algebraic_geometry.presheafed_spaceMathlib.Geometry.RingedSpace.PresheafedSpace

This file has been ported!

Changes since the initial port

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

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -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
 -/
Diff
@@ -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"
 
Diff
@@ -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
 
Diff
@@ -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)`
Diff
@@ -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
 
Diff
@@ -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
 
Diff
@@ -43,12 +43,6 @@ 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}
@@ -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
-  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
 
@@ -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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 /-- 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
 
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 @[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
 
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 -- 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
 
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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
 
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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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 /-- 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
 
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 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
 
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 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
 
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 /- 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
 
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 /-- 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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 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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 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
Diff
@@ -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
Diff
@@ -124,10 +124,7 @@ structure Hom (X Y : PresheafedSpace.{w, v, u} C) where
 #align algebraic_geometry.PresheafedSpace.hom AlgebraicGeometry.PresheafedSpace.Hom
 
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+<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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 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:
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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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+<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:
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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, 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_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} 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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 =
@@ -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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 /-- 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
 
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+<too large>
 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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 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
 
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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
 
 /- warning: category_theory.functor.map_presheaf_map_c -> CategoryTheory.Functor.mapPresheaf_map_c is a dubious translation:
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(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))) 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+<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) :
Diff
@@ -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
Diff
@@ -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
 
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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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(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)
+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
Diff
@@ -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

Changes in mathlib4

mathlib3
mathlib4
chore: adapt to multiple goal linter 3 (#12372)

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

Diff
@@ -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]
style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

  • converts "--porting note" into "-- Porting note";
  • converts "porting note" into "Porting note".
Diff
@@ -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
chore: bump aesop; update syntax (#10955)

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

Diff
@@ -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.
 
chore: improvements to Presheaf simp lemmas (#9542)

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>

Diff
@@ -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
chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

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

Open in Gitpod

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

Diff
@@ -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
 
chore: bump to nightly-2023-07-01 (#5409)

Open in Gitpod

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>

Diff
@@ -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]
chore: remove occurrences of semicolon after space (#5713)

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.

Diff
@@ -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
chore: fix focusing dots (#5708)

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.

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

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

Diff
@@ -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 :=
chore: tidy various files (#5268)
Diff
@@ -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
 
chore: add @[ext] lemmas for NatTrans synonyms (#5228)

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

Diff
@@ -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
chore: clean up porting notes about op_induction (#5035)

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>

Diff
@@ -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
 
refactor: fixes to material on sheaves and stalks (#4571)

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>

Diff
@@ -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
 
chore: cleanup in PresheafedSpace (#4558)

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

Diff
@@ -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
feat: port AlgebraicGeometry.Stalks (#4498)

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

Diff
@@ -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.
 -/
chore: fix typos (#4518)

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

Diff
@@ -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
feat: port AlgebraicGeometry.PresheafedSpace (#4093)

Dependencies 8 + 400

401 files ported (98.0%)
162275 lines ported (97.0%)
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The unported dependencies are