287,26 +328,34 @@ def sheafIsoOfIso (H : X ≅ Y) : Y.2 ≅ H.Hom.base _* X.2
     generalize_proofs h at this 
     simpa using congr_arg (fun f => f ≫ X.presheaf.map (eq_to_hom h.symm)) this
 #align algebraic_geometry.PresheafedSpace.sheaf_iso_of_iso AlgebraicGeometry.PresheafedSpace.sheafIsoOfIso
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.base_isIso_of_iso /-
 instance base_isIso_of_iso (f : X ⟶ Y) [IsIso f] : IsIso f.base :=
   IsIso.of_iso ((forget _).mapIso (asIso f))
 #align algebraic_geometry.PresheafedSpace.base_is_iso_of_iso AlgebraicGeometry.PresheafedSpace.base_isIso_of_iso
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.c_isIso_of_iso /-
 instance c_isIso_of_iso (f : X ⟶ Y) [IsIso f] : IsIso f.c :=
   IsIso.of_iso (sheafIsoOfIso (asIso f))
 #align algebraic_geometry.PresheafedSpace.c_is_iso_of_iso AlgebraicGeometry.PresheafedSpace.c_isIso_of_iso
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.isIso_of_components /-
 /-- This could be used in conjunction with `category_theory.nat_iso.is_iso_of_is_iso_app`. -/
 theorem isIso_of_components (f : X ⟶ Y) [IsIso f.base] [IsIso f.c] : IsIso f :=
   by
   convert is_iso.of_iso (iso_of_components (as_iso f.base) (as_iso f.c).symm)
   ext; · simpa; · simp
 #align algebraic_geometry.PresheafedSpace.is_iso_of_components AlgebraicGeometry.PresheafedSpace.isIso_of_components
+-/
 
 end Iso
 
 section Restrict
 
+#print AlgebraicGeometry.PresheafedSpace.restrict /-
 /-- The restriction of a presheafed space along an open embedding into the space.
 -/
 @[simps]
@@ -316,7 +365,9 @@ def restrict {U : TopCat} (X : PresheafedSpace.{v, v, u} C) {f : U ⟶ (X : TopC
   carrier := U
   Presheaf := h.IsOpenMap.Functor.op ⋙ X.Presheaf
 #align algebraic_geometry.PresheafedSpace.restrict AlgebraicGeometry.PresheafedSpace.restrict
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.ofRestrict /-
 /-- The map from the restriction of a presheafed space.
 -/
 @[simps]
@@ -329,7 +380,9 @@ def ofRestrict {U : TopCat} (X : PresheafedSpace.{v, v, u} C) {f : U ⟶ (X : To
       naturality' := fun U V f =>
         show _ = _ ≫ X.Presheaf.map _ by rw [← map_comp, ← map_comp]; rfl }
 #align algebraic_geometry.PresheafedSpace.of_restrict AlgebraicGeometry.PresheafedSpace.ofRestrict
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.ofRestrict_mono /-
 instance ofRestrict_mono {U : TopCat} (X : PresheafedSpace C) (f : U ⟶ X.1) (hf : OpenEmbedding f) :
     Mono (X.of_restrict hf) :=
   by
@@ -360,13 +413,17 @@ instance ofRestrict_mono {U : TopCat} (X : PresheafedSpace C) (f : U ⟶ X.1) (h
     rw [cancel_mono] at this 
     exact this
 #align algebraic_geometry.PresheafedSpace.of_restrict_mono AlgebraicGeometry.PresheafedSpace.ofRestrict_mono
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf /-
 theorem restrict_top_presheaf (X : PresheafedSpace C) :
     (X.restrict (Opens.openEmbedding ⊤)).Presheaf =
       (Opens.inclusionTopIso X.carrier).inv _* X.Presheaf :=
   by dsimp; rw [opens.inclusion_top_functor X.carrier]; rfl
 #align algebraic_geometry.PresheafedSpace.restrict_top_presheaf AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c /-
 theorem ofRestrict_top_c (X : PresheafedSpace C) :
     (X.of_restrict (Opens.openEmbedding ⊤)).c =
       eqToHom
@@ -383,7 +440,9 @@ theorem ofRestrict_top_c (X : PresheafedSpace C) :
   · induction U using Opposite.rec'; dsimp; congr; ext
     exact ⟨fun h => ⟨⟨x, trivial⟩, h, rfl⟩, fun ⟨⟨_, _⟩, h, rfl⟩ => h⟩
 #align algebraic_geometry.PresheafedSpace.of_restrict_top_c AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.toRestrictTop /-
 /- or `rw [opens.inclusion_top_functor, ←comp_obj, ←opens.map_comp_eq],
          erw iso.inv_hom_id, cases U, refl` after `dsimp` -/
 /-- The map to the restriction of a presheafed space along the canonical inclusion from the top
@@ -395,7 +454,9 @@ def toRestrictTop (X : PresheafedSpace C) : X ⟶ X.restrict (Opens.openEmbeddin
   base := (Opens.inclusionTopIso X.carrier).inv
   c := eqToHom (restrict_top_presheaf X)
 #align algebraic_geometry.PresheafedSpace.to_restrict_top AlgebraicGeometry.PresheafedSpace.toRestrictTop
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.restrictTopIso /-
 /-- The isomorphism from the restriction to the top subspace.
 -/
 @[simps]
@@ -411,9 +472,11 @@ def restrictTopIso (X : PresheafedSpace C) : X.restrict (Opens.openEmbedding ⊤
     AlgebraicGeometry.PresheafedSpace.Hom.ext _ _ rfl <| by erw [comp_c]; rw [X.of_restrict_top_c];
       ext; simpa [-eq_to_hom_refl]
 #align algebraic_geometry.PresheafedSpace.restrict_top_iso AlgebraicGeometry.PresheafedSpace.restrictTopIso
+-/
 
 end Restrict
 
+#print AlgebraicGeometry.PresheafedSpace.Γ /-
 /-- The global sections, notated Gamma.
 -/
 @[simps]
@@ -422,14 +485,19 @@ def Γ : (PresheafedSpace.{v, v, u} C)ᵒᵖ ⥤ C
   obj X := (unop X).Presheaf.obj (op ⊤)
   map X Y f := f.unop.c.app (op ⊤)
 #align algebraic_geometry.PresheafedSpace.Γ AlgebraicGeometry.PresheafedSpace.Γ
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.Γ_obj_op /-
 theorem Γ_obj_op (X : PresheafedSpace C) : Γ.obj (op X) = X.Presheaf.obj (op ⊤) :=
   rfl
 #align algebraic_geometry.PresheafedSpace.Γ_obj_op AlgebraicGeometry.PresheafedSpace.Γ_obj_op
+-/
 
+#print AlgebraicGeometry.PresheafedSpace.Γ_map_op /-
 theorem Γ_map_op {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) : Γ.map f.op = f.c.app (op ⊤) :=
   rfl
 #align algebraic_geometry.PresheafedSpace.Γ_map_op AlgebraicGeometry.PresheafedSpace.Γ_map_op
+-/
 
 end PresheafedSpace
 
@@ -447,6 +515,7 @@ attribute [local simp] presheaf.pushforward_obj
 
 namespace Functor
 
+#print CategoryTheory.Functor.mapPresheaf /-
 /-- We can apply a functor `F : C ⥤ D` to the values of the presheaf in any `PresheafedSpace C`,
     giving a functor `PresheafedSpace C ⥤ PresheafedSpace D` -/
 def mapPresheaf (F : C ⥤ D) : PresheafedSpace.{v, v, u} C ⥤ PresheafedSpace.{v, v, u} D
@@ -458,35 +527,45 @@ def mapPresheaf (F : C ⥤ D) : PresheafedSpace.{v, v, u} C ⥤ PresheafedSpace.
     { base := f.base
       c := whiskerRight f.c F }
 #align category_theory.functor.map_presheaf CategoryTheory.Functor.mapPresheaf
+-/
 
+#print CategoryTheory.Functor.mapPresheaf_obj_X /-
 @[simp]
 theorem mapPresheaf_obj_X (F : C ⥤ D) (X : PresheafedSpace C) :
     (F.mapPresheaf.obj X : TopCat.{v}) = (X : TopCat.{v}) :=
   rfl
 #align category_theory.functor.map_presheaf_obj_X CategoryTheory.Functor.mapPresheaf_obj_X
+-/
 
+#print CategoryTheory.Functor.mapPresheaf_obj_presheaf /-
 @[simp]
 theorem mapPresheaf_obj_presheaf (F : C ⥤ D) (X : PresheafedSpace C) :
     (F.mapPresheaf.obj X).Presheaf = X.Presheaf ⋙ F :=
   rfl
 #align category_theory.functor.map_presheaf_obj_presheaf CategoryTheory.Functor.mapPresheaf_obj_presheaf
+-/
 
+#print CategoryTheory.Functor.mapPresheaf_map_f /-
 @[simp]
 theorem mapPresheaf_map_f (F : C ⥤ D) {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) :
     (F.mapPresheaf.map f).base = f.base :=
   rfl
 #align category_theory.functor.map_presheaf_map_f CategoryTheory.Functor.mapPresheaf_map_f
+-/
 
+#print CategoryTheory.Functor.mapPresheaf_map_c /-
 @[simp]
 theorem mapPresheaf_map_c (F : C ⥤ D) {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) :
     (F.mapPresheaf.map f).c = whiskerRight f.c F :=
   rfl
 #align category_theory.functor.map_presheaf_map_c CategoryTheory.Functor.mapPresheaf_map_c
+-/
 
 end Functor
 
 namespace NatTrans
 
+#print CategoryTheory.NatTrans.onPresheaf /-
 /-- A natural transformation induces a natural transformation between the `map_presheaf` functors.
 -/
 def onPresheaf {F G : C ⥤ D} (α : F ⟶ G) : G.mapPresheaf ⟶ F.mapPresheaf
@@ -494,6 +573,7 @@ def onPresheaf {F G : C ⥤ D} (α : F ⟶ G) : G.mapPresheaf ⟶ F.mapPresheaf
     { base := 𝟙 _
       c := whiskerLeft X.Presheaf α ≫ eqToHom (Presheaf.Pushforward.id_eq _).symm }
 #align category_theory.nat_trans.on_presheaf CategoryTheory.NatTrans.onPresheaf
+-/
 
 -- TODO Assemble the last two constructions into a functor
 --   `(C ⥤ D) ⥤ (PresheafedSpace C ⥤ PresheafedSpace D)`

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

@@ -277,14 +277,14 @@ def sheafIsoOfIso (H : X ≅ Y) : Y.2 ≅ H.Hom.base _* X.2
     ext U
     have := congr_app H.inv_hom_id U
     simp only [comp_c_app, id_c_app, eq_to_hom_map, eq_to_hom_trans] at this 
-    generalize_proofs h  at this 
+    generalize_proofs h at this 
     simpa using congr_arg (fun f => f ≫ eq_to_hom h.symm) this
   inv_hom_id' := by
     ext U
     simp only [presheaf.pushforward_to_of_iso_app, nat_trans.comp_app, category.assoc,
       nat_trans.id_app, H.hom.c.naturality]
     have := congr_app H.hom_inv_id ((opens.map H.hom.base).op.obj U)
-    generalize_proofs h  at this 
+    generalize_proofs h at this 
     simpa using congr_arg (fun f => f ≫ X.presheaf.map (eq_to_hom h.symm)) this
 #align algebraic_geometry.PresheafedSpace.sheaf_iso_of_iso AlgebraicGeometry.PresheafedSpace.sheafIsoOfIso
 

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

@@ -104,7 +104,7 @@ theorem AlgebraicGeometry.PresheafedSpace.Hom.ext {X Y : PresheafedSpace C} (α
 
 -- TODO including `injections` would make tidy work earlier.
 theorem hext {X Y : PresheafedSpace C} (α β : Hom X Y) (w : α.base = β.base) (h : HEq α.c β.c) :
-    α = β := by cases α; cases β; congr ; exacts[w, h]
+    α = β := by cases α; cases β; congr; exacts [w, h]
 #align algebraic_geometry.PresheafedSpace.hext AlgebraicGeometry.PresheafedSpace.hext
 
 /-- The identity morphism of a `PresheafedSpace`. -/
@@ -260,7 +260,7 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.Hom _* X.2 ≅ Y.2) : X ≅ Y
     erw [← α.hom.naturality]
     have := nat_trans.congr_app α.inv_hom_id (op x)
     cases x
-    rw [nat_trans.comp_app] at this
+    rw [nat_trans.comp_app] at this 
     convert this
     · dsimp; simp
     · simp
@@ -276,15 +276,15 @@ def sheafIsoOfIso (H : X ≅ Y) : Y.2 ≅ H.Hom.base _* X.2
   hom_inv_id' := by
     ext U
     have := congr_app H.inv_hom_id U
-    simp only [comp_c_app, id_c_app, eq_to_hom_map, eq_to_hom_trans] at this
-    generalize_proofs h  at this
+    simp only [comp_c_app, id_c_app, eq_to_hom_map, eq_to_hom_trans] at this 
+    generalize_proofs h  at this 
     simpa using congr_arg (fun f => f ≫ eq_to_hom h.symm) this
   inv_hom_id' := by
     ext U
     simp only [presheaf.pushforward_to_of_iso_app, nat_trans.comp_app, category.assoc,
       nat_trans.id_app, H.hom.c.naturality]
     have := congr_app H.hom_inv_id ((opens.map H.hom.base).op.obj U)
-    generalize_proofs h  at this
+    generalize_proofs h  at this 
     simpa using congr_arg (fun f => f ≫ X.presheaf.map (eq_to_hom h.symm)) this
 #align algebraic_geometry.PresheafedSpace.sheaf_iso_of_iso AlgebraicGeometry.PresheafedSpace.sheafIsoOfIso
 
@@ -347,17 +347,17 @@ instance ofRestrict_mono {U : TopCat} (X : PresheafedSpace C) (f : U ⟶ X.1) (h
         _)
     have := PresheafedSpace.congr_app Eq (op (hf.is_open_map.functor.obj V))
     simp only [PresheafedSpace.comp_c_app, PresheafedSpace.of_restrict_c_app, category.assoc,
-      cancel_epi] at this
+      cancel_epi] at this 
     have h : _ ≫ _ = _ ≫ _ ≫ _ :=
       congr_arg (fun f => (X.restrict hf).Presheaf.map (eq_to_hom hV).op ≫ f) this
-    erw [g₁.c.naturality, g₂.c.naturality_assoc] at h
+    erw [g₁.c.naturality, g₂.c.naturality_assoc] at h 
     simp only [presheaf.pushforward_obj_map, eq_to_hom_op, category.assoc, eq_to_hom_map,
-      eq_to_hom_trans] at h
-    rw [← is_iso.comp_inv_eq] at h
+      eq_to_hom_trans] at h 
+    rw [← is_iso.comp_inv_eq] at h 
     simpa using h
   · have := congr_arg PresheafedSpace.hom.base Eq
-    simp only [PresheafedSpace.comp_base, PresheafedSpace.of_restrict_base] at this
-    rw [cancel_mono] at this
+    simp only [PresheafedSpace.comp_base, PresheafedSpace.of_restrict_base] at this 
+    rw [cancel_mono] at this 
     exact this
 #align algebraic_geometry.PresheafedSpace.of_restrict_mono AlgebraicGeometry.PresheafedSpace.ofRestrict_mono
 
@@ -379,8 +379,8 @@ theorem ofRestrict_top_c (X : PresheafedSpace C) :
        issue when `apply nat_iso.is_iso_of_is_iso_app`. -/
   ext U;
   change X.presheaf.map _ = _; convert eq_to_hom_map _ _ using 1
-  congr ; simpa
-  · induction U using Opposite.rec'; dsimp; congr ; ext
+  congr; simpa
+  · induction U using Opposite.rec'; dsimp; congr; ext
     exact ⟨fun h => ⟨⟨x, trivial⟩, h, rfl⟩, fun ⟨⟨_, _⟩, h, rfl⟩ => h⟩
 #align algebraic_geometry.PresheafedSpace.of_restrict_top_c AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c
 

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

@@ -43,12 +43,6 @@ attribute [local tidy] tactic.op_induction' tactic.auto_cases_opens
 
 namespace AlgebraicGeometry
 
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-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace AlgebraicGeometry.PresheafedSpaceₓ'. -/
 /-- A `PresheafedSpace C` is a topological space equipped with a presheaf of `C`s. -/
 structure PresheafedSpace where
   carrier : TopCat.{w}
@@ -61,12 +55,6 @@ namespace PresheafedSpace
 
 attribute [protected] presheaf
 
-/- warning: algebraic_geometry.PresheafedSpace.coe_carrier -> AlgebraicGeometry.PresheafedSpace.coeCarrier is a dubious translation:
-lean 3 declaration is
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 instance coeCarrier : Coe (PresheafedSpace.{w, v, u} C) TopCat.{w} where coe X := X.carrier
 #align algebraic_geometry.PresheafedSpace.coe_carrier AlgebraicGeometry.PresheafedSpace.coeCarrier
 
@@ -75,12 +63,6 @@ theorem as_coe (X : PresheafedSpace.{w, v, u} C) : X.carrier = (X : TopCat.{w})
   rfl
 #align algebraic_geometry.PresheafedSpace.as_coe AlgebraicGeometry.PresheafedSpace.as_coe
 
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 @[simp]
 theorem mk_coe (carrier) (presheaf) :
     (({     carrier
@@ -91,12 +73,6 @@ theorem mk_coe (carrier) (presheaf) :
 instance (X : PresheafedSpace.{v} C) : TopologicalSpace X :=
   X.carrier.str
 
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 /-- The constant presheaf on `X` with value `Z`. -/
 def const (X : TopCat) (Z : C) : PresheafedSpace C
     where
@@ -109,12 +85,6 @@ def const (X : TopCat) (Z : C) : PresheafedSpace C
 instance [Inhabited C] : Inhabited (PresheafedSpace C) :=
   ⟨const (TopCat.of PEmpty) default⟩
 
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-lean 3 declaration is
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 /-- A morphism between presheafed spaces `X` and `Y` consists of a continuous map
     `f` between the underlying topological spaces, and a (notice contravariant!) map
     from the presheaf on `Y` to the pushforward of the presheaf on `X` via `f`. -/
@@ -123,9 +93,6 @@ structure Hom (X Y : PresheafedSpace.{w, v, u} C) where
   c : Y.Presheaf ⟶ base _* X.Presheaf
 #align algebraic_geometry.PresheafedSpace.hom AlgebraicGeometry.PresheafedSpace.Hom
 
-/- warning: algebraic_geometry.PresheafedSpace.ext -> AlgebraicGeometry.PresheafedSpace.Hom.ext is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.ext AlgebraicGeometry.PresheafedSpace.Hom.extₓ'. -/
 @[ext]
 theorem AlgebraicGeometry.PresheafedSpace.Hom.ext {X Y : PresheafedSpace C} (α β : Hom X Y)
     (w : α.base = β.base) (h : α.c ≫ whiskerRight (eqToHom (by rw [w])) _ = β.c) : α = β :=
@@ -135,23 +102,11 @@ theorem AlgebraicGeometry.PresheafedSpace.Hom.ext {X Y : PresheafedSpace C} (α
   tidy
 #align algebraic_geometry.PresheafedSpace.ext AlgebraicGeometry.PresheafedSpace.Hom.ext
 
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 -- TODO including `injections` would make tidy work earlier.
 theorem hext {X Y : PresheafedSpace C} (α β : Hom X Y) (w : α.base = β.base) (h : HEq α.c β.c) :
     α = β := by cases α; cases β; congr ; exacts[w, h]
 #align algebraic_geometry.PresheafedSpace.hext AlgebraicGeometry.PresheafedSpace.hext
 
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 /-- The identity morphism of a `PresheafedSpace`. -/
 def id (X : PresheafedSpace.{w, v, u} C) : Hom X X
     where
@@ -159,22 +114,10 @@ def id (X : PresheafedSpace.{w, v, u} C) : Hom X X
   c := eqToHom (Presheaf.Pushforward.id_eq X.Presheaf).symm
 #align algebraic_geometry.PresheafedSpace.id AlgebraicGeometry.PresheafedSpace.id
 
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 instance homInhabited (X : PresheafedSpace C) : Inhabited (Hom X X) :=
   ⟨id X⟩
 #align algebraic_geometry.PresheafedSpace.hom_inhabited AlgebraicGeometry.PresheafedSpace.homInhabited
 
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 /-- Composition of morphisms of `PresheafedSpace`s. -/
 def comp {X Y Z : PresheafedSpace C} (α : Hom X Y) (β : Hom Y Z) : Hom X Z
     where
@@ -182,9 +125,6 @@ def comp {X Y Z : PresheafedSpace C} (α : Hom X Y) (β : Hom Y Z) : Hom X Z
   c := β.c ≫ (Presheaf.pushforward _ β.base).map α.c
 #align algebraic_geometry.PresheafedSpace.comp AlgebraicGeometry.PresheafedSpace.comp
 
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 theorem comp_c {X Y Z : PresheafedSpace C} (α : Hom X Y) (β : Hom Y Z) :
     (comp α β).c = β.c ≫ (Presheaf.pushforward _ β.base).map α.c :=
   rfl
@@ -196,12 +136,6 @@ section
 
 attribute [local simp] id comp
 
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 /- The proofs below can be done by `tidy`, but it is too slow,
    and we don't have a tactic caching mechanism. -/
 /-- The category of PresheafedSpaces. Morphisms are pairs, a continuous map and a presheaf map
@@ -242,31 +176,16 @@ variable {C}
 
 attribute [local simp] eq_to_hom_map
 
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 @[simp]
 theorem id_base (X : PresheafedSpace.{v, v, u} C) : (𝟙 X : X ⟶ X).base = 𝟙 (X : TopCat.{v}) :=
   rfl
 #align algebraic_geometry.PresheafedSpace.id_base AlgebraicGeometry.PresheafedSpace.id_base
 
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 theorem id_c (X : PresheafedSpace.{v, v, u} C) :
     (𝟙 X : X ⟶ X).c = eqToHom (Presheaf.Pushforward.id_eq X.Presheaf).symm :=
   rfl
 #align algebraic_geometry.PresheafedSpace.id_c AlgebraicGeometry.PresheafedSpace.id_c
 
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-<too large>
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 @[simp]
 theorem id_c_app (X : PresheafedSpace.{v, v, u} C) (U) :
     (𝟙 X : X ⟶ X).c.app U =
@@ -274,12 +193,6 @@ theorem id_c_app (X : PresheafedSpace.{v, v, u} C) (U) :
   by induction U using Opposite.rec'; cases U; simp only [id_c]; dsimp; simp
 #align algebraic_geometry.PresheafedSpace.id_c_app AlgebraicGeometry.PresheafedSpace.id_c_app
 
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 @[simp]
 theorem comp_base {X Y Z : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) (g : Y ⟶ Z) :
     (f ≫ g).base = f.base ≫ g.base :=
@@ -293,9 +206,6 @@ theorem coe_to_fun_eq {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) : (f : X
   rfl
 #align algebraic_geometry.PresheafedSpace.coe_to_fun_eq AlgebraicGeometry.PresheafedSpace.coe_to_fun_eq
 
-/- warning: algebraic_geometry.PresheafedSpace.comp_c_app -> AlgebraicGeometry.PresheafedSpace.comp_c_app is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.comp_c_app AlgebraicGeometry.PresheafedSpace.comp_c_appₓ'. -/
 -- The `reassoc` attribute was added despite the LHS not being a composition of two homs,
 -- for the reasons explained in the docstring.
 /-- Sometimes rewriting with `comp_c_app` doesn't work because of dependent type issues.
@@ -307,9 +217,6 @@ theorem comp_c_app {X Y Z : PresheafedSpace.{v, v, u} C} (α : X ⟶ Y) (β : Y
   rfl
 #align algebraic_geometry.PresheafedSpace.comp_c_app AlgebraicGeometry.PresheafedSpace.comp_c_app
 
-/- warning: algebraic_geometry.PresheafedSpace.congr_app -> AlgebraicGeometry.PresheafedSpace.congr_app is a dubious translation:
-<too large>
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 theorem congr_app {X Y : PresheafedSpace.{v, v, u} C} {α β : X ⟶ Y} (h : α = β) (U) :
     α.c.app U = β.c.app U ≫ X.Presheaf.map (eqToHom (by subst h)) := by subst h; dsimp; simp
 #align algebraic_geometry.PresheafedSpace.congr_app AlgebraicGeometry.PresheafedSpace.congr_app
@@ -318,12 +225,6 @@ section
 
 variable (C)
 
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 /-- The forgetful functor from `PresheafedSpace` to `Top`. -/
 @[simps]
 def forget : PresheafedSpace.{v, v, u} C ⥤ TopCat
@@ -338,12 +239,6 @@ section Iso
 
 variable {X Y : PresheafedSpace.{v, v, u} C}
 
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 /-- An isomorphism of PresheafedSpaces is a homeomorphism of the underlying space, and a
 natural transformation between the sheaves.
 -/
@@ -372,12 +267,6 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.Hom _* X.2 ≅ Y.2) : X ≅ Y
     · simp
 #align algebraic_geometry.PresheafedSpace.iso_of_components AlgebraicGeometry.PresheafedSpace.isoOfComponents
 
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 /-- Isomorphic PresheafedSpaces have natural isomorphic presheaves. -/
 @[simps]
 def sheafIsoOfIso (H : X ≅ Y) : Y.2 ≅ H.Hom.base _* X.2
@@ -399,32 +288,14 @@ def sheafIsoOfIso (H : X ≅ Y) : Y.2 ≅ H.Hom.base _* X.2
     simpa using congr_arg (fun f => f ≫ X.presheaf.map (eq_to_hom h.symm)) this
 #align algebraic_geometry.PresheafedSpace.sheaf_iso_of_iso AlgebraicGeometry.PresheafedSpace.sheafIsoOfIso
 
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 instance base_isIso_of_iso (f : X ⟶ Y) [IsIso f] : IsIso f.base :=
   IsIso.of_iso ((forget _).mapIso (asIso f))
 #align algebraic_geometry.PresheafedSpace.base_is_iso_of_iso AlgebraicGeometry.PresheafedSpace.base_isIso_of_iso
 
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 instance c_isIso_of_iso (f : X ⟶ Y) [IsIso f] : IsIso f.c :=
   IsIso.of_iso (sheafIsoOfIso (asIso f))
 #align algebraic_geometry.PresheafedSpace.c_is_iso_of_iso AlgebraicGeometry.PresheafedSpace.c_isIso_of_iso
 
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 /-- This could be used in conjunction with `category_theory.nat_iso.is_iso_of_is_iso_app`. -/
 theorem isIso_of_components (f : X ⟶ Y) [IsIso f.base] [IsIso f.c] : IsIso f :=
   by
@@ -436,9 +307,6 @@ end Iso
 
 section Restrict
 
-/- warning: algebraic_geometry.PresheafedSpace.restrict -> AlgebraicGeometry.PresheafedSpace.restrict is a dubious translation:
-<too large>
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 /-- The restriction of a presheafed space along an open embedding into the space.
 -/
 @[simps]
@@ -449,9 +317,6 @@ def restrict {U : TopCat} (X : PresheafedSpace.{v, v, u} C) {f : U ⟶ (X : TopC
   Presheaf := h.IsOpenMap.Functor.op ⋙ X.Presheaf
 #align algebraic_geometry.PresheafedSpace.restrict AlgebraicGeometry.PresheafedSpace.restrict
 
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-<too large>
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 /-- The map from the restriction of a presheafed space.
 -/
 @[simps]
@@ -465,12 +330,6 @@ def ofRestrict {U : TopCat} (X : PresheafedSpace.{v, v, u} C) {f : U ⟶ (X : To
         show _ = _ ≫ X.Presheaf.map _ by rw [← map_comp, ← map_comp]; rfl }
 #align algebraic_geometry.PresheafedSpace.of_restrict AlgebraicGeometry.PresheafedSpace.ofRestrict
 
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 instance ofRestrict_mono {U : TopCat} (X : PresheafedSpace C) (f : U ⟶ X.1) (hf : OpenEmbedding f) :
     Mono (X.of_restrict hf) :=
   by
@@ -502,18 +361,12 @@ instance ofRestrict_mono {U : TopCat} (X : PresheafedSpace C) (f : U ⟶ X.1) (h
     exact this
 #align algebraic_geometry.PresheafedSpace.of_restrict_mono AlgebraicGeometry.PresheafedSpace.ofRestrict_mono
 
-/- warning: algebraic_geometry.PresheafedSpace.restrict_top_presheaf -> AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.restrict_top_presheaf AlgebraicGeometry.PresheafedSpace.restrict_top_presheafₓ'. -/
 theorem restrict_top_presheaf (X : PresheafedSpace C) :
     (X.restrict (Opens.openEmbedding ⊤)).Presheaf =
       (Opens.inclusionTopIso X.carrier).inv _* X.Presheaf :=
   by dsimp; rw [opens.inclusion_top_functor X.carrier]; rfl
 #align algebraic_geometry.PresheafedSpace.restrict_top_presheaf AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf
 
-/- warning: algebraic_geometry.PresheafedSpace.of_restrict_top_c -> AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.of_restrict_top_c AlgebraicGeometry.PresheafedSpace.ofRestrict_top_cₓ'. -/
 theorem ofRestrict_top_c (X : PresheafedSpace C) :
     (X.of_restrict (Opens.openEmbedding ⊤)).c =
       eqToHom
@@ -531,9 +384,6 @@ theorem ofRestrict_top_c (X : PresheafedSpace C) :
     exact ⟨fun h => ⟨⟨x, trivial⟩, h, rfl⟩, fun ⟨⟨_, _⟩, h, rfl⟩ => h⟩
 #align algebraic_geometry.PresheafedSpace.of_restrict_top_c AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c
 
-/- warning: algebraic_geometry.PresheafedSpace.to_restrict_top -> AlgebraicGeometry.PresheafedSpace.toRestrictTop is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.to_restrict_top AlgebraicGeometry.PresheafedSpace.toRestrictTopₓ'. -/
 /- or `rw [opens.inclusion_top_functor, ←comp_obj, ←opens.map_comp_eq],
          erw iso.inv_hom_id, cases U, refl` after `dsimp` -/
 /-- The map to the restriction of a presheafed space along the canonical inclusion from the top
@@ -546,9 +396,6 @@ def toRestrictTop (X : PresheafedSpace C) : X ⟶ X.restrict (Opens.openEmbeddin
   c := eqToHom (restrict_top_presheaf X)
 #align algebraic_geometry.PresheafedSpace.to_restrict_top AlgebraicGeometry.PresheafedSpace.toRestrictTop
 
-/- warning: algebraic_geometry.PresheafedSpace.restrict_top_iso -> AlgebraicGeometry.PresheafedSpace.restrictTopIso is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.restrict_top_iso AlgebraicGeometry.PresheafedSpace.restrictTopIsoₓ'. -/
 /-- The isomorphism from the restriction to the top subspace.
 -/
 @[simps]
@@ -567,12 +414,6 @@ def restrictTopIso (X : PresheafedSpace C) : X.restrict (Opens.openEmbedding ⊤
 
 end Restrict
 
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 /-- The global sections, notated Gamma.
 -/
 @[simps]
@@ -582,16 +423,10 @@ def Γ : (PresheafedSpace.{v, v, u} C)ᵒᵖ ⥤ C
   map X Y f := f.unop.c.app (op ⊤)
 #align algebraic_geometry.PresheafedSpace.Γ AlgebraicGeometry.PresheafedSpace.Γ
 
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-<too large>
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 theorem Γ_obj_op (X : PresheafedSpace C) : Γ.obj (op X) = X.Presheaf.obj (op ⊤) :=
   rfl
 #align algebraic_geometry.PresheafedSpace.Γ_obj_op AlgebraicGeometry.PresheafedSpace.Γ_obj_op
 
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-<too large>
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 theorem Γ_map_op {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) : Γ.map f.op = f.c.app (op ⊤) :=
   rfl
 #align algebraic_geometry.PresheafedSpace.Γ_map_op AlgebraicGeometry.PresheafedSpace.Γ_map_op
@@ -612,12 +447,6 @@ attribute [local simp] presheaf.pushforward_obj
 
 namespace Functor
 
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 /-- We can apply a functor `F : C ⥤ D` to the values of the presheaf in any `PresheafedSpace C`,
     giving a functor `PresheafedSpace C ⥤ PresheafedSpace D` -/
 def mapPresheaf (F : C ⥤ D) : PresheafedSpace.{v, v, u} C ⥤ PresheafedSpace.{v, v, u} D
@@ -630,39 +459,24 @@ def mapPresheaf (F : C ⥤ D) : PresheafedSpace.{v, v, u} C ⥤ PresheafedSpace.
       c := whiskerRight f.c F }
 #align category_theory.functor.map_presheaf CategoryTheory.Functor.mapPresheaf
 
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 @[simp]
 theorem mapPresheaf_obj_X (F : C ⥤ D) (X : PresheafedSpace C) :
     (F.mapPresheaf.obj X : TopCat.{v}) = (X : TopCat.{v}) :=
   rfl
 #align category_theory.functor.map_presheaf_obj_X CategoryTheory.Functor.mapPresheaf_obj_X
 
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 @[simp]
 theorem mapPresheaf_obj_presheaf (F : C ⥤ D) (X : PresheafedSpace C) :
     (F.mapPresheaf.obj X).Presheaf = X.Presheaf ⋙ F :=
   rfl
 #align category_theory.functor.map_presheaf_obj_presheaf CategoryTheory.Functor.mapPresheaf_obj_presheaf
 
-/- warning: category_theory.functor.map_presheaf_map_f -> CategoryTheory.Functor.mapPresheaf_map_f is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_presheaf_map_f CategoryTheory.Functor.mapPresheaf_map_fₓ'. -/
 @[simp]
 theorem mapPresheaf_map_f (F : C ⥤ D) {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) :
     (F.mapPresheaf.map f).base = f.base :=
   rfl
 #align category_theory.functor.map_presheaf_map_f CategoryTheory.Functor.mapPresheaf_map_f
 
-/- warning: category_theory.functor.map_presheaf_map_c -> CategoryTheory.Functor.mapPresheaf_map_c is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_presheaf_map_c CategoryTheory.Functor.mapPresheaf_map_cₓ'. -/
 @[simp]
 theorem mapPresheaf_map_c (F : C ⥤ D) {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) :
     (F.mapPresheaf.map f).c = whiskerRight f.c F :=
@@ -673,12 +487,6 @@ end Functor
 
 namespace NatTrans
 
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 /-- A natural transformation induces a natural transformation between the `map_presheaf` functors.
 -/
 def onPresheaf {F G : C ⥤ D} (α : F ⟶ G) : G.mapPresheaf ⟶ F.mapPresheaf

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

@@ -143,11 +143,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.hext AlgebraicGeometry.PresheafedSpace.hextₓ'. -/
 -- TODO including `injections` would make tidy work earlier.
 theorem hext {X Y : PresheafedSpace C} (α β : Hom X Y) (w : α.base = β.base) (h : HEq α.c β.c) :
-    α = β := by
-  cases α
-  cases β
-  congr
-  exacts[w, h]
+    α = β := by cases α; cases β; congr ; exacts[w, h]
 #align algebraic_geometry.PresheafedSpace.hext AlgebraicGeometry.PresheafedSpace.hext
 
 /- warning: algebraic_geometry.PresheafedSpace.id -> AlgebraicGeometry.PresheafedSpace.id is a dubious translation:
@@ -274,18 +270,8 @@ Case conversion may be inaccurate. Consider using '#align algebraic_geometry.Pre
 @[simp]
 theorem id_c_app (X : PresheafedSpace.{v, v, u} C) (U) :
     (𝟙 X : X ⟶ X).c.app U =
-      X.Presheaf.map
-        (eqToHom
-          (by
-            induction U using Opposite.rec'
-            cases U
-            rfl)) :=
-  by
-  induction U using Opposite.rec'
-  cases U
-  simp only [id_c]
-  dsimp
-  simp
+      X.Presheaf.map (eqToHom (by induction U using Opposite.rec'; cases U; rfl)) :=
+  by induction U using Opposite.rec'; cases U; simp only [id_c]; dsimp; simp
 #align algebraic_geometry.PresheafedSpace.id_c_app AlgebraicGeometry.PresheafedSpace.id_c_app
 
 /- warning: algebraic_geometry.PresheafedSpace.comp_base -> AlgebraicGeometry.PresheafedSpace.comp_base is a dubious translation:
@@ -325,11 +311,7 @@ theorem comp_c_app {X Y Z : PresheafedSpace.{v, v, u} C} (α : X ⟶ Y) (β : Y
 <too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.congr_app AlgebraicGeometry.PresheafedSpace.congr_appₓ'. -/
 theorem congr_app {X Y : PresheafedSpace.{v, v, u} C} {α β : X ⟶ Y} (h : α = β) (U) :
-    α.c.app U = β.c.app U ≫ X.Presheaf.map (eqToHom (by subst h)) :=
-  by
-  subst h
-  dsimp
-  simp
+    α.c.app U = β.c.app U ≫ X.Presheaf.map (eqToHom (by subst h)) := by subst h; dsimp; simp
 #align algebraic_geometry.PresheafedSpace.congr_app AlgebraicGeometry.PresheafedSpace.congr_app
 
 section
@@ -374,12 +356,7 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.Hom _* X.2 ≅ Y.2) : X ≅ Y
   inv :=
     { base := H.inv
       c := Presheaf.toPushforwardOfIso H α.Hom }
-  hom_inv_id' := by
-    ext
-    · simp
-      erw [category.id_comp]
-      simpa
-    simp
+  hom_inv_id' := by ext; · simp; erw [category.id_comp]; simpa; simp
   inv_hom_id' := by
     ext x
     induction x using Opposite.rec'
@@ -390,8 +367,7 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.Hom _* X.2 ≅ Y.2) : X ≅ Y
     cases x
     rw [nat_trans.comp_app] at this
     convert this
-    · dsimp
-      simp
+    · dsimp; simp
     · simp
     · simp
 #align algebraic_geometry.PresheafedSpace.iso_of_components AlgebraicGeometry.PresheafedSpace.isoOfComponents
@@ -486,9 +462,7 @@ def ofRestrict {U : TopCat} (X : PresheafedSpace.{v, v, u} C) {f : U ⟶ (X : To
   c :=
     { app := fun V => X.Presheaf.map (h.IsOpenMap.Adjunction.counit.app V.unop).op
       naturality' := fun U V f =>
-        show _ = _ ≫ X.Presheaf.map _ by
-          rw [← map_comp, ← map_comp]
-          rfl }
+        show _ = _ ≫ X.Presheaf.map _ by rw [← map_comp, ← map_comp]; rfl }
 #align algebraic_geometry.PresheafedSpace.of_restrict AlgebraicGeometry.PresheafedSpace.ofRestrict
 
 /- warning: algebraic_geometry.PresheafedSpace.of_restrict_mono -> AlgebraicGeometry.PresheafedSpace.ofRestrict_mono is a dubious translation:
@@ -505,9 +479,7 @@ instance ofRestrict_mono {U : TopCat} (X : PresheafedSpace C) (f : U ⟶ X.1) (h
   intro Z g₁ g₂ eq
   ext V
   · induction V using Opposite.rec'
-    have hV : (opens.map (X.of_restrict hf).base).obj (hf.is_open_map.functor.obj V) = V :=
-      by
-      ext1
+    have hV : (opens.map (X.of_restrict hf).base).obj (hf.is_open_map.functor.obj V) = V := by ext1;
       exact Set.preimage_image_eq _ hf.inj
     haveI :
       is_iso (hf.is_open_map.adjunction.counit.app (unop (op (hf.is_open_map.functor.obj V)))) :=
@@ -536,10 +508,7 @@ Case conversion may be inaccurate. Consider using '#align algebraic_geometry.Pre
 theorem restrict_top_presheaf (X : PresheafedSpace C) :
     (X.restrict (Opens.openEmbedding ⊤)).Presheaf =
       (Opens.inclusionTopIso X.carrier).inv _* X.Presheaf :=
-  by
-  dsimp
-  rw [opens.inclusion_top_functor X.carrier]
-  rfl
+  by dsimp; rw [opens.inclusion_top_functor X.carrier]; rfl
 #align algebraic_geometry.PresheafedSpace.restrict_top_presheaf AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf
 
 /- warning: algebraic_geometry.PresheafedSpace.of_restrict_top_c -> AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c is a dubious translation:
@@ -550,8 +519,7 @@ theorem ofRestrict_top_c (X : PresheafedSpace C) :
       eqToHom
         (by
           rw [restrict_top_presheaf, ← presheaf.pushforward.comp_eq]
-          erw [iso.inv_hom_id]
-          rw [presheaf.pushforward.id_eq]) :=
+          erw [iso.inv_hom_id]; rw [presheaf.pushforward.id_eq]) :=
   by
   /- another approach would be to prove the left hand side
        is a natural isoomorphism, but I encountered a universe
@@ -559,10 +527,7 @@ theorem ofRestrict_top_c (X : PresheafedSpace C) :
   ext U;
   change X.presheaf.map _ = _; convert eq_to_hom_map _ _ using 1
   congr ; simpa
-  · induction U using Opposite.rec'
-    dsimp
-    congr
-    ext
+  · induction U using Opposite.rec'; dsimp; congr ; ext
     exact ⟨fun h => ⟨⟨x, trivial⟩, h, rfl⟩, fun ⟨⟨_, _⟩, h, rfl⟩ => h⟩
 #align algebraic_geometry.PresheafedSpace.of_restrict_top_c AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c
 
@@ -594,18 +559,10 @@ def restrictTopIso (X : PresheafedSpace C) : X.restrict (Opens.openEmbedding ⊤
   hom_inv_id' :=
     AlgebraicGeometry.PresheafedSpace.Hom.ext _ _
         (ConcreteCategory.hom_ext _ _ fun ⟨x, _⟩ => rfl) <|
-      by
-      erw [comp_c]
-      rw [X.of_restrict_top_c]
-      ext
-      simp
+      by erw [comp_c]; rw [X.of_restrict_top_c]; ext; simp
   inv_hom_id' :=
-    AlgebraicGeometry.PresheafedSpace.Hom.ext _ _ rfl <|
-      by
-      erw [comp_c]
-      rw [X.of_restrict_top_c]
-      ext
-      simpa [-eq_to_hom_refl]
+    AlgebraicGeometry.PresheafedSpace.Hom.ext _ _ rfl <| by erw [comp_c]; rw [X.of_restrict_top_c];
+      ext; simpa [-eq_to_hom_refl]
 #align algebraic_geometry.PresheafedSpace.restrict_top_iso AlgebraicGeometry.PresheafedSpace.restrictTopIso
 
 end Restrict

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

@@ -124,10 +124,7 @@ structure Hom (X Y : PresheafedSpace.{w, v, u} C) where
 #align algebraic_geometry.PresheafedSpace.hom AlgebraicGeometry.PresheafedSpace.Hom
 
 /- warning: algebraic_geometry.PresheafedSpace.ext -> AlgebraicGeometry.PresheafedSpace.Hom.ext is a dubious translation:
-lean 3 declaration is
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C _inst_1 X Y β)))))) (AlgebraicGeometry.PresheafedSpace.presheaf.{u3, u2, u1} C _inst_1 X))) (AlgebraicGeometry.PresheafedSpace.Hom.c.{u3, u2, u1} C _inst_1 X Y β)) -> (Eq.{max (succ u2) (succ u1)} (AlgebraicGeometry.PresheafedSpace.Hom.{u3, u2, u1} C _inst_1 X Y) α β)
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.ext AlgebraicGeometry.PresheafedSpace.Hom.extₓ'. -/
 @[ext]
 theorem AlgebraicGeometry.PresheafedSpace.Hom.ext {X Y : PresheafedSpace C} (α β : Hom X Y)
@@ -190,10 +187,7 @@ def comp {X Y Z : PresheafedSpace C} (α : Hom X Y) (β : Hom Y Z) : Hom X Z
 #align algebraic_geometry.PresheafedSpace.comp AlgebraicGeometry.PresheafedSpace.comp
 
 /- warning: algebraic_geometry.PresheafedSpace.comp_c -> AlgebraicGeometry.PresheafedSpace.comp_c is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.comp_c AlgebraicGeometry.PresheafedSpace.comp_cₓ'. -/
 theorem comp_c {X Y Z : PresheafedSpace C} (α : Hom X Y) (β : Hom Y Z) :
     (comp α β).c = β.c ≫ (Presheaf.pushforward _ β.base).map α.c :=
@@ -275,10 +269,7 @@ theorem id_c (X : PresheafedSpace.{v, v, u} C) :
 #align algebraic_geometry.PresheafedSpace.id_c AlgebraicGeometry.PresheafedSpace.id_c
 
 /- warning: algebraic_geometry.PresheafedSpace.id_c_app -> AlgebraicGeometry.PresheafedSpace.id_c_app is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.id_c_app AlgebraicGeometry.PresheafedSpace.id_c_appₓ'. -/
 @[simp]
 theorem id_c_app (X : PresheafedSpace.{v, v, u} C) (U) :
@@ -317,10 +308,7 @@ theorem coe_to_fun_eq {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) : (f : X
 #align algebraic_geometry.PresheafedSpace.coe_to_fun_eq AlgebraicGeometry.PresheafedSpace.coe_to_fun_eq
 
 /- warning: algebraic_geometry.PresheafedSpace.comp_c_app -> AlgebraicGeometry.PresheafedSpace.comp_c_app is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.comp_c_app AlgebraicGeometry.PresheafedSpace.comp_c_appₓ'. -/
 -- The `reassoc` attribute was added despite the LHS not being a composition of two homs,
 -- for the reasons explained in the docstring.
@@ -334,10 +322,7 @@ theorem comp_c_app {X Y Z : PresheafedSpace.{v, v, u} C} (α : X ⟶ Y) (β : Y
 #align algebraic_geometry.PresheafedSpace.comp_c_app AlgebraicGeometry.PresheafedSpace.comp_c_app
 
 /- warning: algebraic_geometry.PresheafedSpace.congr_app -> AlgebraicGeometry.PresheafedSpace.congr_app is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.congr_app AlgebraicGeometry.PresheafedSpace.congr_appₓ'. -/
 theorem congr_app {X Y : PresheafedSpace.{v, v, u} C} {α β : X ⟶ Y} (h : α = β) (U) :
     α.c.app U = β.c.app U ≫ X.Presheaf.map (eqToHom (by subst h)) :=
@@ -476,10 +461,7 @@ end Iso
 section Restrict
 
 /- warning: algebraic_geometry.PresheafedSpace.restrict -> AlgebraicGeometry.PresheafedSpace.restrict is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.restrict AlgebraicGeometry.PresheafedSpace.restrictₓ'. -/
 /-- The restriction of a presheafed space along an open embedding into the space.
 -/
@@ -492,10 +474,7 @@ def restrict {U : TopCat} (X : PresheafedSpace.{v, v, u} C) {f : U ⟶ (X : TopC
 #align algebraic_geometry.PresheafedSpace.restrict AlgebraicGeometry.PresheafedSpace.restrict
 
 /- warning: algebraic_geometry.PresheafedSpace.of_restrict -> AlgebraicGeometry.PresheafedSpace.ofRestrict is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.of_restrict AlgebraicGeometry.PresheafedSpace.ofRestrictₓ'. -/
 /-- The map from the restriction of a presheafed space.
 -/
@@ -552,10 +531,7 @@ instance ofRestrict_mono {U : TopCat} (X : PresheafedSpace C) (f : U ⟶ X.1) (h
 #align algebraic_geometry.PresheafedSpace.of_restrict_mono AlgebraicGeometry.PresheafedSpace.ofRestrict_mono
 
 /- warning: algebraic_geometry.PresheafedSpace.restrict_top_presheaf -> AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf is a dubious translation:
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X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))))))))) (AlgebraicGeometry.PresheafedSpace.presheaf.{u_1, u_2, u_3} C _inst_1 (AlgebraicGeometry.PresheafedSpace.restrict.{u_1, u_2, u_3} C _inst_1 (Prefunctor.obj.{succ u_3, succ u_3, u_3, succ u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (CategoryTheory.CategoryStruct.toQuiver.{u_3, u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (CategoryTheory.Category.toCategoryStruct.{u_3, u_3} (TopologicalSpace.Opens.{u_3} 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(TopologicalSpace.Opens.inclusion.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X) (Top.top.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (CompleteLattice.toTop.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)))))) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.restrict_top_presheaf AlgebraicGeometry.PresheafedSpace.restrict_top_presheafₓ'. -/
 theorem restrict_top_presheaf (X : PresheafedSpace C) :
     (X.restrict (Opens.openEmbedding ⊤)).Presheaf =
@@ -567,10 +543,7 @@ theorem restrict_top_presheaf (X : PresheafedSpace C) :
 #align algebraic_geometry.PresheafedSpace.restrict_top_presheaf AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf
 
 /- warning: algebraic_geometry.PresheafedSpace.of_restrict_top_c -> AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c is a dubious translation:
-lean 3 declaration is
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_inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)))))) X (TopologicalSpace.Opens.inclusion.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X) (Top.top.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (CompleteLattice.toTop.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} 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X))) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)))))) (TopologicalSpace.Opens.openEmbedding.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X) (Top.top.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (CompleteLattice.toTop.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C 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C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)))))) (TopologicalSpace.Opens.openEmbedding.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X) (Top.top.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (CompleteLattice.toTop.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, 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_inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))))))))) TopCat.{u_3} (CategoryTheory.CategoryStruct.toQuiver.{u_3, succ u_3} TopCat.{u_3} (CategoryTheory.Category.toCategoryStruct.{u_3, succ u_3} TopCat.{u_3} instTopCatLargeCategory.{u_3})) (CategoryTheory.Functor.toPrefunctor.{u_3, u_3, u_3, succ u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (Preorder.smallCategory.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (PartialOrder.toPreorder.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (CompleteSemilatticeInf.toPartialOrder.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (CompleteLattice.toCompleteSemilatticeInf.{u_3} (TopologicalSpace.Opens.{u_3} 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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.of_restrict_top_c AlgebraicGeometry.PresheafedSpace.ofRestrict_top_cₓ'. -/
 theorem ofRestrict_top_c (X : PresheafedSpace C) :
     (X.of_restrict (Opens.openEmbedding ⊤)).c =
@@ -594,10 +567,7 @@ theorem ofRestrict_top_c (X : PresheafedSpace C) :
 #align algebraic_geometry.PresheafedSpace.of_restrict_top_c AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c
 
 /- warning: algebraic_geometry.PresheafedSpace.to_restrict_top -> AlgebraicGeometry.PresheafedSpace.toRestrictTop is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.to_restrict_top AlgebraicGeometry.PresheafedSpace.toRestrictTopₓ'. -/
 /- or `rw [opens.inclusion_top_functor, ←comp_obj, ←opens.map_comp_eq],
          erw iso.inv_hom_id, cases U, refl` after `dsimp` -/
@@ -612,10 +582,7 @@ def toRestrictTop (X : PresheafedSpace C) : X ⟶ X.restrict (Opens.openEmbeddin
 #align algebraic_geometry.PresheafedSpace.to_restrict_top AlgebraicGeometry.PresheafedSpace.toRestrictTop
 
 /- warning: algebraic_geometry.PresheafedSpace.restrict_top_iso -> AlgebraicGeometry.PresheafedSpace.restrictTopIso is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.restrict_top_iso AlgebraicGeometry.PresheafedSpace.restrictTopIsoₓ'. -/
 /-- The isomorphism from the restriction to the top subspace.
 -/
@@ -659,20 +626,14 @@ def Γ : (PresheafedSpace.{v, v, u} C)ᵒᵖ ⥤ C
 #align algebraic_geometry.PresheafedSpace.Γ AlgebraicGeometry.PresheafedSpace.Γ
 
 /- warning: algebraic_geometry.PresheafedSpace.Γ_obj_op -> AlgebraicGeometry.PresheafedSpace.Γ_obj_op is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.Γ_obj_op AlgebraicGeometry.PresheafedSpace.Γ_obj_opₓ'. -/
 theorem Γ_obj_op (X : PresheafedSpace C) : Γ.obj (op X) = X.Presheaf.obj (op ⊤) :=
   rfl
 #align algebraic_geometry.PresheafedSpace.Γ_obj_op AlgebraicGeometry.PresheafedSpace.Γ_obj_op
 
 /- warning: algebraic_geometry.PresheafedSpace.Γ_map_op -> AlgebraicGeometry.PresheafedSpace.Γ_map_op is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.Γ_map_op AlgebraicGeometry.PresheafedSpace.Γ_map_opₓ'. -/
 theorem Γ_map_op {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) : Γ.map f.op = f.c.app (op ⊤) :=
   rfl
@@ -725,10 +686,7 @@ theorem mapPresheaf_obj_X (F : C ⥤ D) (X : PresheafedSpace C) :
 #align category_theory.functor.map_presheaf_obj_X CategoryTheory.Functor.mapPresheaf_obj_X
 
 /- warning: category_theory.functor.map_presheaf_obj_presheaf -> CategoryTheory.Functor.mapPresheaf_obj_presheaf is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_presheaf_obj_presheaf CategoryTheory.Functor.mapPresheaf_obj_presheafₓ'. -/
 @[simp]
 theorem mapPresheaf_obj_presheaf (F : C ⥤ D) (X : PresheafedSpace C) :
@@ -737,10 +695,7 @@ theorem mapPresheaf_obj_presheaf (F : C ⥤ D) (X : PresheafedSpace C) :
 #align category_theory.functor.map_presheaf_obj_presheaf CategoryTheory.Functor.mapPresheaf_obj_presheaf
 
 /- warning: category_theory.functor.map_presheaf_map_f -> CategoryTheory.Functor.mapPresheaf_map_f is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_presheaf_map_f CategoryTheory.Functor.mapPresheaf_map_fₓ'. -/
 @[simp]
 theorem mapPresheaf_map_f (F : C ⥤ D) {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) :
@@ -749,10 +704,7 @@ theorem mapPresheaf_map_f (F : C ⥤ D) {X Y : PresheafedSpace.{v, v, u} C} (f :
 #align category_theory.functor.map_presheaf_map_f CategoryTheory.Functor.mapPresheaf_map_f
 
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(AlgebraicGeometry.PresheafedSpace.{u_4, u_2, u_5} D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u_2 u_5, max (max u_4 u_2) (succ u_5)} (AlgebraicGeometry.PresheafedSpace.{u_4, u_2, u_5} D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u_2 u_5, max (max u_4 u_2) (succ u_5)} (AlgebraicGeometry.PresheafedSpace.{u_4, u_2, u_5} D _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_4, u_2, u_5} D _inst_2))) (CategoryTheory.Functor.toPrefunctor.{max u_1 u_5, max u_2 u_5, max (max u_3 u_1) (succ u_5), max (max u_4 u_2) (succ u_5)} (AlgebraicGeometry.PresheafedSpace.{u_3, u_1, u_5} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_3, u_1, u_5} C _inst_1) (AlgebraicGeometry.PresheafedSpace.{u_4, u_2, u_5} D _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_4, u_2, u_5} D _inst_2) (CategoryTheory.Functor.mapPresheaf.{u_3, u_1, u_4, u_2, u_5} C _inst_1 D _inst_2 F)) X Y f)) (CategoryTheory.whiskerRight.{u_5, u_5, u_3, u_1, u_4, u_2} (Opposite.{succ u_5} (TopologicalSpace.Opens.{u_5} (CategoryTheory.Bundled.α.{u_5, u_5} TopologicalSpace.{u_5} (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_5} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_5} (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_5} C _inst_1 Y)))) (CategoryTheory.Category.opposite.{u_5, u_5} (TopologicalSpace.Opens.{u_5} (CategoryTheory.Bundled.α.{u_5, u_5} TopologicalSpace.{u_5} (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_5} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_5} (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_5} C _inst_1 Y))) (Preorder.smallCategory.{u_5} (TopologicalSpace.Opens.{u_5} (CategoryTheory.Bundled.α.{u_5, u_5} TopologicalSpace.{u_5} (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_5} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_5} (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_5} C _inst_1 Y))) (PartialOrder.toPreorder.{u_5} (TopologicalSpace.Opens.{u_5} (CategoryTheory.Bundled.α.{u_5, u_5} TopologicalSpace.{u_5} (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_5} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_5} (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_5} C _inst_1 Y))) (CompleteSemilatticeInf.toPartialOrder.{u_5} (TopologicalSpace.Opens.{u_5} (CategoryTheory.Bundled.α.{u_5, u_5} TopologicalSpace.{u_5} (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_5} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_5} (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_5} C _inst_1 Y))) (CompleteLattice.toCompleteSemilatticeInf.{u_5} (TopologicalSpace.Opens.{u_5} (CategoryTheory.Bundled.α.{u_5, u_5} TopologicalSpace.{u_5} (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_5} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_5} (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_5} C _inst_1 Y))) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u_5} (CategoryTheory.Bundled.α.{u_5, u_5} TopologicalSpace.{u_5} (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_5} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_5} (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_5} C _inst_1 Y)))))))) C _inst_1 D _inst_2 (AlgebraicGeometry.PresheafedSpace.presheaf.{u_3, u_1, u_5} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{u_5, u_1, u_3} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_5} C _inst_1 X) (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_5} C _inst_1 Y) (AlgebraicGeometry.PresheafedSpace.Hom.base.{u_3, u_1, u_5} C _inst_1 X Y f) (AlgebraicGeometry.PresheafedSpace.presheaf.{u_3, u_1, u_5} C _inst_1 X)) (AlgebraicGeometry.PresheafedSpace.Hom.c.{u_3, u_1, u_5} C _inst_1 X Y f) F)
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_presheaf_map_c CategoryTheory.Functor.mapPresheaf_map_cₓ'. -/
 @[simp]
 theorem mapPresheaf_map_c (F : C ⥤ D) {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) :

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module algebraic_geometry.presheafed_space
-! leanprover-community/mathlib commit d39590fc8728fbf6743249802486f8c91ffe07bc
+! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.CategoryTheory.Adjunction.FullyFaithful
 /-!
 # Presheafed spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Introduces the category of topological spaces equipped with a presheaf (taking values in an
 arbitrary target category `C`.)
 
@@ -324,7 +327,7 @@ Case conversion may be inaccurate. Consider using '#align algebraic_geometry.Pre
 /-- Sometimes rewriting with `comp_c_app` doesn't work because of dependent type issues.
 In that case, `erw comp_c_app_assoc` might make progress.
 The lemma `comp_c_app_assoc` is also better suited for rewrites in the opposite direction. -/
-@[reassoc.1, simp]
+@[reassoc, simp]
 theorem comp_c_app {X Y Z : PresheafedSpace.{v, v, u} C} (α : X ⟶ Y) (β : Y ⟶ Z) (U) :
     (α ≫ β).c.app U = β.c.app U ≫ α.c.app (op ((Opens.map β.base).obj (unop U))) :=
   rfl

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

@@ -40,6 +40,12 @@ attribute [local tidy] tactic.op_induction' tactic.auto_cases_opens
 
 namespace AlgebraicGeometry
 
+/- warning: algebraic_geometry.PresheafedSpace -> AlgebraicGeometry.PresheafedSpace is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u3}) [_inst_1 : CategoryTheory.Category.{u2, u3} C], Sort.{max (succ u3) (succ u2) (succ (succ u1))}
+but is expected to have type
+  forall (C : Type.{u1}) [_inst_1 : CategoryTheory.Category.{u2, u1} C], Sort.{max (max (succ u1) (succ u2)) (succ (succ u3))}
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace AlgebraicGeometry.PresheafedSpaceₓ'. -/
 /-- A `PresheafedSpace C` is a topological space equipped with a presheaf of `C`s. -/
 structure PresheafedSpace where
   carrier : TopCat.{w}
@@ -52,6 +58,12 @@ namespace PresheafedSpace
 
 attribute [protected] presheaf
 
+/- warning: algebraic_geometry.PresheafedSpace.coe_carrier -> AlgebraicGeometry.PresheafedSpace.coeCarrier is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C], Coe.{max (succ u3) (succ u2) (succ (succ u1)), succ (succ u1)} (AlgebraicGeometry.PresheafedSpace.{u1, u2, u3} C _inst_1) TopCat.{u1}
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C], CoeOut.{max (max (succ (succ u3)) (succ u2)) (succ u1), succ (succ u3)} (AlgebraicGeometry.PresheafedSpace.{u1, u2, u3} C _inst_1) TopCat.{u3}
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.coe_carrier AlgebraicGeometry.PresheafedSpace.coeCarrierₓ'. -/
 instance coeCarrier : Coe (PresheafedSpace.{w, v, u} C) TopCat.{w} where coe X := X.carrier
 #align algebraic_geometry.PresheafedSpace.coe_carrier AlgebraicGeometry.PresheafedSpace.coeCarrier
 
@@ -60,6 +72,12 @@ theorem as_coe (X : PresheafedSpace.{w, v, u} C) : X.carrier = (X : TopCat.{w})
   rfl
 #align algebraic_geometry.PresheafedSpace.as_coe AlgebraicGeometry.PresheafedSpace.as_coe
 
+/- warning: algebraic_geometry.PresheafedSpace.mk_coe -> AlgebraicGeometry.PresheafedSpace.mk_coe is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u}} [_inst_1 : CategoryTheory.Category.{v, u} C] (carrier : TopCat.{v}) (presheaf : TopCat.Presheaf.{v, v, u} C _inst_1 carrier), Eq.{succ (succ v)} TopCat.{v} ((fun (a : Sort.{max (succ u) (succ (succ v))}) (b : Type.{succ v}) [self : HasLiftT.{max (succ u) (succ (succ v)), succ (succ v)} a b] => self.0) (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (HasLiftT.mk.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (CoeTCₓ.coe.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (coeBase.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (AlgebraicGeometry.PresheafedSpace.coeCarrier.{v, v, u} C _inst_1)))) (AlgebraicGeometry.PresheafedSpace.mk.{v, v, u} C _inst_1 carrier presheaf)) carrier
+but is expected to have type
+  forall {C : Type.{u_3}} [_inst_1 : CategoryTheory.Category.{u_2, u_3} C] (carrier : TopCat.{u_1}) (presheaf : TopCat.Presheaf.{u_1, u_2, u_3} C _inst_1 carrier), Eq.{succ (succ u_1)} TopCat.{u_1} (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_2, u_1} C _inst_1 (AlgebraicGeometry.PresheafedSpace.mk.{u_3, u_2, u_1} C _inst_1 carrier presheaf)) carrier
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.mk_coe AlgebraicGeometry.PresheafedSpace.mk_coeₓ'. -/
 @[simp]
 theorem mk_coe (carrier) (presheaf) :
     (({     carrier
@@ -70,6 +88,12 @@ theorem mk_coe (carrier) (presheaf) :
 instance (X : PresheafedSpace.{v} C) : TopologicalSpace X :=
   X.carrier.str
 
+/- warning: algebraic_geometry.PresheafedSpace.const -> AlgebraicGeometry.PresheafedSpace.const is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C], TopCat.{u3} -> C -> (AlgebraicGeometry.PresheafedSpace.{u3, u1, u2} C _inst_1)
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C], TopCat.{u3} -> C -> (AlgebraicGeometry.PresheafedSpace.{u1, u2, u3} C _inst_1)
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.const AlgebraicGeometry.PresheafedSpace.constₓ'. -/
 /-- The constant presheaf on `X` with value `Z`. -/
 def const (X : TopCat) (Z : C) : PresheafedSpace C
     where
@@ -82,6 +106,12 @@ def const (X : TopCat) (Z : C) : PresheafedSpace C
 instance [Inhabited C] : Inhabited (PresheafedSpace C) :=
   ⟨const (TopCat.of PEmpty) default⟩
 
+/- warning: algebraic_geometry.PresheafedSpace.hom -> AlgebraicGeometry.PresheafedSpace.Hom is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C], (AlgebraicGeometry.PresheafedSpace.{u1, u2, u3} C _inst_1) -> (AlgebraicGeometry.PresheafedSpace.{u1, u2, u3} C _inst_1) -> Sort.{max (succ u2) (succ u1)}
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C], (AlgebraicGeometry.PresheafedSpace.{u1, u2, u3} C _inst_1) -> (AlgebraicGeometry.PresheafedSpace.{u1, u2, u3} C _inst_1) -> Sort.{max (succ u2) (succ u3)}
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.hom AlgebraicGeometry.PresheafedSpace.Homₓ'. -/
 /-- A morphism between presheafed spaces `X` and `Y` consists of a continuous map
     `f` between the underlying topological spaces, and a (notice contravariant!) map
     from the presheaf on `Y` to the pushforward of the presheaf on `X` via `f`. -/
@@ -90,15 +120,27 @@ structure Hom (X Y : PresheafedSpace.{w, v, u} C) where
   c : Y.Presheaf ⟶ base _* X.Presheaf
 #align algebraic_geometry.PresheafedSpace.hom AlgebraicGeometry.PresheafedSpace.Hom
 
+/- warning: algebraic_geometry.PresheafedSpace.ext -> AlgebraicGeometry.PresheafedSpace.Hom.ext is a dubious translation:
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C _inst_1 X Y β)))))) (AlgebraicGeometry.PresheafedSpace.presheaf.{u3, u2, u1} C _inst_1 X))) (AlgebraicGeometry.PresheafedSpace.Hom.c.{u3, u2, u1} C _inst_1 X Y β)) -> (Eq.{max (succ u2) (succ u1)} (AlgebraicGeometry.PresheafedSpace.Hom.{u3, u2, u1} C _inst_1 X Y) α β)
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.ext AlgebraicGeometry.PresheafedSpace.Hom.extₓ'. -/
 @[ext]
-theorem ext {X Y : PresheafedSpace C} (α β : Hom X Y) (w : α.base = β.base)
-    (h : α.c ≫ whiskerRight (eqToHom (by rw [w])) _ = β.c) : α = β :=
+theorem AlgebraicGeometry.PresheafedSpace.Hom.ext {X Y : PresheafedSpace C} (α β : Hom X Y)
+    (w : α.base = β.base) (h : α.c ≫ whiskerRight (eqToHom (by rw [w])) _ = β.c) : α = β :=
   by
   cases α; cases β
   dsimp [presheaf.pushforward_obj] at *
   tidy
-#align algebraic_geometry.PresheafedSpace.ext AlgebraicGeometry.PresheafedSpace.ext
-
+#align algebraic_geometry.PresheafedSpace.ext AlgebraicGeometry.PresheafedSpace.Hom.ext
+
+/- warning: algebraic_geometry.PresheafedSpace.hext -> AlgebraicGeometry.PresheafedSpace.hext is a dubious translation:
+lean 3 declaration is
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 -- TODO including `injections` would make tidy work earlier.
 theorem hext {X Y : PresheafedSpace C} (α β : Hom X Y) (w : α.base = β.base) (h : HEq α.c β.c) :
     α = β := by
@@ -108,6 +150,12 @@ theorem hext {X Y : PresheafedSpace C} (α β : Hom X Y) (w : α.base = β.base)
   exacts[w, h]
 #align algebraic_geometry.PresheafedSpace.hext AlgebraicGeometry.PresheafedSpace.hext
 
+/- warning: algebraic_geometry.PresheafedSpace.id -> AlgebraicGeometry.PresheafedSpace.id is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.id AlgebraicGeometry.PresheafedSpace.idₓ'. -/
 /-- The identity morphism of a `PresheafedSpace`. -/
 def id (X : PresheafedSpace.{w, v, u} C) : Hom X X
     where
@@ -115,10 +163,22 @@ def id (X : PresheafedSpace.{w, v, u} C) : Hom X X
   c := eqToHom (Presheaf.Pushforward.id_eq X.Presheaf).symm
 #align algebraic_geometry.PresheafedSpace.id AlgebraicGeometry.PresheafedSpace.id
 
+/- warning: algebraic_geometry.PresheafedSpace.hom_inhabited -> AlgebraicGeometry.PresheafedSpace.homInhabited is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.hom_inhabited AlgebraicGeometry.PresheafedSpace.homInhabitedₓ'. -/
 instance homInhabited (X : PresheafedSpace C) : Inhabited (Hom X X) :=
   ⟨id X⟩
 #align algebraic_geometry.PresheafedSpace.hom_inhabited AlgebraicGeometry.PresheafedSpace.homInhabited
 
+/- warning: algebraic_geometry.PresheafedSpace.comp -> AlgebraicGeometry.PresheafedSpace.comp is a dubious translation:
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 /-- Composition of morphisms of `PresheafedSpace`s. -/
 def comp {X Y Z : PresheafedSpace C} (α : Hom X Y) (β : Hom Y Z) : Hom X Z
     where
@@ -126,6 +186,12 @@ def comp {X Y Z : PresheafedSpace C} (α : Hom X Y) (β : Hom Y Z) : Hom X Z
   c := β.c ≫ (Presheaf.pushforward _ β.base).map α.c
 #align algebraic_geometry.PresheafedSpace.comp AlgebraicGeometry.PresheafedSpace.comp
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.comp_c AlgebraicGeometry.PresheafedSpace.comp_cₓ'. -/
 theorem comp_c {X Y Z : PresheafedSpace C} (α : Hom X Y) (β : Hom Y Z) :
     (comp α β).c = β.c ≫ (Presheaf.pushforward _ β.base).map α.c :=
   rfl
@@ -137,6 +203,12 @@ section
 
 attribute [local simp] id comp
 
+/- warning: algebraic_geometry.PresheafedSpace.category_of_PresheafedSpaces -> AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u}) [_inst_1 : CategoryTheory.Category.{v, u} C], CategoryTheory.Category.{v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1)
+but is expected to have type
+  forall (C : Type.{u_1}) [_inst_1 : CategoryTheory.Category.{u_2, u_1} C], CategoryTheory.Category.{max u_2 u_3, max (max (succ u_3) u_2) u_1} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1)
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.category_of_PresheafedSpaces AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpacesₓ'. -/
 /- The proofs below can be done by `tidy`, but it is too slow,
    and we don't have a tactic caching mechanism. -/
 /-- The category of PresheafedSpaces. Morphisms are pairs, a continuous map and a presheaf map
@@ -177,16 +249,34 @@ variable {C}
 
 attribute [local simp] eq_to_hom_map
 
+/- warning: algebraic_geometry.PresheafedSpace.id_base -> AlgebraicGeometry.PresheafedSpace.id_base is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.id_base AlgebraicGeometry.PresheafedSpace.id_baseₓ'. -/
 @[simp]
 theorem id_base (X : PresheafedSpace.{v, v, u} C) : (𝟙 X : X ⟶ X).base = 𝟙 (X : TopCat.{v}) :=
   rfl
 #align algebraic_geometry.PresheafedSpace.id_base AlgebraicGeometry.PresheafedSpace.id_base
 
+/- warning: algebraic_geometry.PresheafedSpace.id_c -> AlgebraicGeometry.PresheafedSpace.id_c is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.id_c AlgebraicGeometry.PresheafedSpace.id_cₓ'. -/
 theorem id_c (X : PresheafedSpace.{v, v, u} C) :
     (𝟙 X : X ⟶ X).c = eqToHom (Presheaf.Pushforward.id_eq X.Presheaf).symm :=
   rfl
 #align algebraic_geometry.PresheafedSpace.id_c AlgebraicGeometry.PresheafedSpace.id_c
 
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(CompleteLattice.toCompleteSemilatticeInf.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))))))))) U))
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.id_c_app AlgebraicGeometry.PresheafedSpace.id_c_appₓ'. -/
 @[simp]
 theorem id_c_app (X : PresheafedSpace.{v, v, u} C) (U) :
     (𝟙 X : X ⟶ X).c.app U =
@@ -204,6 +294,12 @@ theorem id_c_app (X : PresheafedSpace.{v, v, u} C) (U) :
   simp
 #align algebraic_geometry.PresheafedSpace.id_c_app AlgebraicGeometry.PresheafedSpace.id_c_app
 
+/- warning: algebraic_geometry.PresheafedSpace.comp_base -> AlgebraicGeometry.PresheafedSpace.comp_base is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.comp_base AlgebraicGeometry.PresheafedSpace.comp_baseₓ'. -/
 @[simp]
 theorem comp_base {X Y Z : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) (g : Y ⟶ Z) :
     (f ≫ g).base = f.base ≫ g.base :=
@@ -217,6 +313,12 @@ theorem coe_to_fun_eq {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) : (f : X
   rfl
 #align algebraic_geometry.PresheafedSpace.coe_to_fun_eq AlgebraicGeometry.PresheafedSpace.coe_to_fun_eq
 
+/- warning: algebraic_geometry.PresheafedSpace.comp_c_app -> AlgebraicGeometry.PresheafedSpace.comp_c_app is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.comp_c_app AlgebraicGeometry.PresheafedSpace.comp_c_appₓ'. -/
 -- The `reassoc` attribute was added despite the LHS not being a composition of two homs,
 -- for the reasons explained in the docstring.
 /-- Sometimes rewriting with `comp_c_app` doesn't work because of dependent type issues.
@@ -228,6 +330,12 @@ theorem comp_c_app {X Y Z : PresheafedSpace.{v, v, u} C} (α : X ⟶ Y) (β : Y
   rfl
 #align algebraic_geometry.PresheafedSpace.comp_c_app AlgebraicGeometry.PresheafedSpace.comp_c_app
 
+/- warning: algebraic_geometry.PresheafedSpace.congr_app -> AlgebraicGeometry.PresheafedSpace.congr_app is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)))))))))) (CategoryTheory.Functor.toPrefunctor.{u_3, u_3, u_3, u_3} (Opposite.{succ u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)))) (CategoryTheory.Category.opposite.{u_3, u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y))) (Preorder.smallCategory.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y))) (PartialOrder.toPreorder.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y))) (CompleteSemilatticeInf.toPartialOrder.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y))) (CompleteLattice.toCompleteSemilatticeInf.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y))) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)))))))) (Opposite.{succ u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)))) (CategoryTheory.Category.opposite.{u_3, u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (Preorder.smallCategory.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (PartialOrder.toPreorder.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (CompleteSemilatticeInf.toPartialOrder.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (CompleteLattice.toCompleteSemilatticeInf.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)))))))) (CategoryTheory.Functor.op.{u_3, u_3, u_3, u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y))) (Preorder.smallCategory.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y))) (PartialOrder.toPreorder.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y))) (CompleteSemilatticeInf.toPartialOrder.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y))) (CompleteLattice.toCompleteSemilatticeInf.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y))) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y))))))) (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (Preorder.smallCategory.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (PartialOrder.toPreorder.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (CompleteSemilatticeInf.toPartialOrder.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (CompleteLattice.toCompleteSemilatticeInf.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))))))) (TopologicalSpace.Opens.map.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X) (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y) (AlgebraicGeometry.PresheafedSpace.Hom.base.{u_1, u_2, u_3} C _inst_1 X Y α)))) U)) β h))))
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.congr_app AlgebraicGeometry.PresheafedSpace.congr_appₓ'. -/
 theorem congr_app {X Y : PresheafedSpace.{v, v, u} C} {α β : X ⟶ Y} (h : α = β) (U) :
     α.c.app U = β.c.app U ≫ X.Presheaf.map (eqToHom (by subst h)) :=
   by
@@ -240,6 +348,12 @@ section
 
 variable (C)
 
+/- warning: algebraic_geometry.PresheafedSpace.forget -> AlgebraicGeometry.PresheafedSpace.forget is a dubious translation:
+lean 3 declaration is
+  forall (C : Type.{u}) [_inst_1 : CategoryTheory.Category.{v, u} C], CategoryTheory.Functor.{v, v, max u (succ v), succ v} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} C _inst_1) TopCat.{v} TopCat.largeCategory.{v}
+but is expected to have type
+  forall (C : Type.{u_1}) [_inst_1 : CategoryTheory.Category.{u_2, u_1} C], CategoryTheory.Functor.{max u_2 u_3, u_3, max (max (succ u_3) u_2) u_1, succ u_3} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_1, u_2, u_3} C _inst_1) TopCat.{u_3} instTopCatLargeCategory.{u_3}
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.forget AlgebraicGeometry.PresheafedSpace.forgetₓ'. -/
 /-- The forgetful functor from `PresheafedSpace` to `Top`. -/
 @[simps]
 def forget : PresheafedSpace.{v, v, u} C ⥤ TopCat
@@ -254,6 +368,12 @@ section Iso
 
 variable {X Y : PresheafedSpace.{v, v, u} C}
 
+/- warning: algebraic_geometry.PresheafedSpace.iso_of_components -> AlgebraicGeometry.PresheafedSpace.isoOfComponents is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u}} [_inst_1 : CategoryTheory.Category.{v, u} C] {X : AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1} {Y : AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1} (H : CategoryTheory.Iso.{v, succ v} TopCat.{v} TopCat.largeCategory.{v} (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 X) (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 Y)), (CategoryTheory.Iso.{v, max u v} (TopCat.Presheaf.{v, v, u} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 Y)) (TopCat.Presheaf.category.{v, v, u} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 Y)) (TopCat.Presheaf.pushforwardObj.{v, v, u} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 X) (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 Y) (CategoryTheory.Iso.hom.{v, succ v} TopCat.{v} TopCat.largeCategory.{v} (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 X) (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 Y) H) (AlgebraicGeometry.PresheafedSpace.presheaf.{v, v, u} C _inst_1 X)) (AlgebraicGeometry.PresheafedSpace.presheaf.{v, v, u} C _inst_1 Y)) -> (CategoryTheory.Iso.{v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} C _inst_1) X Y)
+but is expected to have type
+  forall {C : Type.{u_1}} [_inst_1 : CategoryTheory.Category.{u_2, u_1} C] {X : AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1} {Y : AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1} (H : CategoryTheory.Iso.{u_3, succ u_3} TopCat.{u_3} instTopCatLargeCategory.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X) (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)), (CategoryTheory.Iso.{max u_2 u_3, max (max u_1 u_2) u_3} (TopCat.Presheaf.{u_3, u_2, u_1} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.instCategoryPresheaf.{u_3, u_2, u_1} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.Presheaf.pushforwardObj.{u_3, u_2, u_1} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X) (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y) (CategoryTheory.Iso.hom.{u_3, succ u_3} TopCat.{u_3} instTopCatLargeCategory.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X) (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y) H) (AlgebraicGeometry.PresheafedSpace.presheaf.{u_1, u_2, u_3} C _inst_1 X)) (AlgebraicGeometry.PresheafedSpace.presheaf.{u_1, u_2, u_3} C _inst_1 Y)) -> (CategoryTheory.Iso.{max u_2 u_3, max (max u_1 u_2) (succ u_3)} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_1, u_2, u_3} C _inst_1) X Y)
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.iso_of_components AlgebraicGeometry.PresheafedSpace.isoOfComponentsₓ'. -/
 /-- An isomorphism of PresheafedSpaces is a homeomorphism of the underlying space, and a
 natural transformation between the sheaves.
 -/
@@ -288,6 +408,12 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.Hom _* X.2 ≅ Y.2) : X ≅ Y
     · simp
 #align algebraic_geometry.PresheafedSpace.iso_of_components AlgebraicGeometry.PresheafedSpace.isoOfComponents
 
+/- warning: algebraic_geometry.PresheafedSpace.sheaf_iso_of_iso -> AlgebraicGeometry.PresheafedSpace.sheafIsoOfIso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u}} [_inst_1 : CategoryTheory.Category.{v, u} C] {X : AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1} {Y : AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1} (H : CategoryTheory.Iso.{v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} C _inst_1) X Y), CategoryTheory.Iso.{v, max u v} (TopCat.Presheaf.{v, v, u} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 Y)) (TopCat.Presheaf.category.{v, v, u} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 Y)) (AlgebraicGeometry.PresheafedSpace.presheaf.{v, v, u} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{v, v, u} C _inst_1 ((fun (a : Sort.{max (succ u) (succ (succ v))}) (b : Type.{succ v}) [self : HasLiftT.{max (succ u) (succ (succ v)), succ (succ v)} a b] => self.0) (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (HasLiftT.mk.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (CoeTCₓ.coe.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (coeBase.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (AlgebraicGeometry.PresheafedSpace.coeCarrier.{v, v, u} C _inst_1)))) X) (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 Y) (AlgebraicGeometry.PresheafedSpace.Hom.base.{v, v, u} C _inst_1 X Y (CategoryTheory.Iso.hom.{v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} C _inst_1) X Y H)) (AlgebraicGeometry.PresheafedSpace.presheaf.{v, v, u} C _inst_1 X))
+but is expected to have type
+  forall {C : Type.{u_1}} [_inst_1 : CategoryTheory.Category.{u_2, u_1} C] {X : AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1} {Y : AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1} (H : CategoryTheory.Iso.{max u_2 u_3, max (max u_1 u_2) (succ u_3)} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_1, u_2, u_3} C _inst_1) X Y), CategoryTheory.Iso.{max u_2 u_3, max (max u_1 u_2) u_3} (TopCat.Presheaf.{u_3, u_2, u_1} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.instCategoryPresheaf.{u_3, u_2, u_1} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (AlgebraicGeometry.PresheafedSpace.presheaf.{u_1, u_2, u_3} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{u_3, u_2, u_1} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X) (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y) (AlgebraicGeometry.PresheafedSpace.Hom.base.{u_1, u_2, u_3} C _inst_1 X Y (CategoryTheory.Iso.hom.{max u_2 u_3, max (max u_1 u_2) (succ u_3)} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_1, u_2, u_3} C _inst_1) X Y H)) (AlgebraicGeometry.PresheafedSpace.presheaf.{u_1, u_2, u_3} C _inst_1 X))
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.sheaf_iso_of_iso AlgebraicGeometry.PresheafedSpace.sheafIsoOfIsoₓ'. -/
 /-- Isomorphic PresheafedSpaces have natural isomorphic presheaves. -/
 @[simps]
 def sheafIsoOfIso (H : X ≅ Y) : Y.2 ≅ H.Hom.base _* X.2
@@ -309,14 +435,32 @@ def sheafIsoOfIso (H : X ≅ Y) : Y.2 ≅ H.Hom.base _* X.2
     simpa using congr_arg (fun f => f ≫ X.presheaf.map (eq_to_hom h.symm)) this
 #align algebraic_geometry.PresheafedSpace.sheaf_iso_of_iso AlgebraicGeometry.PresheafedSpace.sheafIsoOfIso
 
+/- warning: algebraic_geometry.PresheafedSpace.base_is_iso_of_iso -> AlgebraicGeometry.PresheafedSpace.base_isIso_of_iso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u}} [_inst_1 : CategoryTheory.Category.{v, u} C] {X : AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1} {Y : AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1} (f : Quiver.Hom.{succ v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} C _inst_1))) X Y) [_inst_2 : CategoryTheory.IsIso.{v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} C _inst_1) X Y f], CategoryTheory.IsIso.{v, succ v} TopCat.{v} TopCat.largeCategory.{v} ((fun (a : Sort.{max (succ u) (succ (succ v))}) (b : Type.{succ v}) [self : HasLiftT.{max (succ u) (succ (succ v)), succ (succ v)} a b] => self.0) (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (HasLiftT.mk.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (CoeTCₓ.coe.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (coeBase.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (AlgebraicGeometry.PresheafedSpace.coeCarrier.{v, v, u} C _inst_1)))) X) ((fun (a : Sort.{max (succ u) (succ (succ v))}) (b : Type.{succ v}) [self : HasLiftT.{max (succ u) (succ (succ v)), succ (succ v)} a b] => self.0) (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (HasLiftT.mk.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (CoeTCₓ.coe.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (coeBase.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (AlgebraicGeometry.PresheafedSpace.coeCarrier.{v, v, u} C _inst_1)))) Y) (AlgebraicGeometry.PresheafedSpace.Hom.base.{v, v, u} C _inst_1 X Y f)
+but is expected to have type
+  forall {C : Type.{u_1}} [_inst_1 : CategoryTheory.Category.{u_2, u_1} C] {X : AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1} {Y : AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1} (f : Quiver.Hom.{max (succ u_2) (succ u_3), max (max u_1 u_2) (succ u_3)} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{max u_2 u_3, max (max u_1 u_2) (succ u_3)} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{max u_2 u_3, max (max u_1 u_2) (succ u_3)} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_1, u_2, u_3} C _inst_1))) X Y) [_inst_2 : CategoryTheory.IsIso.{max u_2 u_3, max (max u_1 u_2) (succ u_3)} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_1, u_2, u_3} C _inst_1) X Y f], CategoryTheory.IsIso.{u_3, succ u_3} TopCat.{u_3} instTopCatLargeCategory.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X) (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y) (AlgebraicGeometry.PresheafedSpace.Hom.base.{u_1, u_2, u_3} C _inst_1 X Y f)
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.base_is_iso_of_iso AlgebraicGeometry.PresheafedSpace.base_isIso_of_isoₓ'. -/
 instance base_isIso_of_iso (f : X ⟶ Y) [IsIso f] : IsIso f.base :=
   IsIso.of_iso ((forget _).mapIso (asIso f))
 #align algebraic_geometry.PresheafedSpace.base_is_iso_of_iso AlgebraicGeometry.PresheafedSpace.base_isIso_of_iso
 
+/- warning: algebraic_geometry.PresheafedSpace.c_is_iso_of_iso -> AlgebraicGeometry.PresheafedSpace.c_isIso_of_iso is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u}} [_inst_1 : CategoryTheory.Category.{v, u} C] {X : AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1} {Y : AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1} (f : Quiver.Hom.{succ v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} C _inst_1))) X Y) [_inst_2 : CategoryTheory.IsIso.{v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} C _inst_1) X Y f], CategoryTheory.IsIso.{v, max u v} (TopCat.Presheaf.{v, v, u} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 Y)) (TopCat.Presheaf.category.{v, v, u} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 Y)) (AlgebraicGeometry.PresheafedSpace.presheaf.{v, v, u} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{v, v, u} C _inst_1 ((fun (a : Sort.{max (succ u) (succ (succ v))}) (b : Type.{succ v}) [self : HasLiftT.{max (succ u) (succ (succ v)), succ (succ v)} a b] => self.0) (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (HasLiftT.mk.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (CoeTCₓ.coe.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (coeBase.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (AlgebraicGeometry.PresheafedSpace.coeCarrier.{v, v, u} C _inst_1)))) X) (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 Y) (AlgebraicGeometry.PresheafedSpace.Hom.base.{v, v, u} C _inst_1 X Y f) (AlgebraicGeometry.PresheafedSpace.presheaf.{v, v, u} C _inst_1 X)) (AlgebraicGeometry.PresheafedSpace.Hom.c.{v, v, u} C _inst_1 X Y f)
+but is expected to have type
+  forall {C : Type.{u_1}} [_inst_1 : CategoryTheory.Category.{u_2, u_1} C] {X : AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1} {Y : AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1} (f : Quiver.Hom.{max (succ u_2) (succ u_3), max (max u_1 u_2) (succ u_3)} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{max u_2 u_3, max (max u_1 u_2) (succ u_3)} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{max u_2 u_3, max (max u_1 u_2) (succ u_3)} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_1, u_2, u_3} C _inst_1))) X Y) [_inst_2 : CategoryTheory.IsIso.{max u_2 u_3, max (max u_1 u_2) (succ u_3)} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_1, u_2, u_3} C _inst_1) X Y f], CategoryTheory.IsIso.{max u_2 u_3, max (max u_1 u_2) u_3} (TopCat.Presheaf.{u_3, u_2, u_1} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (TopCat.instCategoryPresheaf.{u_3, u_2, u_1} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y)) (AlgebraicGeometry.PresheafedSpace.presheaf.{u_1, u_2, u_3} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{u_3, u_2, u_1} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X) (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 Y) (AlgebraicGeometry.PresheafedSpace.Hom.base.{u_1, u_2, u_3} C _inst_1 X Y f) (AlgebraicGeometry.PresheafedSpace.presheaf.{u_1, u_2, u_3} C _inst_1 X)) (AlgebraicGeometry.PresheafedSpace.Hom.c.{u_1, u_2, u_3} C _inst_1 X Y f)
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.c_is_iso_of_iso AlgebraicGeometry.PresheafedSpace.c_isIso_of_isoₓ'. -/
 instance c_isIso_of_iso (f : X ⟶ Y) [IsIso f] : IsIso f.c :=
   IsIso.of_iso (sheafIsoOfIso (asIso f))
 #align algebraic_geometry.PresheafedSpace.c_is_iso_of_iso AlgebraicGeometry.PresheafedSpace.c_isIso_of_iso
 
+/- warning: algebraic_geometry.PresheafedSpace.is_iso_of_components -> AlgebraicGeometry.PresheafedSpace.isIso_of_components is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u}} [_inst_1 : CategoryTheory.Category.{v, u} C] {X : AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1} {Y : AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1} (f : Quiver.Hom.{succ v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} C _inst_1))) X Y) [_inst_2 : CategoryTheory.IsIso.{v, succ v} TopCat.{v} TopCat.largeCategory.{v} ((fun (a : Sort.{max (succ u) (succ (succ v))}) (b : Type.{succ v}) [self : HasLiftT.{max (succ u) (succ (succ v)), succ (succ v)} a b] => self.0) (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (HasLiftT.mk.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (CoeTCₓ.coe.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (coeBase.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (AlgebraicGeometry.PresheafedSpace.coeCarrier.{v, v, u} C _inst_1)))) X) ((fun (a : Sort.{max (succ u) (succ (succ v))}) (b : Type.{succ v}) [self : HasLiftT.{max (succ u) (succ (succ v)), succ (succ v)} a b] => self.0) (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (HasLiftT.mk.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (CoeTCₓ.coe.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (coeBase.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (AlgebraicGeometry.PresheafedSpace.coeCarrier.{v, v, u} C _inst_1)))) Y) (AlgebraicGeometry.PresheafedSpace.Hom.base.{v, v, u} C _inst_1 X Y f)] [_inst_3 : CategoryTheory.IsIso.{v, max u v} (TopCat.Presheaf.{v, v, u} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 Y)) (TopCat.Presheaf.category.{v, v, u} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 Y)) (AlgebraicGeometry.PresheafedSpace.presheaf.{v, v, u} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{v, v, u} C _inst_1 ((fun (a : Sort.{max (succ u) (succ (succ v))}) (b : Type.{succ v}) [self : HasLiftT.{max (succ u) (succ (succ v)), succ (succ v)} a b] => self.0) (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (HasLiftT.mk.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (CoeTCₓ.coe.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (coeBase.{max (succ u) (succ (succ v)), succ (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) TopCat.{v} (AlgebraicGeometry.PresheafedSpace.coeCarrier.{v, v, u} C _inst_1)))) X) (AlgebraicGeometry.PresheafedSpace.carrier.{v, v, u} C _inst_1 Y) (AlgebraicGeometry.PresheafedSpace.Hom.base.{v, v, u} C _inst_1 X Y f) (AlgebraicGeometry.PresheafedSpace.presheaf.{v, v, u} C _inst_1 X)) (AlgebraicGeometry.PresheafedSpace.Hom.c.{v, v, u} C _inst_1 X Y f)], CategoryTheory.IsIso.{v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} C _inst_1) X Y f
+but is expected to have type
+  forall {C : Type.{u_3}} [_inst_1 : CategoryTheory.Category.{u_1, u_3} C] {X : AlgebraicGeometry.PresheafedSpace.{u_3, u_1, u_2} C _inst_1} {Y : AlgebraicGeometry.PresheafedSpace.{u_3, u_1, u_2} C _inst_1} (f : Quiver.Hom.{max (succ u_1) (succ u_2), max (max u_3 u_1) (succ u_2)} (AlgebraicGeometry.PresheafedSpace.{u_3, u_1, u_2} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{max u_1 u_2, max (max u_3 u_1) (succ u_2)} (AlgebraicGeometry.PresheafedSpace.{u_3, u_1, u_2} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{max u_1 u_2, max (max u_3 u_1) (succ u_2)} (AlgebraicGeometry.PresheafedSpace.{u_3, u_1, u_2} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_3, u_1, u_2} C _inst_1))) X Y) [_inst_2 : CategoryTheory.IsIso.{u_2, succ u_2} TopCat.{u_2} instTopCatLargeCategory.{u_2} (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_2} C _inst_1 X) (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_2} C _inst_1 Y) (AlgebraicGeometry.PresheafedSpace.Hom.base.{u_3, u_1, u_2} C _inst_1 X Y f)] [_inst_3 : CategoryTheory.IsIso.{max u_1 u_2, max (max u_3 u_1) u_2} (TopCat.Presheaf.{u_2, u_1, u_3} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_2} C _inst_1 Y)) (TopCat.instCategoryPresheaf.{u_2, u_1, u_3} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_2} C _inst_1 Y)) (AlgebraicGeometry.PresheafedSpace.presheaf.{u_3, u_1, u_2} C _inst_1 Y) (TopCat.Presheaf.pushforwardObj.{u_2, u_1, u_3} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_2} C _inst_1 X) (AlgebraicGeometry.PresheafedSpace.carrier.{u_3, u_1, u_2} C _inst_1 Y) (AlgebraicGeometry.PresheafedSpace.Hom.base.{u_3, u_1, u_2} C _inst_1 X Y f) (AlgebraicGeometry.PresheafedSpace.presheaf.{u_3, u_1, u_2} C _inst_1 X)) (AlgebraicGeometry.PresheafedSpace.Hom.c.{u_3, u_1, u_2} C _inst_1 X Y f)], CategoryTheory.IsIso.{max u_1 u_2, max (max u_3 u_1) (succ u_2)} (AlgebraicGeometry.PresheafedSpace.{u_3, u_1, u_2} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_3, u_1, u_2} C _inst_1) X Y f
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.is_iso_of_components AlgebraicGeometry.PresheafedSpace.isIso_of_componentsₓ'. -/
 /-- This could be used in conjunction with `category_theory.nat_iso.is_iso_of_is_iso_app`. -/
 theorem isIso_of_components (f : X ⟶ Y) [IsIso f.base] [IsIso f.c] : IsIso f :=
   by
@@ -328,6 +472,12 @@ end Iso
 
 section Restrict
 
+/- warning: algebraic_geometry.PresheafedSpace.restrict -> AlgebraicGeometry.PresheafedSpace.restrict is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.restrict AlgebraicGeometry.PresheafedSpace.restrictₓ'. -/
 /-- The restriction of a presheafed space along an open embedding into the space.
 -/
 @[simps]
@@ -338,6 +488,12 @@ def restrict {U : TopCat} (X : PresheafedSpace.{v, v, u} C) {f : U ⟶ (X : TopC
   Presheaf := h.IsOpenMap.Functor.op ⋙ X.Presheaf
 #align algebraic_geometry.PresheafedSpace.restrict AlgebraicGeometry.PresheafedSpace.restrict
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.of_restrict AlgebraicGeometry.PresheafedSpace.ofRestrictₓ'. -/
 /-- The map from the restriction of a presheafed space.
 -/
 @[simps]
@@ -353,6 +509,12 @@ def ofRestrict {U : TopCat} (X : PresheafedSpace.{v, v, u} C) {f : U ⟶ (X : To
           rfl }
 #align algebraic_geometry.PresheafedSpace.of_restrict AlgebraicGeometry.PresheafedSpace.ofRestrict
 
+/- warning: algebraic_geometry.PresheafedSpace.of_restrict_mono -> AlgebraicGeometry.PresheafedSpace.ofRestrict_mono is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.of_restrict_mono AlgebraicGeometry.PresheafedSpace.ofRestrict_monoₓ'. -/
 instance ofRestrict_mono {U : TopCat} (X : PresheafedSpace C) (f : U ⟶ X.1) (hf : OpenEmbedding f) :
     Mono (X.of_restrict hf) :=
   by
@@ -386,6 +548,12 @@ instance ofRestrict_mono {U : TopCat} (X : PresheafedSpace C) (f : U ⟶ X.1) (h
     exact this
 #align algebraic_geometry.PresheafedSpace.of_restrict_mono AlgebraicGeometry.PresheafedSpace.ofRestrict_mono
 
+/- warning: algebraic_geometry.PresheafedSpace.restrict_top_presheaf -> AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.restrict_top_presheaf AlgebraicGeometry.PresheafedSpace.restrict_top_presheafₓ'. -/
 theorem restrict_top_presheaf (X : PresheafedSpace C) :
     (X.restrict (Opens.openEmbedding ⊤)).Presheaf =
       (Opens.inclusionTopIso X.carrier).inv _* X.Presheaf :=
@@ -395,6 +563,12 @@ theorem restrict_top_presheaf (X : PresheafedSpace C) :
   rfl
 #align algebraic_geometry.PresheafedSpace.restrict_top_presheaf AlgebraicGeometry.PresheafedSpace.restrict_top_presheaf
 
+/- warning: algebraic_geometry.PresheafedSpace.of_restrict_top_c -> AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c is a dubious translation:
+lean 3 declaration is
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_inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)))))) X (TopologicalSpace.Opens.inclusion.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X) (Top.top.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (CompleteLattice.toTop.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)))))) (TopologicalSpace.Opens.openEmbedding.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X) (Top.top.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (CompleteLattice.toTop.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (TopologicalSpace.Opens.instCompleteLatticeOpens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))))))))) => Eq.{1} Prop (Eq.{succ (max (max u_1 u_2) u_3)} (TopCat.Presheaf.{u_3, u_2, u_1} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (AlgebraicGeometry.PresheafedSpace.presheaf.{u_1, u_2, u_3} C _inst_1 X) (TopCat.Presheaf.pushforwardObj.{u_3, u_2, u_1} C _inst_1 (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 (AlgebraicGeometry.PresheafedSpace.restrict.{u_1, u_2, u_3} C _inst_1 (Prefunctor.obj.{succ u_3, succ u_3, u_3, succ u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (CategoryTheory.CategoryStruct.toQuiver.{u_3, u_3} (TopologicalSpace.Opens.{u_3} 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_inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))))))))) TopCat.{u_3} (CategoryTheory.CategoryStruct.toQuiver.{u_3, succ u_3} TopCat.{u_3} (CategoryTheory.Category.toCategoryStruct.{u_3, succ u_3} TopCat.{u_3} instTopCatLargeCategory.{u_3})) (CategoryTheory.Functor.toPrefunctor.{u_3, u_3, u_3, succ u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (Preorder.smallCategory.{u_3} (TopologicalSpace.Opens.{u_3} (CategoryTheory.Bundled.α.{u_3, u_3} TopologicalSpace.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X)) (TopCat.topologicalSpace_coe.{u_3} (AlgebraicGeometry.PresheafedSpace.carrier.{u_1, u_2, u_3} C _inst_1 X))) (PartialOrder.toPreorder.{u_3} 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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.of_restrict_top_c AlgebraicGeometry.PresheafedSpace.ofRestrict_top_cₓ'. -/
 theorem ofRestrict_top_c (X : PresheafedSpace C) :
     (X.of_restrict (Opens.openEmbedding ⊤)).c =
       eqToHom
@@ -416,6 +590,12 @@ theorem ofRestrict_top_c (X : PresheafedSpace C) :
     exact ⟨fun h => ⟨⟨x, trivial⟩, h, rfl⟩, fun ⟨⟨_, _⟩, h, rfl⟩ => h⟩
 #align algebraic_geometry.PresheafedSpace.of_restrict_top_c AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c
 
+/- warning: algebraic_geometry.PresheafedSpace.to_restrict_top -> AlgebraicGeometry.PresheafedSpace.toRestrictTop is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.to_restrict_top AlgebraicGeometry.PresheafedSpace.toRestrictTopₓ'. -/
 /- or `rw [opens.inclusion_top_functor, ←comp_obj, ←opens.map_comp_eq],
          erw iso.inv_hom_id, cases U, refl` after `dsimp` -/
 /-- The map to the restriction of a presheafed space along the canonical inclusion from the top
@@ -428,6 +608,12 @@ def toRestrictTop (X : PresheafedSpace C) : X ⟶ X.restrict (Opens.openEmbeddin
   c := eqToHom (restrict_top_presheaf X)
 #align algebraic_geometry.PresheafedSpace.to_restrict_top AlgebraicGeometry.PresheafedSpace.toRestrictTop
 
+/- warning: algebraic_geometry.PresheafedSpace.restrict_top_iso -> AlgebraicGeometry.PresheafedSpace.restrictTopIso is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.restrict_top_iso AlgebraicGeometry.PresheafedSpace.restrictTopIsoₓ'. -/
 /-- The isomorphism from the restriction to the top subspace.
 -/
 @[simps]
@@ -436,14 +622,16 @@ def restrictTopIso (X : PresheafedSpace C) : X.restrict (Opens.openEmbedding ⊤
   Hom := X.of_restrict _
   inv := X.toRestrictTop
   hom_inv_id' :=
-    ext _ _ (ConcreteCategory.hom_ext _ _ fun ⟨x, _⟩ => rfl) <|
+    AlgebraicGeometry.PresheafedSpace.Hom.ext _ _
+        (ConcreteCategory.hom_ext _ _ fun ⟨x, _⟩ => rfl) <|
       by
       erw [comp_c]
       rw [X.of_restrict_top_c]
       ext
       simp
   inv_hom_id' :=
-    ext _ _ rfl <| by
+    AlgebraicGeometry.PresheafedSpace.Hom.ext _ _ rfl <|
+      by
       erw [comp_c]
       rw [X.of_restrict_top_c]
       ext
@@ -452,6 +640,12 @@ def restrictTopIso (X : PresheafedSpace C) : X.restrict (Opens.openEmbedding ⊤
 
 end Restrict
 
+/- warning: algebraic_geometry.PresheafedSpace.Γ -> AlgebraicGeometry.PresheafedSpace.Γ is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u}} [_inst_1 : CategoryTheory.Category.{v, u} C], CategoryTheory.Functor.{v, v, max u (succ v), u} (Opposite.{succ (max u (succ v))} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1)) (CategoryTheory.Category.opposite.{v, max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} C _inst_1)) C _inst_1
+but is expected to have type
+  forall {C : Type.{u_1}} [_inst_1 : CategoryTheory.Category.{u_2, u_1} C], CategoryTheory.Functor.{max u_2 u_3, u_2, max (max u_1 u_2) (succ u_3), u_1} (Opposite.{max (max (succ (succ u_3)) (succ u_2)) (succ u_1)} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1)) (CategoryTheory.Category.opposite.{max u_2 u_3, max (max u_1 u_2) (succ u_3)} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_3} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_1, u_2, u_3} C _inst_1)) C _inst_1
+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.Γ AlgebraicGeometry.PresheafedSpace.Γₓ'. -/
 /-- The global sections, notated Gamma.
 -/
 @[simps]
@@ -461,10 +655,22 @@ def Γ : (PresheafedSpace.{v, v, u} C)ᵒᵖ ⥤ C
   map X Y f := f.unop.c.app (op ⊤)
 #align algebraic_geometry.PresheafedSpace.Γ AlgebraicGeometry.PresheafedSpace.Γ
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.Γ_obj_op AlgebraicGeometry.PresheafedSpace.Γ_obj_opₓ'. -/
 theorem Γ_obj_op (X : PresheafedSpace C) : Γ.obj (op X) = X.Presheaf.obj (op ⊤) :=
   rfl
 #align algebraic_geometry.PresheafedSpace.Γ_obj_op AlgebraicGeometry.PresheafedSpace.Γ_obj_op
 
+/- warning: algebraic_geometry.PresheafedSpace.Γ_map_op -> AlgebraicGeometry.PresheafedSpace.Γ_map_op is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebraic_geometry.PresheafedSpace.Γ_map_op AlgebraicGeometry.PresheafedSpace.Γ_map_opₓ'. -/
 theorem Γ_map_op {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) : Γ.map f.op = f.c.app (op ⊤) :=
   rfl
 #align algebraic_geometry.PresheafedSpace.Γ_map_op AlgebraicGeometry.PresheafedSpace.Γ_map_op
@@ -485,6 +691,12 @@ attribute [local simp] presheaf.pushforward_obj
 
 namespace Functor
 
+/- warning: category_theory.functor.map_presheaf -> CategoryTheory.Functor.mapPresheaf is a dubious translation:
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+but is expected to have type
+  forall {C : Type.{u_1}} [_inst_1 : CategoryTheory.Category.{u_2, u_1} C] {D : Type.{u_3}} [_inst_2 : CategoryTheory.Category.{u_4, u_3} D], (CategoryTheory.Functor.{u_2, u_4, u_1, u_3} C _inst_1 D _inst_2) -> (CategoryTheory.Functor.{max u_2 u_5, max u_4 u_5, max (max (succ u_5) u_2) u_1, max (max (succ u_5) u_4) u_3} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_5} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_1, u_2, u_5} C _inst_1) (AlgebraicGeometry.PresheafedSpace.{u_3, u_4, u_5} D _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_3, u_4, u_5} D _inst_2))
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_presheaf CategoryTheory.Functor.mapPresheafₓ'. -/
 /-- We can apply a functor `F : C ⥤ D` to the values of the presheaf in any `PresheafedSpace C`,
     giving a functor `PresheafedSpace C ⥤ PresheafedSpace D` -/
 def mapPresheaf (F : C ⥤ D) : PresheafedSpace.{v, v, u} C ⥤ PresheafedSpace.{v, v, u} D
@@ -497,24 +709,48 @@ def mapPresheaf (F : C ⥤ D) : PresheafedSpace.{v, v, u} C ⥤ PresheafedSpace.
       c := whiskerRight f.c F }
 #align category_theory.functor.map_presheaf CategoryTheory.Functor.mapPresheaf
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_presheaf_obj_X CategoryTheory.Functor.mapPresheaf_obj_Xₓ'. -/
 @[simp]
 theorem mapPresheaf_obj_X (F : C ⥤ D) (X : PresheafedSpace C) :
     (F.mapPresheaf.obj X : TopCat.{v}) = (X : TopCat.{v}) :=
   rfl
 #align category_theory.functor.map_presheaf_obj_X CategoryTheory.Functor.mapPresheaf_obj_X
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_presheaf_obj_presheaf CategoryTheory.Functor.mapPresheaf_obj_presheafₓ'. -/
 @[simp]
 theorem mapPresheaf_obj_presheaf (F : C ⥤ D) (X : PresheafedSpace C) :
     (F.mapPresheaf.obj X).Presheaf = X.Presheaf ⋙ F :=
   rfl
 #align category_theory.functor.map_presheaf_obj_presheaf CategoryTheory.Functor.mapPresheaf_obj_presheaf
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_presheaf_map_f CategoryTheory.Functor.mapPresheaf_map_fₓ'. -/
 @[simp]
 theorem mapPresheaf_map_f (F : C ⥤ D) {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) :
     (F.mapPresheaf.map f).base = f.base :=
   rfl
 #align category_theory.functor.map_presheaf_map_f CategoryTheory.Functor.mapPresheaf_map_f
 
+/- warning: category_theory.functor.map_presheaf_map_c -> CategoryTheory.Functor.mapPresheaf_map_c is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_presheaf_map_c CategoryTheory.Functor.mapPresheaf_map_cₓ'. -/
 @[simp]
 theorem mapPresheaf_map_c (F : C ⥤ D) {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) :
     (F.mapPresheaf.map f).c = whiskerRight f.c F :=
@@ -525,6 +761,12 @@ end Functor
 
 namespace NatTrans
 
+/- warning: category_theory.nat_trans.on_presheaf -> CategoryTheory.NatTrans.onPresheaf is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u}} [_inst_1 : CategoryTheory.Category.{v, u} C] {D : Type.{u}} [_inst_2 : CategoryTheory.Category.{v, u} D] {F : CategoryTheory.Functor.{v, v, u, u} C _inst_1 D _inst_2} {G : CategoryTheory.Functor.{v, v, u, u} C _inst_1 D _inst_2}, (Quiver.Hom.{succ (max u v), max v u} (CategoryTheory.Functor.{v, v, u, u} C _inst_1 D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u v, max v u} (CategoryTheory.Functor.{v, v, u, u} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u v, max v u} (CategoryTheory.Functor.{v, v, u, u} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{v, v, u, u} C _inst_1 D _inst_2))) F G) -> (Quiver.Hom.{succ (max (max u (succ v)) v), max v u (succ v)} (CategoryTheory.Functor.{v, v, max u (succ v), max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.{v, v, u} D _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} D _inst_2)) (CategoryTheory.CategoryStruct.toQuiver.{max (max u (succ v)) v, max v u (succ v)} (CategoryTheory.Functor.{v, v, max u (succ v), max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.{v, v, u} D _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} D _inst_2)) (CategoryTheory.Category.toCategoryStruct.{max (max u (succ v)) v, max v u (succ v)} (CategoryTheory.Functor.{v, v, max u (succ v), max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.{v, v, u} D _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} D _inst_2)) (CategoryTheory.Functor.category.{v, v, max u (succ v), max u (succ v)} (AlgebraicGeometry.PresheafedSpace.{v, v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} C _inst_1) (AlgebraicGeometry.PresheafedSpace.{v, v, u} D _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{v, u} D _inst_2)))) (CategoryTheory.Functor.mapPresheaf.{v, u} C _inst_1 D _inst_2 G) (CategoryTheory.Functor.mapPresheaf.{v, u} C _inst_1 D _inst_2 F))
+but is expected to have type
+  forall {C : Type.{u_1}} [_inst_1 : CategoryTheory.Category.{u_2, u_1} C] {D : Type.{u_3}} [_inst_2 : CategoryTheory.Category.{u_4, u_3} D] {F : CategoryTheory.Functor.{u_2, u_4, u_1, u_3} C _inst_1 D _inst_2} {G : CategoryTheory.Functor.{u_2, u_4, u_1, u_3} C _inst_1 D _inst_2}, (Quiver.Hom.{max (succ u_1) (succ u_4), max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_2, u_4, u_1, u_3} C _inst_1 D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_2, u_4, u_1, u_3} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u_1 u_4, max (max (max u_1 u_2) u_3) u_4} (CategoryTheory.Functor.{u_2, u_4, u_1, u_3} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u_2, u_4, u_1, u_3} C _inst_1 D _inst_2))) F G) -> (Quiver.Hom.{max (max (max (succ u_1) (succ u_2)) (succ u_4)) (succ (succ u_5)), max (max (max (max u_1 u_2) u_3) u_4) (succ u_5)} (CategoryTheory.Functor.{max u_2 u_5, max u_4 u_5, max (max (succ u_5) u_2) u_1, max (max (succ u_5) u_4) u_3} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_5} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_1, u_2, u_5} C _inst_1) (AlgebraicGeometry.PresheafedSpace.{u_3, u_4, u_5} D _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_3, u_4, u_5} D _inst_2)) (CategoryTheory.CategoryStruct.toQuiver.{max (max (max u_1 u_2) u_4) (succ u_5), max (max (max (max u_1 u_2) u_3) u_4) (succ u_5)} (CategoryTheory.Functor.{max u_2 u_5, max u_4 u_5, max (max (succ u_5) u_2) u_1, max (max (succ u_5) u_4) u_3} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_5} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_1, u_2, u_5} C _inst_1) (AlgebraicGeometry.PresheafedSpace.{u_3, u_4, u_5} D _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_3, u_4, u_5} D _inst_2)) (CategoryTheory.Category.toCategoryStruct.{max (max (max u_1 u_2) u_4) (succ u_5), max (max (max (max u_1 u_2) u_3) u_4) (succ u_5)} (CategoryTheory.Functor.{max u_2 u_5, max u_4 u_5, max (max (succ u_5) u_2) u_1, max (max (succ u_5) u_4) u_3} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_5} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_1, u_2, u_5} C _inst_1) (AlgebraicGeometry.PresheafedSpace.{u_3, u_4, u_5} D _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_3, u_4, u_5} D _inst_2)) (CategoryTheory.Functor.category.{max u_2 u_5, max u_4 u_5, max (max u_1 u_2) (succ u_5), max (max u_3 u_4) (succ u_5)} (AlgebraicGeometry.PresheafedSpace.{u_1, u_2, u_5} C _inst_1) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_1, u_2, u_5} C _inst_1) (AlgebraicGeometry.PresheafedSpace.{u_3, u_4, u_5} D _inst_2) (AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces.{u_3, u_4, u_5} D _inst_2)))) (CategoryTheory.Functor.mapPresheaf.{u_1, u_2, u_3, u_4, u_5} C _inst_1 D _inst_2 G) (CategoryTheory.Functor.mapPresheaf.{u_1, u_2, u_3, u_4, u_5} C _inst_1 D _inst_2 F))
+Case conversion may be inaccurate. Consider using '#align category_theory.nat_trans.on_presheaf CategoryTheory.NatTrans.onPresheafₓ'. -/
 /-- A natural transformation induces a natural transformation between the `map_presheaf` functors.
 -/
 def onPresheaf {F G : C ⥤ D} (α : F ⟶ G) : G.mapPresheaf ⟶ F.mapPresheaf

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

@@ -193,11 +193,11 @@ theorem id_c_app (X : PresheafedSpace.{v, v, u} C) (U) :
       X.Presheaf.map
         (eqToHom
           (by
-            induction U using Opposite.rec
+            induction U using Opposite.rec'
             cases U
             rfl)) :=
   by
-  induction U using Opposite.rec
+  induction U using Opposite.rec'
   cases U
   simp only [id_c]
   dsimp
@@ -274,7 +274,7 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.Hom _* X.2 ≅ Y.2) : X ≅ Y
     simp
   inv_hom_id' := by
     ext x
-    induction x using Opposite.rec
+    induction x using Opposite.rec'
     simp only [comp_c_app, whisker_right_app, presheaf.to_pushforward_of_iso_app,
       nat_trans.comp_app, eq_to_hom_app, id_c_app, category.assoc]
     erw [← α.hom.naturality]
@@ -360,7 +360,7 @@ instance ofRestrict_mono {U : TopCat} (X : PresheafedSpace C) (f : U ⟶ X.1) (h
   constructor
   intro Z g₁ g₂ eq
   ext V
-  · induction V using Opposite.rec
+  · induction V using Opposite.rec'
     have hV : (opens.map (X.of_restrict hf).base).obj (hf.is_open_map.functor.obj V) = V :=
       by
       ext1
@@ -409,7 +409,7 @@ theorem ofRestrict_top_c (X : PresheafedSpace C) :
   ext U;
   change X.presheaf.map _ = _; convert eq_to_hom_map _ _ using 1
   congr ; simpa
-  · induction U using Opposite.rec
+  · induction U using Opposite.rec'
     dsimp
     congr
     ext

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

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

@@ -286,7 +286,7 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.hom _* X.2 ≅ Y.2) : X ≅ Y wher
       c := Presheaf.toPushforwardOfIso H α.hom }
   hom_inv_id := by
     ext
-    simp only [comp_base, Iso.hom_inv_id, FunctorToTypes.map_id_apply, id_base]
+    · simp only [comp_base, Iso.hom_inv_id, FunctorToTypes.map_id_apply, id_base]
     rw [NatTrans.comp_app]
     simp only [id_base, comp_obj, op_obj, comp_base, Presheaf.pushforwardObj_obj,
       Opens.map_comp_obj, comp_c_app, unop_op, Presheaf.toPushforwardOfIso_app, assoc,
@@ -294,8 +294,8 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.hom _* X.2 ≅ Y.2) : X ≅ Y wher
       ← Functor.map_comp, eqToHom_trans, eqToHom_refl]
   inv_hom_id := by
     ext
-    dsimp
-    rw [H.inv_hom_id]
+    · dsimp
+      rw [H.inv_hom_id]
     dsimp
     simp only [Presheaf.pushforwardObj_obj, op_obj, Opens.map_comp_obj, comp_obj,
       comp_c_app, unop_op, Presheaf.toPushforwardOfIso_app, whiskerRight_app, eqToHom_app,
@@ -516,12 +516,12 @@ def mapPresheaf (F : C ⥤ D) : PresheafedSpace C ⥤ PresheafedSpace D where
   -- Porting note: these proofs were automatic in mathlib3
   map_id X := by
     ext U
-    rfl
-    simp
+    · rfl
+    · simp
   map_comp f g := by
     ext U
-    rfl
-    simp
+    · rfl
+    · simp
 #align category_theory.functor.map_presheaf CategoryTheory.Functor.mapPresheaf
 
 @[simp]

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

@@ -38,7 +38,7 @@ variable (C : Type*) [Category C]
 
 namespace AlgebraicGeometry
 
--- porting note: `PresheafSpace.{w} C` is the type of topological spaces in `Type w` equipped
+-- Porting note: `PresheafSpace.{w} C` is the type of topological spaces in `Type w` equipped
 -- with a presheaf with values in `C`; then there is a total of three universe parameters
 -- in `PresheafSpace.{w, v, u} C`, where `C : Type u` and `Category.{v} C`.
 -- In mathlib3, some definitions in this file unnecessarily assumed `w=v`. This restriction
@@ -55,7 +55,7 @@ variable {C}
 
 namespace PresheafedSpace
 
--- porting note: using `Coe` here triggers an error, `CoeOut` seems an acceptable alternative
+-- Porting note: using `Coe` here triggers an error, `CoeOut` seems an acceptable alternative
 instance coeCarrier : CoeOut (PresheafedSpace C) TopCat where coe X := X.carrier
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.coe_carrier AlgebraicGeometry.PresheafedSpace.coeCarrier
@@ -66,14 +66,14 @@ attribute [coe] PresheafedSpace.carrier
 -- in downstream files.
 instance : CoeSort (PresheafedSpace C) (Type*) where coe := fun X => X.carrier
 
--- porting note: the following lemma is removed because it is a syntactic tauto
+-- Porting note: the following lemma is removed because it is a syntactic tauto
 /-@[simp]
 theorem as_coe (X : PresheafedSpace.{w, v, u} C) : X.carrier = (X : TopCat.{w}) :=
   rfl-/
 set_option linter.uppercaseLean3 false in
 #noalign algebraic_geometry.PresheafedSpace.as_coe
 
--- porting note: removed @[simp] as the `simpVarHead` linter complains
+-- Porting note: removed @[simp] as the `simpVarHead` linter complains
 -- @[simp]
 theorem mk_coe (carrier) (presheaf) :
     (({ carrier
@@ -104,7 +104,7 @@ structure Hom (X Y : PresheafedSpace C) where
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.hom AlgebraicGeometry.PresheafedSpace.Hom
 
--- porting note: eventually, the ext lemma shall be applied to terms in `X ⟶ Y`
+-- Porting note: eventually, the ext lemma shall be applied to terms in `X ⟶ Y`
 -- rather than `Hom X Y`, this one was renamed `Hom.ext` instead of `ext`,
 -- and the more practical lemma `ext` is defined just after the definition
 -- of the `Category` instance
@@ -131,7 +131,7 @@ theorem hext {X Y : PresheafedSpace C} (α β : Hom X Y) (w : α.base = β.base)
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.hext AlgebraicGeometry.PresheafedSpace.hext
 
--- porting note: `eqToHom` is no longer necessary in the definition of `c`
+-- Porting note: `eqToHom` is no longer necessary in the definition of `c`
 /-- The identity morphism of a `PresheafedSpace`. -/
 def id (X : PresheafedSpace C) : Hom X X where
   base := 𝟙 (X : TopCat)
@@ -163,7 +163,7 @@ section
 
 attribute [local simp] id comp
 
--- porting note: in mathlib3, `tidy` could (almost) prove the category axioms, but proofs
+-- Porting note: in mathlib3, `tidy` could (almost) prove the category axioms, but proofs
 -- were included because `tidy` was slow. Here, `aesop_cat` succeeds reasonably quickly
 -- for `comp_id` and `assoc`
 /-- The category of PresheafedSpaces. Morphisms are pairs, a continuous map and a presheaf map
@@ -204,7 +204,7 @@ theorem id_base (X : PresheafedSpace C) : (𝟙 X : X ⟶ X).base = 𝟙 (X : To
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.id_base AlgebraicGeometry.PresheafedSpace.id_base
 
--- porting note: `eqToHom` is no longer needed in the statements of `id_c` and `id_c_app`
+-- Porting note: `eqToHom` is no longer needed in the statements of `id_c` and `id_c_app`
 theorem id_c (X : PresheafedSpace C) :
     (𝟙 X : X ⟶ X).c = 𝟙 X.presheaf :=
   rfl
@@ -229,14 +229,14 @@ set_option linter.uppercaseLean3 false in
 instance (X Y : PresheafedSpace C) : CoeFun (X ⟶ Y) fun _ => (↑X → ↑Y) :=
   ⟨fun f => f.base⟩
 
--- porting note: removed as this is a syntactic tauto
+-- Porting note: removed as this is a syntactic tauto
 --theorem coe_to_fun_eq {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) : (f : ↑X → ↑Y) = f.base :=
 --  rfl
 #noalign algebraic_geometry.PresheafedSpace.coe_to_fun_eq
 
 -- The `reassoc` attribute was added despite the LHS not being a composition of two homs,
 -- for the reasons explained in the docstring.
--- porting note: as there is no composition in the LHS it is purposely `@[reassoc, simp]` rather
+-- Porting note: as there is no composition in the LHS it is purposely `@[reassoc, simp]` rather
 -- than `@[reassoc (attr := simp)]`
 /-- Sometimes rewriting with `comp_c_app` doesn't work because of dependent type issues.
 In that case, `erw comp_c_app_assoc` might make progress.
@@ -513,7 +513,7 @@ def mapPresheaf (F : C ⥤ D) : PresheafedSpace C ⥤ PresheafedSpace D where
   map f :=
     { base := f.base
       c := whiskerRight f.c F }
-  -- porting note: these proofs were automatic in mathlib3
+  -- Porting note: these proofs were automatic in mathlib3
   map_id X := by
     ext U
     rfl

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -26,13 +26,13 @@ variable (C : Type*) [Category C]
 -- Porting note: we used to have:
 -- local attribute [tidy] tactic.auto_cases_opens
 -- We would replace this by:
--- attribute [local aesop safe cases (rule_sets [CategoryTheory])] Opens
+-- attribute [local aesop safe cases (rule_sets := [CategoryTheory])] Opens
 -- although it doesn't appear to help in this file, in any case.
 
 -- Porting note: we used to have:
 -- local attribute [tidy] tactic.op_induction'
 -- A possible replacement would be:
--- attribute [local aesop safe cases (rule_sets [CategoryTheory])] Opposite
+-- attribute [local aesop safe cases (rule_sets := [CategoryTheory])] Opposite
 -- but this would probably require https://github.com/JLimperg/aesop/issues/59
 -- In any case, it doesn't seem necessary here.
 

Various things break in the simpset for Presheaf when the simp algorithm changes in leanprover/lean4#3124. These backwards compatible fixes are, I think, improvements anyway.

One could further add a Presheaf.id_app lemma, and do further cleanup in the proofs which now use dsimp [-Presheaf.comp_app], but I'd prefer if these are done in a followup PR in order to not hold up #9500.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -297,7 +297,6 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.hom _* X.2 ≅ Y.2) : X ≅ Y wher
     dsimp
     rw [H.inv_hom_id]
     dsimp
-    rw [NatTrans.comp_app]
     simp only [Presheaf.pushforwardObj_obj, op_obj, Opens.map_comp_obj, comp_obj,
       comp_c_app, unop_op, Presheaf.toPushforwardOfIso_app, whiskerRight_app, eqToHom_app,
       assoc, id_c_app, map_id]
@@ -319,7 +318,7 @@ def sheafIsoOfIso (H : X ≅ Y) : Y.2 ≅ H.hom.base _* X.2 where
   inv_hom_id := by
     ext U
     dsimp
-    rw [NatTrans.comp_app, NatTrans.id_app]
+    rw [NatTrans.id_app]
     simp only [Presheaf.pushforwardObj_obj, op_obj, Presheaf.pushforwardToOfIso_app,
       Iso.symm_inv, mapIso_hom, forget_map, Iso.symm_hom, mapIso_inv,
       unop_op, eqToHom_map, assoc]
@@ -456,15 +455,13 @@ def restrictTopIso (X : PresheafedSpace C) : X.restrict (Opens.openEmbedding ⊤
   hom_inv_id := by
     ext
     · rfl
-    · dsimp
-      erw [comp_c, toRestrictTop_c, whiskerRight_id',
+    · erw [comp_c, toRestrictTop_c, whiskerRight_id',
         comp_id, ofRestrict_top_c, eqToHom_map, eqToHom_trans, eqToHom_refl]
       rfl
   inv_hom_id := by
     ext
     · rfl
-    · dsimp
-      erw [comp_c, ofRestrict_top_c, toRestrictTop_c, eqToHom_map, whiskerRight_id', comp_id,
+    · erw [comp_c, ofRestrict_top_c, toRestrictTop_c, eqToHom_map, whiskerRight_id', comp_id,
         eqToHom_trans, eqToHom_refl]
       rfl
 set_option linter.uppercaseLean3 false in

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

This has nice performance benefits.

@@ -21,7 +21,7 @@ presheaves.
 
 open Opposite CategoryTheory CategoryTheory.Category CategoryTheory.Functor TopCat TopologicalSpace
 
-variable (C : Type _) [Category C]
+variable (C : Type*) [Category C]
 
 -- Porting note: we used to have:
 -- local attribute [tidy] tactic.auto_cases_opens
@@ -64,7 +64,7 @@ attribute [coe] PresheafedSpace.carrier
 
 -- Porting note: we add this instance, as Lean does not reliably use the `CoeOut` instance above
 -- in downstream files.
-instance : CoeSort (PresheafedSpace C) (Type _) where coe := fun X => X.carrier
+instance : CoeSort (PresheafedSpace C) (Type*) where coe := fun X => X.carrier
 
 -- porting note: the following lemma is removed because it is a syntactic tauto
 /-@[simp]
@@ -501,7 +501,7 @@ variable {C}
 
 namespace CategoryTheory
 
-variable {D : Type _} [Category D]
+variable {D : Type*} [Category D]
 
 attribute [local simp] Presheaf.pushforwardObj
 

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module algebraic_geometry.presheafed_space
-! leanprover-community/mathlib commit d39590fc8728fbf6743249802486f8c91ffe07bc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Sheaves.Presheaf
 import Mathlib.CategoryTheory.Adjunction.FullyFaithful
 
+#align_import algebraic_geometry.presheafed_space from "leanprover-community/mathlib"@"d39590fc8728fbf6743249802486f8c91ffe07bc"
+
 /-!
 # Presheafed spaces
 

• depends on: https://github.com/leanprover/std4/pull/163
• depends on: #5584
• depends on: #5715
• depends on: #5729
• depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -178,11 +178,11 @@ instance categoryOfPresheafedSpaces : Category (PresheafedSpace C) where
   id_comp _ := by
     dsimp
     ext
+    · dsimp
+      simp
     · dsimp
       simp only [map_id, whiskerRight_id', assoc]
       erw [comp_id, comp_id]
-    · dsimp
-      simp
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.category_of_PresheafedSpaces AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces
 
@@ -289,15 +289,17 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.hom _* X.2 ≅ Y.2) : X ≅ Y wher
       c := Presheaf.toPushforwardOfIso H α.hom }
   hom_inv_id := by
     ext
+    simp only [comp_base, Iso.hom_inv_id, FunctorToTypes.map_id_apply, id_base]
     rw [NatTrans.comp_app]
     simp only [id_base, comp_obj, op_obj, comp_base, Presheaf.pushforwardObj_obj,
       Opens.map_comp_obj, comp_c_app, unop_op, Presheaf.toPushforwardOfIso_app, assoc,
       Iso.hom_inv_id_app, comp_id, whiskerRight_app, eqToHom_app, id_c_app, map_id,
       ← Functor.map_comp, eqToHom_trans, eqToHom_refl]
-    simp only [comp_base, Iso.hom_inv_id, FunctorToTypes.map_id_apply, id_base]
   inv_hom_id := by
     ext
     dsimp
+    rw [H.inv_hom_id]
+    dsimp
     rw [NatTrans.comp_app]
     simp only [Presheaf.pushforwardObj_obj, op_obj, Opens.map_comp_obj, comp_obj,
       comp_c_app, unop_op, Presheaf.toPushforwardOfIso_app, whiskerRight_app, eqToHom_app,
@@ -305,8 +307,6 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.hom _* X.2 ≅ Y.2) : X ≅ Y wher
     rw [← α.hom.naturality, Presheaf.pushforwardObj_map, eqToHom_map, eqToHom_map,
       eqToHom_map, eqToHom_trans_assoc, eqToHom_refl, id_comp]
     apply Iso.inv_hom_id_app
-    dsimp
-    rw [H.inv_hom_id]
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.iso_of_components AlgebraicGeometry.PresheafedSpace.isoOfComponents
 
@@ -387,7 +387,6 @@ instance ofRestrict_mono {U : TopCat} (X : PresheafedSpace C) (f : U ⟶ X.1) (h
   constructor
   intro Z g₁ g₂ eq
   ext1
-  swap
   · have := congr_arg PresheafedSpace.Hom.base eq
     simp only [PresheafedSpace.comp_base, PresheafedSpace.ofRestrict_base] at this
     rw [cancel_mono] at this
@@ -459,18 +458,18 @@ def restrictTopIso (X : PresheafedSpace C) : X.restrict (Opens.openEmbedding ⊤
   inv := X.toRestrictTop
   hom_inv_id := by
     ext
+    · rfl
     · dsimp
       erw [comp_c, toRestrictTop_c, whiskerRight_id',
         comp_id, ofRestrict_top_c, eqToHom_map, eqToHom_trans, eqToHom_refl]
       rfl
-    · rfl
   inv_hom_id := by
     ext
+    · rfl
     · dsimp
       erw [comp_c, ofRestrict_top_c, toRestrictTop_c, eqToHom_map, whiskerRight_id', comp_id,
         eqToHom_trans, eqToHom_refl]
       rfl
-    · rfl
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.restrict_top_iso AlgebraicGeometry.PresheafedSpace.restrictTopIso
 
@@ -523,12 +522,12 @@ def mapPresheaf (F : C ⥤ D) : PresheafedSpace C ⥤ PresheafedSpace D where
   -- porting note: these proofs were automatic in mathlib3
   map_id X := by
     ext U
-    simp
     rfl
+    simp
   map_comp f g := by
     ext U
-    simp
     rfl
+    simp
 #align category_theory.functor.map_presheaf CategoryTheory.Functor.mapPresheaf
 
 @[simp]

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -252,7 +252,7 @@ set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.comp_c_app AlgebraicGeometry.PresheafedSpace.comp_c_app
 
 theorem congr_app {X Y : PresheafedSpace C} {α β : X ⟶ Y} (h : α = β) (U) :
-    α.c.app U = β.c.app U ≫ X.presheaf.map (eqToHom (by subst h ; rfl)) := by
+    α.c.app U = β.c.app U ≫ X.presheaf.map (eqToHom (by subst h; rfl)) := by
   subst h
   simp
 set_option linter.uppercaseLean3 false in

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

@@ -178,7 +178,7 @@ instance categoryOfPresheafedSpaces : Category (PresheafedSpace C) where
   id_comp _ := by
     dsimp
     ext
-    . dsimp
+    · dsimp
       simp only [map_id, whiskerRight_id', assoc]
       erw [comp_id, comp_id]
     · dsimp
@@ -392,7 +392,7 @@ instance ofRestrict_mono {U : TopCat} (X : PresheafedSpace C) (f : U ⟶ X.1) (h
     simp only [PresheafedSpace.comp_base, PresheafedSpace.ofRestrict_base] at this
     rw [cancel_mono] at this
     exact this
-  . ext V
+  · ext V
     have hV : (Opens.map (X.ofRestrict hf).base).obj (hf.isOpenMap.functor.obj V) = V := by
       ext1
       exact Set.preimage_image_eq _ hf.inj

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

@@ -186,6 +186,10 @@ instance categoryOfPresheafedSpaces : Category (PresheafedSpace C) where
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.category_of_PresheafedSpaces AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces
 
+variable {C}
+
+-- Porting note: adding an ext lemma.
+-- See https://github.com/leanprover-community/mathlib4/issues/5229
 @[ext]
 theorem ext {X Y : PresheafedSpace C} (α β : X ⟶ Y) (w : α.base = β.base)
     (h : α.c ≫ whiskerRight (eqToHom (by rw [w])) _ = β.c) : α = β :=

@@ -72,9 +72,9 @@ instance : CoeSort (PresheafedSpace C) (Type _) where coe := fun X => X.carrier
 -- porting note: the following lemma is removed because it is a syntactic tauto
 /-@[simp]
 theorem as_coe (X : PresheafedSpace.{w, v, u} C) : X.carrier = (X : TopCat.{w}) :=
-  rfl
+  rfl-/
 set_option linter.uppercaseLean3 false in
-#align algebraic_geometry.PresheafedSpace.as_coe AlgebraicGeometry.PresheafedSpace.as_coe-/
+#noalign algebraic_geometry.PresheafedSpace.as_coe
 
 -- porting note: removed @[simp] as the `simpVarHead` linter complains
 -- @[simp]
@@ -181,7 +181,7 @@ instance categoryOfPresheafedSpaces : Category (PresheafedSpace C) where
     . dsimp
       simp only [map_id, whiskerRight_id', assoc]
       erw [comp_id, comp_id]
-    . dsimp
+    · dsimp
       simp
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.category_of_PresheafedSpaces AlgebraicGeometry.PresheafedSpace.categoryOfPresheafedSpaces
@@ -231,7 +231,7 @@ instance (X Y : PresheafedSpace C) : CoeFun (X ⟶ Y) fun _ => (↑X → ↑Y) :
 -- porting note: removed as this is a syntactic tauto
 --theorem coe_to_fun_eq {X Y : PresheafedSpace.{v, v, u} C} (f : X ⟶ Y) : (f : ↑X → ↑Y) = f.base :=
 --  rfl
---#align algebraic_geometry.PresheafedSpace.coe_to_fun_eq AlgebraicGeometry.PresheafedSpace.coe_to_fun_eq
+#noalign algebraic_geometry.PresheafedSpace.coe_to_fun_eq
 
 -- The `reassoc` attribute was added despite the LHS not being a composition of two homs,
 -- for the reasons explained in the docstring.
@@ -455,18 +455,18 @@ def restrictTopIso (X : PresheafedSpace C) : X.restrict (Opens.openEmbedding ⊤
   inv := X.toRestrictTop
   hom_inv_id := by
     ext
-    . dsimp
+    · dsimp
       erw [comp_c, toRestrictTop_c, whiskerRight_id',
         comp_id, ofRestrict_top_c, eqToHom_map, eqToHom_trans, eqToHom_refl]
       rfl
-    . rfl
+    · rfl
   inv_hom_id := by
     ext
-    . dsimp
+    · dsimp
       erw [comp_c, ofRestrict_top_c, toRestrictTop_c, eqToHom_map, whiskerRight_id', comp_id,
         eqToHom_trans, eqToHom_refl]
       rfl
-    . rfl
+    · rfl
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.restrict_top_iso AlgebraicGeometry.PresheafedSpace.restrictTopIso
 

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

@@ -178,8 +178,7 @@ instance categoryOfPresheafedSpaces : Category (PresheafedSpace C) where
   id_comp _ := by
     dsimp
     ext
-    . apply NatTrans.ext
-      dsimp
+    . dsimp
       simp only [map_id, whiskerRight_id', assoc]
       erw [comp_id, comp_id]
     . dsimp
@@ -273,7 +272,7 @@ section Iso
 
 variable {X Y : PresheafedSpace C}
 
-/-- An isomorphism of PresheafedSpaces is a homeomorphism of the underlying space, and a
+/-- An isomorphism of `PresheafedSpace`s is a homeomorphism of the underlying space, and a
 natural transformation between the sheaves.
 -/
 @[simps hom inv]
@@ -286,8 +285,6 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.hom _* X.2 ≅ Y.2) : X ≅ Y wher
       c := Presheaf.toPushforwardOfIso H α.hom }
   hom_inv_id := by
     ext
-    apply NatTrans.ext
-    ext U
     rw [NatTrans.comp_app]
     simp only [id_base, comp_obj, op_obj, comp_base, Presheaf.pushforwardObj_obj,
       Opens.map_comp_obj, comp_c_app, unop_op, Presheaf.toPushforwardOfIso_app, assoc,
@@ -296,8 +293,6 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.hom _* X.2 ≅ Y.2) : X ≅ Y wher
     simp only [comp_base, Iso.hom_inv_id, FunctorToTypes.map_id_apply, id_base]
   inv_hom_id := by
     ext
-    apply NatTrans.ext
-    ext U
     dsimp
     rw [NatTrans.comp_app]
     simp only [Presheaf.pushforwardObj_obj, op_obj, Opens.map_comp_obj, comp_obj,
@@ -311,27 +306,25 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.hom _* X.2 ≅ Y.2) : X ≅ Y wher
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.iso_of_components AlgebraicGeometry.PresheafedSpace.isoOfComponents
 
-/-- Isomorphic PresheafedSpaces have naturally isomorphic presheaves. -/
+/-- Isomorphic `PresheafedSpace`s have naturally isomorphic presheaves. -/
 @[simps]
 def sheafIsoOfIso (H : X ≅ Y) : Y.2 ≅ H.hom.base _* X.2 where
   hom := H.hom.c
   inv := Presheaf.pushforwardToOfIso ((forget _).mapIso H).symm H.inv.c
   hom_inv_id := by
-    apply NatTrans.ext
     ext U
     rw [NatTrans.comp_app]
-    simpa using congr_arg (fun f => f ≫ eqToHom _) (congr_app H.inv_hom_id U)
+    simpa using congr_arg (fun f => f ≫ eqToHom _) (congr_app H.inv_hom_id (op U))
   inv_hom_id := by
-    apply NatTrans.ext
     ext U
     dsimp
     rw [NatTrans.comp_app, NatTrans.id_app]
     simp only [Presheaf.pushforwardObj_obj, op_obj, Presheaf.pushforwardToOfIso_app,
       Iso.symm_inv, mapIso_hom, forget_map, Iso.symm_hom, mapIso_inv,
       unop_op, eqToHom_map, assoc]
-    have eq₁ := congr_app H.hom_inv_id ((Opens.map H.hom.base).op.obj U)
+    have eq₁ := congr_app H.hom_inv_id (op ((Opens.map H.hom.base).obj U))
     have eq₂ := H.hom.c.naturality (eqToHom (congr_obj (congr_arg Opens.map
-      ((forget C).congr_map H.inv_hom_id.symm)) (Opposite.unop U))).op
+      ((forget C).congr_map H.inv_hom_id.symm)) U)).op
     rw [id_c, NatTrans.id_app, id_comp, eqToHom_map, comp_c_app] at eq₁
     rw [eqToHom_op, eqToHom_map] at eq₂
     erw [eq₂, reassoc_of% eq₁]
@@ -395,8 +388,7 @@ instance ofRestrict_mono {U : TopCat} (X : PresheafedSpace C) (f : U ⟶ X.1) (h
     simp only [PresheafedSpace.comp_base, PresheafedSpace.ofRestrict_base] at this
     rw [cancel_mono] at this
     exact this
-  . apply NatTrans.ext
-    ext ⟨V⟩
+  . ext V
     have hV : (Opens.map (X.ofRestrict hf).base).obj (hf.isOpenMap.functor.obj V) = V := by
       ext1
       exact Set.preimage_image_eq _ hf.inj
@@ -438,8 +430,7 @@ theorem ofRestrict_top_c (X : PresheafedSpace C) :
   /- another approach would be to prove the left hand side
        is a natural isomorphism, but I encountered a universe
        issue when `apply NatIso.isIso_of_isIso_app`. -/
-  apply NatTrans.ext
-  ext1 U
+  ext
   dsimp [ofRestrict]
   erw [eqToHom_map, eqToHom_app]
   simp
@@ -527,15 +518,13 @@ def mapPresheaf (F : C ⥤ D) : PresheafedSpace C ⥤ PresheafedSpace D where
       c := whiskerRight f.c F }
   -- porting note: these proofs were automatic in mathlib3
   map_id X := by
-    -- Porting note: I don't understand why neither `ext` nor `aesop_cat` can apply `NatTrans.ext'`.
-    ext
-    apply NatTrans.ext'
-    aesop_cat
+    ext U
+    simp
+    rfl
   map_comp f g := by
-    -- Porting note: I don't understand why neither `ext` nor `aesop_cat` can apply `NatTrans.ext'`.
-    ext
-    apply NatTrans.ext'
-    aesop_cat
+    ext U
+    simp
+    rfl
 #align category_theory.functor.map_presheaf CategoryTheory.Functor.mapPresheaf
 
 @[simp]
@@ -573,12 +562,6 @@ def onPresheaf {F G : C ⥤ D} (α : F ⟶ G) : G.mapPresheaf ⟶ F.mapPresheaf
   app X :=
     { base := 𝟙 _
       c := whiskerLeft X.presheaf α ≫ eqToHom (Presheaf.Pushforward.id_eq _).symm }
-  -- porting note: this proof was automatic in mathlib3
-  naturality X Y f := by
-    -- Porting note: I don't understand why neither `ext` nor `aesop_cat` can apply `NatTrans.ext'`.
-    ext
-    apply NatTrans.ext
-    aesop_cat
 #align category_theory.nat_trans.on_presheaf CategoryTheory.NatTrans.onPresheaf
 
 -- TODO Assemble the last two constructions into a functor

Closes #4551.

Essentially op_induction is not necessary, now that Opposite.rec' is labelled with @[eliminator]. It would be nice if we could use this from inside aesop, see https://github.com/JLimperg/aesop/issues/59.

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

@@ -36,7 +36,8 @@ variable (C : Type _) [Category C]
 -- local attribute [tidy] tactic.op_induction'
 -- A possible replacement would be:
 -- attribute [local aesop safe cases (rule_sets [CategoryTheory])] Opposite
--- but it doesn't seem necessary here.
+-- but this would probably require https://github.com/JLimperg/aesop/issues/59
+-- In any case, it doesn't seem necessary here.
 
 namespace AlgebraicGeometry
 

Mostly this is installing the Opposite.rec' induction principle as the default @[eliminator], but also many other fixes and removing unnecessary steps from proofs.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -22,15 +22,7 @@ presheaves.
 -/
 
 
-open CategoryTheory
-
-open TopCat
-
-open TopologicalSpace
-
-open Opposite
-
-open CategoryTheory.Category CategoryTheory.Functor
+open Opposite CategoryTheory CategoryTheory.Category CategoryTheory.Functor TopCat TopologicalSpace
 
 variable (C : Type _) [Category C]
 
@@ -44,7 +36,7 @@ variable (C : Type _) [Category C]
 -- local attribute [tidy] tactic.op_induction'
 -- A possible replacement would be:
 -- attribute [local aesop safe cases (rule_sets [CategoryTheory])] Opposite
--- but this would require further investigation.
+-- but it doesn't seem necessary here.
 
 namespace AlgebraicGeometry
 

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -34,16 +34,26 @@ open CategoryTheory.Category CategoryTheory.Functor
 
 variable (C : Type _) [Category C]
 
---attribute [local tidy] tactic.op_induction' tactic.auto_cases_opens
+-- Porting note: we used to have:
+-- local attribute [tidy] tactic.auto_cases_opens
+-- We would replace this by:
+-- attribute [local aesop safe cases (rule_sets [CategoryTheory])] Opens
+-- although it doesn't appear to help in this file, in any case.
+
+-- Porting note: we used to have:
+-- local attribute [tidy] tactic.op_induction'
+-- A possible replacement would be:
+-- attribute [local aesop safe cases (rule_sets [CategoryTheory])] Opposite
+-- but this would require further investigation.
 
 namespace AlgebraicGeometry
 
 -- porting note: `PresheafSpace.{w} C` is the type of topological spaces in `Type w` equipped
--- with a presheaf with values in `C`; then there is a total three universe parameters
+-- with a presheaf with values in `C`; then there is a total of three universe parameters
 -- in `PresheafSpace.{w, v, u} C`, where `C : Type u` and `Category.{v} C`.
 -- In mathlib3, some definitions in this file unnecessarily assumed `w=v`. This restriction
 -- has been removed.
---
+
 /-- A `PresheafedSpace C` is a topological space equipped with a presheaf of `C`s. -/
 structure PresheafedSpace where
   carrier : TopCat
@@ -62,9 +72,11 @@ set_option linter.uppercaseLean3 false in
 
 attribute [coe] PresheafedSpace.carrier
 
+-- Porting note: we add this instance, as Lean does not reliably use the `CoeOut` instance above
+-- in downstream files.
 instance : CoeSort (PresheafedSpace C) (Type _) where coe := fun X => X.carrier
 
--- porting note: the following lemma is removed because it is a syntatic tauto
+-- porting note: the following lemma is removed because it is a syntactic tauto
 /-@[simp]
 theorem as_coe (X : PresheafedSpace.{w, v, u} C) : X.carrier = (X : TopCat.{w}) :=
   rfl
@@ -72,7 +84,7 @@ set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.as_coe AlgebraicGeometry.PresheafedSpace.as_coe-/
 
 -- porting note: removed @[simp] as the `simpVarHead` linter complains
---@[simp]
+-- @[simp]
 theorem mk_coe (carrier) (presheaf) :
     (({ carrier
         presheaf } : PresheafedSpace C) : TopCat) = carrier :=
@@ -86,9 +98,7 @@ instance (X : PresheafedSpace C) : TopologicalSpace X :=
 /-- The constant presheaf on `X` with value `Z`. -/
 def const (X : TopCat) (Z : C) : PresheafedSpace C where
   carrier := X
-  presheaf :=
-    { obj := fun _ => Z
-      map := fun _ => 𝟙 Z }
+  presheaf := (Functor.const _).obj Z
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.const AlgebraicGeometry.PresheafedSpace.const
 
@@ -164,7 +174,7 @@ section
 attribute [local simp] id comp
 
 -- porting note: in mathlib3, `tidy` could (almost) prove the category axioms, but proofs
--- were included because `tidy` was slow. Here, `aesop_cat` succeeds reasonably fast
+-- were included because `tidy` was slow. Here, `aesop_cat` succeeds reasonably quickly
 -- for `comp_id` and `assoc`
 /-- The category of PresheafedSpaces. Morphisms are pairs, a continuous map and a presheaf map
     from the presheaf on the target to the pushforward of the presheaf on the source. -/
@@ -203,7 +213,7 @@ set_option linter.uppercaseLean3 false in
 
 -- porting note: `eqToHom` is no longer needed in the statements of `id_c` and `id_c_app`
 theorem id_c (X : PresheafedSpace C) :
-    (𝟙 X : X ⟶ X).c = 𝟙 _ :=
+    (𝟙 X : X ⟶ X).c = 𝟙 X.presheaf :=
   rfl
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.id_c AlgebraicGeometry.PresheafedSpace.id_c
@@ -248,7 +258,6 @@ set_option linter.uppercaseLean3 false in
 theorem congr_app {X Y : PresheafedSpace C} {α β : X ⟶ Y} (h : α = β) (U) :
     α.c.app U = β.c.app U ≫ X.presheaf.map (eqToHom (by subst h ; rfl)) := by
   subst h
-  dsimp
   simp
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.congr_app AlgebraicGeometry.PresheafedSpace.congr_app
@@ -284,33 +293,32 @@ def isoOfComponents (H : X.1 ≅ Y.1) (α : H.hom _* X.2 ≅ Y.2) : X ≅ Y wher
       c := Presheaf.toPushforwardOfIso H α.hom }
   hom_inv_id := by
     ext
-    · apply NatTrans.ext
-      ext U
-      rw [NatTrans.comp_app]
-      simp only [id_base, comp_obj, op_obj, comp_base, Presheaf.pushforwardObj_obj,
-        Opens.map_comp_obj, comp_c_app, unop_op, Presheaf.toPushforwardOfIso_app, assoc,
-        Iso.hom_inv_id_app, comp_id, whiskerRight_app, eqToHom_app, id_c_app, map_id,
-        ← Functor.map_comp, eqToHom_trans, eqToHom_refl]
-      dsimp
-      rw [Iso.hom_inv_id]
+    apply NatTrans.ext
+    ext U
+    rw [NatTrans.comp_app]
+    simp only [id_base, comp_obj, op_obj, comp_base, Presheaf.pushforwardObj_obj,
+      Opens.map_comp_obj, comp_c_app, unop_op, Presheaf.toPushforwardOfIso_app, assoc,
+      Iso.hom_inv_id_app, comp_id, whiskerRight_app, eqToHom_app, id_c_app, map_id,
+      ← Functor.map_comp, eqToHom_trans, eqToHom_refl]
+    simp only [comp_base, Iso.hom_inv_id, FunctorToTypes.map_id_apply, id_base]
   inv_hom_id := by
     ext
-    . apply NatTrans.ext
-      ext U
-      dsimp
-      rw [NatTrans.comp_app]
-      simp only [Presheaf.pushforwardObj_obj, op_obj, Opens.map_comp_obj, comp_obj,
-        comp_c_app, unop_op, Presheaf.toPushforwardOfIso_app, whiskerRight_app, eqToHom_app,
-        assoc, id_c_app, map_id]
-      rw [← α.hom.naturality, Presheaf.pushforwardObj_map, eqToHom_map, eqToHom_map,
-        eqToHom_map, eqToHom_trans_assoc, eqToHom_refl, id_comp]
-      apply Iso.inv_hom_id_app
-      dsimp
-      rw [H.inv_hom_id]
+    apply NatTrans.ext
+    ext U
+    dsimp
+    rw [NatTrans.comp_app]
+    simp only [Presheaf.pushforwardObj_obj, op_obj, Opens.map_comp_obj, comp_obj,
+      comp_c_app, unop_op, Presheaf.toPushforwardOfIso_app, whiskerRight_app, eqToHom_app,
+      assoc, id_c_app, map_id]
+    rw [← α.hom.naturality, Presheaf.pushforwardObj_map, eqToHom_map, eqToHom_map,
+      eqToHom_map, eqToHom_trans_assoc, eqToHom_refl, id_comp]
+    apply Iso.inv_hom_id_app
+    dsimp
+    rw [H.inv_hom_id]
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.iso_of_components AlgebraicGeometry.PresheafedSpace.isoOfComponents
 
-/-- Isomorphic PresheafedSpaces have natural isomorphic presheaves. -/
+/-- Isomorphic PresheafedSpaces have naturally isomorphic presheaves. -/
 @[simps]
 def sheafIsoOfIso (H : X ≅ Y) : Y.2 ≅ H.hom.base _* X.2 where
   hom := H.hom.c
@@ -526,23 +534,15 @@ def mapPresheaf (F : C ⥤ D) : PresheafedSpace C ⥤ PresheafedSpace D where
       c := whiskerRight f.c F }
   -- porting note: these proofs were automatic in mathlib3
   map_id X := by
+    -- Porting note: I don't understand why neither `ext` nor `aesop_cat` can apply `NatTrans.ext'`.
     ext
-    . apply NatTrans.ext
-      ext U
-      dsimp
-      erw [id_c, id_c, whiskerRight_id', id_comp, whiskerRight_app,
-        Functor.map_id, NatTrans.id_app]
-      rfl
-    . rfl
+    apply NatTrans.ext'
+    aesop_cat
   map_comp f g := by
+    -- Porting note: I don't understand why neither `ext` nor `aesop_cat` can apply `NatTrans.ext'`.
     ext
-    . apply NatTrans.ext
-      ext U
-      dsimp
-      erw [comp_c, whiskerRight_id', comp_id, whiskerRight_app,
-        NatTrans.comp_app, F.map_comp]
-      rfl
-    . rfl
+    apply NatTrans.ext'
+    aesop_cat
 #align category_theory.functor.map_presheaf CategoryTheory.Functor.mapPresheaf
 
 @[simp]
@@ -582,16 +582,10 @@ def onPresheaf {F G : C ⥤ D} (α : F ⟶ G) : G.mapPresheaf ⟶ F.mapPresheaf
       c := whiskerLeft X.presheaf α ≫ eqToHom (Presheaf.Pushforward.id_eq _).symm }
   -- porting note: this proof was automatic in mathlib3
   naturality X Y f := by
+    -- Porting note: I don't understand why neither `ext` nor `aesop_cat` can apply `NatTrans.ext'`.
     ext
-    . apply NatTrans.ext
-      ext U
-      dsimp
-      erw [comp_c]
-      dsimp
-      rw [whiskerRight_id', comp_id, comp_id, comp_id, whiskerLeft_app, naturality,
-        NatTrans.comp_app, whiskerLeft_app, Presheaf.pushforward_map_app', whiskerRight_app]
-      rfl
-    . rfl
+    apply NatTrans.ext
+    aesop_cat
 #align category_theory.nat_trans.on_presheaf CategoryTheory.NatTrans.onPresheaf
 
 -- TODO Assemble the last two constructions into a functor

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -60,7 +60,11 @@ instance coeCarrier : CoeOut (PresheafedSpace C) TopCat where coe X := X.carrier
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.coe_carrier AlgebraicGeometry.PresheafedSpace.coeCarrier
 
--- porting note: the following lemma is removed because it is a syntactic tauto
+attribute [coe] PresheafedSpace.carrier
+
+instance : CoeSort (PresheafedSpace C) (Type _) where coe := fun X => X.carrier
+
+-- porting note: the following lemma is removed because it is a syntatic tauto
 /-@[simp]
 theorem as_coe (X : PresheafedSpace.{w, v, u} C) : X.carrier = (X : TopCat.{w}) :=
   rfl
@@ -431,7 +435,7 @@ theorem ofRestrict_top_c (X : PresheafedSpace C) :
           erw [Iso.inv_hom_id]
           rw [Presheaf.Pushforward.id_eq]) := by
   /- another approach would be to prove the left hand side
-       is a natural isoomorphism, but I encountered a universe
+       is a natural isomorphism, but I encountered a universe
        issue when `apply NatIso.isIso_of_isIso_app`. -/
   apply NatTrans.ext
   ext1 U
@@ -441,8 +445,6 @@ theorem ofRestrict_top_c (X : PresheafedSpace C) :
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.of_restrict_top_c AlgebraicGeometry.PresheafedSpace.ofRestrict_top_c
 
-/- or `rw [opens.inclusion_top_functor, ←comp_obj, ←opens.map_comp_eq],
-         erw iso.inv_hom_id, cases U, refl` after `dsimp` -/
 /-- The map to the restriction of a presheafed space along the canonical inclusion from the top
 subspace.
 -/

I ran codespell Mathlib and got tired halfway through the suggestions.

@@ -60,7 +60,7 @@ instance coeCarrier : CoeOut (PresheafedSpace C) TopCat where coe X := X.carrier
 set_option linter.uppercaseLean3 false in
 #align algebraic_geometry.PresheafedSpace.coe_carrier AlgebraicGeometry.PresheafedSpace.coeCarrier
 
--- porting note: the following lemma is removed because it is a syntatic tauto
+-- porting note: the following lemma is removed because it is a syntactic tauto
 /-@[simp]
 theorem as_coe (X : PresheafedSpace.{w, v, u} C) : X.carrier = (X : TopCat.{w}) :=
   rfl