category_theory.yoneda ⟷ Mathlib.CategoryTheory.Yoneda

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

@@ -80,14 +80,14 @@ theorem naturality {X Y : C} (α : yoneda.obj X ⟶ yoneda.obj Y) {Z Z' : C} (f
 #align category_theory.yoneda.naturality CategoryTheory.Yoneda.naturality
 -/
 
-#print CategoryTheory.Yoneda.yonedaFull /-
+#print CategoryTheory.Yoneda.yoneda_full /-
 /-- The Yoneda embedding is full.
 
 See <https://stacks.math.columbia.edu/tag/001P>.
 -/
-instance yonedaFull : CategoryTheory.Functor.Full (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁)
+instance yoneda_full : CategoryTheory.Functor.Full (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁)
     where preimage X Y f := f.app (op X) (𝟙 X)
-#align category_theory.yoneda.yoneda_full CategoryTheory.Yoneda.yonedaFull
+#align category_theory.yoneda.yoneda_full CategoryTheory.Yoneda.yoneda_full
 -/
 
 #print CategoryTheory.Yoneda.yoneda_faithful /-
@@ -142,10 +142,10 @@ theorem naturality {X Y : Cᵒᵖ} (α : coyoneda.obj X ⟶ coyoneda.obj Y) {Z Z
 #align category_theory.coyoneda.naturality CategoryTheory.Coyoneda.naturality
 -/
 
-#print CategoryTheory.Coyoneda.coyonedaFull /-
-instance coyonedaFull : CategoryTheory.Functor.Full (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁)
+#print CategoryTheory.Coyoneda.coyoneda_full /-
+instance coyoneda_full : CategoryTheory.Functor.Full (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁)
     where preimage X Y f := (f.app _ (𝟙 X.unop)).op
-#align category_theory.coyoneda.coyoneda_full CategoryTheory.Coyoneda.coyonedaFull
+#align category_theory.coyoneda.coyoneda_full CategoryTheory.Coyoneda.coyoneda_full
 -/
 
 #print CategoryTheory.Coyoneda.coyoneda_faithful /-

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

@@ -228,11 +228,11 @@ noncomputable def reprX : C :=
 #align category_theory.functor.repr_X CategoryTheory.Functor.reprX
 -/
 
-#print CategoryTheory.Functor.reprF /-
+#print CategoryTheory.Functor.reprW /-
 /-- The (forward direction of the) isomorphism witnessing `F` is representable. -/
-noncomputable def reprF : yoneda.obj F.reprX ⟶ F :=
+noncomputable def reprW : yoneda.obj F.reprX ⟶ F :=
   Representable.has_representation.choose_spec.some
-#align category_theory.functor.repr_f CategoryTheory.Functor.reprF
+#align category_theory.functor.repr_f CategoryTheory.Functor.reprW
 -/
 
 #print CategoryTheory.Functor.reprx /-
@@ -240,28 +240,28 @@ noncomputable def reprF : yoneda.obj F.reprX ⟶ F :=
 element of the functor.
 -/
 noncomputable def reprx : F.obj (op F.reprX) :=
-  F.reprF.app (op F.reprX) (𝟙 F.reprX)
+  F.reprW.app (op F.reprX) (𝟙 F.reprX)
 #align category_theory.functor.repr_x CategoryTheory.Functor.reprx
 -/
 
-instance : IsIso F.reprF :=
+instance : IsIso F.reprW :=
   Representable.has_representation.choose_spec.choose_spec
 
+/- warning: category_theory.functor.repr_w clashes with category_theory.functor.repr_f -> CategoryTheory.Functor.reprW
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.repr_w CategoryTheory.Functor.reprWₓ'. -/
 #print CategoryTheory.Functor.reprW /-
 /-- An isomorphism between `F` and a functor of the form `C(-, F.repr_X)`.  Note the components
 `F.repr_w.app X` definitionally have type `(X.unop ⟶ F.repr_X) ≅ F.obj X`.
 -/
 noncomputable def reprW : yoneda.obj F.reprX ≅ F :=
-  asIso F.reprF
+  asIso F.reprW
 #align category_theory.functor.repr_w CategoryTheory.Functor.reprW
 -/
 
-#print CategoryTheory.Functor.reprW_hom /-
 @[simp]
-theorem reprW_hom : F.reprW.Hom = F.reprF :=
+theorem reprW_hom : F.reprW.Hom = F.reprW :=
   rfl
 #align category_theory.functor.repr_w_hom CategoryTheory.Functor.reprW_hom
--/
 
 #print CategoryTheory.Functor.reprW_app_hom /-
 theorem reprW_app_hom (X : Cᵒᵖ) (f : unop X ⟶ F.reprX) :
@@ -289,11 +289,11 @@ noncomputable def coreprX : C :=
 #align category_theory.functor.corepr_X CategoryTheory.Functor.coreprX
 -/
 
-#print CategoryTheory.Functor.coreprF /-
+#print CategoryTheory.Functor.coreprW /-
 /-- The (forward direction of the) isomorphism witnessing `F` is corepresentable. -/
-noncomputable def coreprF : coyoneda.obj (op F.coreprX) ⟶ F :=
+noncomputable def coreprW : coyoneda.obj (op F.coreprX) ⟶ F :=
   Corepresentable.has_corepresentation.choose_spec.some
-#align category_theory.functor.corepr_f CategoryTheory.Functor.coreprF
+#align category_theory.functor.corepr_f CategoryTheory.Functor.coreprW
 -/
 
 #print CategoryTheory.Functor.coreprx /-
@@ -301,19 +301,21 @@ noncomputable def coreprF : coyoneda.obj (op F.coreprX) ⟶ F :=
 element of the functor.
 -/
 noncomputable def coreprx : F.obj F.coreprX :=
-  F.coreprF.app F.coreprX (𝟙 F.coreprX)
+  F.coreprW.app F.coreprX (𝟙 F.coreprX)
 #align category_theory.functor.corepr_x CategoryTheory.Functor.coreprx
 -/
 
-instance : IsIso F.coreprF :=
+instance : IsIso F.coreprW :=
   Corepresentable.has_corepresentation.choose_spec.choose_spec
 
+/- warning: category_theory.functor.corepr_w clashes with category_theory.functor.corepr_f -> CategoryTheory.Functor.coreprW
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.corepr_w CategoryTheory.Functor.coreprWₓ'. -/
 #print CategoryTheory.Functor.coreprW /-
 /-- An isomorphism between `F` and a functor of the form `C(F.corepr X, -)`. Note the components
 `F.corepr_w.app X` definitionally have type `F.corepr_X ⟶ X ≅ F.obj X`.
 -/
 noncomputable def coreprW : coyoneda.obj (op F.coreprX) ≅ F :=
-  asIso F.coreprF
+  asIso F.coreprW
 #align category_theory.functor.corepr_w CategoryTheory.Functor.coreprW
 -/
 
@@ -331,22 +333,22 @@ end Corepresentable
 
 end Functor
 
-#print CategoryTheory.representable_of_nat_iso /-
-theorem representable_of_nat_iso (F : Cᵒᵖ ⥤ Type v₁) {G} (i : F ≅ G) [F.Representable] :
+#print CategoryTheory.representable_of_natIso /-
+theorem representable_of_natIso (F : Cᵒᵖ ⥤ Type v₁) {G} (i : F ≅ G) [F.Representable] :
     G.Representable :=
-  { has_representation := ⟨F.reprX, F.reprF ≫ i.Hom, inferInstance⟩ }
-#align category_theory.representable_of_nat_iso CategoryTheory.representable_of_nat_iso
+  { has_representation := ⟨F.reprX, F.reprW ≫ i.Hom, inferInstance⟩ }
+#align category_theory.representable_of_nat_iso CategoryTheory.representable_of_natIso
 -/
 
-#print CategoryTheory.corepresentable_of_nat_iso /-
-theorem corepresentable_of_nat_iso (F : C ⥤ Type v₁) {G} (i : F ≅ G) [F.Corepresentable] :
+#print CategoryTheory.corepresentable_of_natIso /-
+theorem corepresentable_of_natIso (F : C ⥤ Type v₁) {G} (i : F ≅ G) [F.Corepresentable] :
     G.Corepresentable :=
-  { has_corepresentation := ⟨op F.coreprX, F.coreprF ≫ i.Hom, inferInstance⟩ }
-#align category_theory.corepresentable_of_nat_iso CategoryTheory.corepresentable_of_nat_iso
+  { has_corepresentation := ⟨op F.coreprX, F.coreprW ≫ i.Hom, inferInstance⟩ }
+#align category_theory.corepresentable_of_nat_iso CategoryTheory.corepresentable_of_natIso
 -/
 
 instance : Functor.Corepresentable (𝟭 (Type v₁)) :=
-  corepresentable_of_nat_iso (coyoneda.obj (op PUnit)) Coyoneda.punitIso
+  corepresentable_of_natIso (coyoneda.obj (op PUnit)) Coyoneda.punitIso
 
 open Opposite
 

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

@@ -85,7 +85,8 @@ theorem naturality {X Y : C} (α : yoneda.obj X ⟶ yoneda.obj Y) {Z Z' : C} (f
 
 See <https://stacks.math.columbia.edu/tag/001P>.
 -/
-instance yonedaFull : Full (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁) where preimage X Y f := f.app (op X) (𝟙 X)
+instance yonedaFull : CategoryTheory.Functor.Full (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁)
+    where preimage X Y f := f.app (op X) (𝟙 X)
 #align category_theory.yoneda.yoneda_full CategoryTheory.Yoneda.yonedaFull
 -/
 
@@ -94,7 +95,7 @@ instance yonedaFull : Full (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁) where preimage
 
 See <https://stacks.math.columbia.edu/tag/001P>.
 -/
-instance yoneda_faithful : Faithful (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁)
+instance yoneda_faithful : CategoryTheory.Functor.Faithful (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁)
     where map_injective' X Y f g p := by
     convert congr_fun (congr_app p (op X)) (𝟙 X) <;> dsimp <;> simp
 #align category_theory.yoneda.yoneda_faithful CategoryTheory.Yoneda.yoneda_faithful
@@ -142,13 +143,13 @@ theorem naturality {X Y : Cᵒᵖ} (α : coyoneda.obj X ⟶ coyoneda.obj Y) {Z Z
 -/
 
 #print CategoryTheory.Coyoneda.coyonedaFull /-
-instance coyonedaFull : Full (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁)
+instance coyonedaFull : CategoryTheory.Functor.Full (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁)
     where preimage X Y f := (f.app _ (𝟙 X.unop)).op
 #align category_theory.coyoneda.coyoneda_full CategoryTheory.Coyoneda.coyonedaFull
 -/
 
 #print CategoryTheory.Coyoneda.coyoneda_faithful /-
-instance coyoneda_faithful : Faithful (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁)
+instance coyoneda_faithful : CategoryTheory.Functor.Faithful (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁)
     where map_injective' X Y f g p :=
     by
     have t := congr_fun (congr_app p X.unop) (𝟙 _)

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

@@ -3,9 +3,9 @@ Copyright (c) 2017 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.CategoryTheory.Functor.Hom
-import Mathbin.CategoryTheory.Functor.Currying
-import Mathbin.CategoryTheory.Products.Basic
+import CategoryTheory.Functor.Hom
+import CategoryTheory.Functor.Currying
+import CategoryTheory.Products.Basic
 
 #align_import category_theory.yoneda from "leanprover-community/mathlib"@"23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2017 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 category_theory.yoneda
-! leanprover-community/mathlib commit 23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Functor.Hom
 import Mathbin.CategoryTheory.Functor.Currying
 import Mathbin.CategoryTheory.Products.Basic
 
+#align_import category_theory.yoneda from "leanprover-community/mathlib"@"23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6"
+
 /-!
 # The Yoneda embedding
 

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

@@ -69,15 +69,19 @@ def coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁
 
 namespace Yoneda
 
+#print CategoryTheory.Yoneda.obj_map_id /-
 theorem obj_map_id {X Y : C} (f : op X ⟶ op Y) :
     (yoneda.obj X).map f (𝟙 X) = (yoneda.map f.unop).app (op Y) (𝟙 Y) := by dsimp; simp
 #align category_theory.yoneda.obj_map_id CategoryTheory.Yoneda.obj_map_id
+-/
 
+#print CategoryTheory.Yoneda.naturality /-
 @[simp]
 theorem naturality {X Y : C} (α : yoneda.obj X ⟶ yoneda.obj Y) {Z Z' : C} (f : Z ⟶ Z')
     (h : Z' ⟶ X) : f ≫ α.app (op Z') h = α.app (op Z) (f ≫ h) :=
   (FunctorToTypes.naturality _ _ α f.op h).symm
 #align category_theory.yoneda.naturality CategoryTheory.Yoneda.naturality
+-/
 
 #print CategoryTheory.Yoneda.yonedaFull /-
 /-- The Yoneda embedding is full.
@@ -120,21 +124,25 @@ def ext (X Y : C) (p : ∀ {Z : C}, (Z ⟶ X) → (Z ⟶ Y)) (q : ∀ {Z : C}, (
 #align category_theory.yoneda.ext CategoryTheory.Yoneda.ext
 -/
 
+#print CategoryTheory.Yoneda.isIso /-
 /-- If `yoneda.map f` is an isomorphism, so was `f`.
 -/
 theorem isIso {X Y : C} (f : X ⟶ Y) [IsIso (yoneda.map f)] : IsIso f :=
   isIso_of_fully_faithful yoneda f
 #align category_theory.yoneda.is_iso CategoryTheory.Yoneda.isIso
+-/
 
 end Yoneda
 
 namespace Coyoneda
 
+#print CategoryTheory.Coyoneda.naturality /-
 @[simp]
 theorem naturality {X Y : Cᵒᵖ} (α : coyoneda.obj X ⟶ coyoneda.obj Y) {Z Z' : C} (f : Z' ⟶ Z)
     (h : unop X ⟶ Z') : α.app Z' h ≫ f = α.app Z (h ≫ f) :=
   (FunctorToTypes.naturality _ _ α f h).symm
 #align category_theory.coyoneda.naturality CategoryTheory.Coyoneda.naturality
+-/
 
 #print CategoryTheory.Coyoneda.coyonedaFull /-
 instance coyonedaFull : Full (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁)
@@ -151,12 +159,15 @@ instance coyoneda_faithful : Faithful (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁)
 #align category_theory.coyoneda.coyoneda_faithful CategoryTheory.Coyoneda.coyoneda_faithful
 -/
 
+#print CategoryTheory.Coyoneda.isIso /-
 /-- If `coyoneda.map f` is an isomorphism, so was `f`.
 -/
 theorem isIso {X Y : Cᵒᵖ} (f : X ⟶ Y) [IsIso (coyoneda.map f)] : IsIso f :=
   isIso_of_fully_faithful coyoneda f
 #align category_theory.coyoneda.is_iso CategoryTheory.Coyoneda.isIso
+-/
 
+#print CategoryTheory.Coyoneda.punitIso /-
 /-- The identity functor on `Type` is isomorphic to the coyoneda functor coming from `punit`. -/
 def punitIso : coyoneda.obj (Opposite.op PUnit) ≅ 𝟭 (Type v₁) :=
   NatIso.ofComponents
@@ -165,12 +176,15 @@ def punitIso : coyoneda.obj (Opposite.op PUnit) ≅ 𝟭 (Type v₁) :=
         inv := fun x _ => x })
     (by tidy)
 #align category_theory.coyoneda.punit_iso CategoryTheory.Coyoneda.punitIso
+-/
 
+#print CategoryTheory.Coyoneda.objOpOp /-
 /-- Taking the `unop` of morphisms is a natural isomorphism. -/
 @[simps]
 def objOpOp (X : C) : coyoneda.obj (op (op X)) ≅ yoneda.obj X :=
   NatIso.ofComponents (fun Y => (opEquiv _ _).toIso) fun X Y f => rfl
 #align category_theory.coyoneda.obj_op_op CategoryTheory.Coyoneda.objOpOp
+-/
 
 end Coyoneda
 
@@ -216,33 +230,42 @@ noncomputable def reprX : C :=
 #align category_theory.functor.repr_X CategoryTheory.Functor.reprX
 -/
 
+#print CategoryTheory.Functor.reprF /-
 /-- The (forward direction of the) isomorphism witnessing `F` is representable. -/
 noncomputable def reprF : yoneda.obj F.reprX ⟶ F :=
   Representable.has_representation.choose_spec.some
 #align category_theory.functor.repr_f CategoryTheory.Functor.reprF
+-/
 
+#print CategoryTheory.Functor.reprx /-
 /-- The representing element for the representable functor `F`, sometimes called the universal
 element of the functor.
 -/
 noncomputable def reprx : F.obj (op F.reprX) :=
   F.reprF.app (op F.reprX) (𝟙 F.reprX)
 #align category_theory.functor.repr_x CategoryTheory.Functor.reprx
+-/
 
 instance : IsIso F.reprF :=
   Representable.has_representation.choose_spec.choose_spec
 
+#print CategoryTheory.Functor.reprW /-
 /-- An isomorphism between `F` and a functor of the form `C(-, F.repr_X)`.  Note the components
 `F.repr_w.app X` definitionally have type `(X.unop ⟶ F.repr_X) ≅ F.obj X`.
 -/
 noncomputable def reprW : yoneda.obj F.reprX ≅ F :=
   asIso F.reprF
 #align category_theory.functor.repr_w CategoryTheory.Functor.reprW
+-/
 
+#print CategoryTheory.Functor.reprW_hom /-
 @[simp]
 theorem reprW_hom : F.reprW.Hom = F.reprF :=
   rfl
 #align category_theory.functor.repr_w_hom CategoryTheory.Functor.reprW_hom
+-/
 
+#print CategoryTheory.Functor.reprW_app_hom /-
 theorem reprW_app_hom (X : Cᵒᵖ) (f : unop X ⟶ F.reprX) :
     (F.reprW.app X).Hom f = F.map f.op F.reprx :=
   by
@@ -251,6 +274,7 @@ theorem reprW_app_hom (X : Cᵒᵖ) (f : unop X ⟶ F.reprX) :
   dsimp
   simp
 #align category_theory.functor.repr_w_app_hom CategoryTheory.Functor.reprW_app_hom
+-/
 
 end Representable
 
@@ -267,28 +291,35 @@ noncomputable def coreprX : C :=
 #align category_theory.functor.corepr_X CategoryTheory.Functor.coreprX
 -/
 
+#print CategoryTheory.Functor.coreprF /-
 /-- The (forward direction of the) isomorphism witnessing `F` is corepresentable. -/
 noncomputable def coreprF : coyoneda.obj (op F.coreprX) ⟶ F :=
   Corepresentable.has_corepresentation.choose_spec.some
 #align category_theory.functor.corepr_f CategoryTheory.Functor.coreprF
+-/
 
+#print CategoryTheory.Functor.coreprx /-
 /-- The representing element for the corepresentable functor `F`, sometimes called the universal
 element of the functor.
 -/
 noncomputable def coreprx : F.obj F.coreprX :=
   F.coreprF.app F.coreprX (𝟙 F.coreprX)
 #align category_theory.functor.corepr_x CategoryTheory.Functor.coreprx
+-/
 
 instance : IsIso F.coreprF :=
   Corepresentable.has_corepresentation.choose_spec.choose_spec
 
+#print CategoryTheory.Functor.coreprW /-
 /-- An isomorphism between `F` and a functor of the form `C(F.corepr X, -)`. Note the components
 `F.corepr_w.app X` definitionally have type `F.corepr_X ⟶ X ≅ F.obj X`.
 -/
 noncomputable def coreprW : coyoneda.obj (op F.coreprX) ≅ F :=
   asIso F.coreprF
 #align category_theory.functor.corepr_w CategoryTheory.Functor.coreprW
+-/
 
+#print CategoryTheory.Functor.coreprW_app_hom /-
 theorem coreprW_app_hom (X : C) (f : F.coreprX ⟶ X) : (F.coreprW.app X).Hom f = F.map f F.coreprx :=
   by
   change F.corepr_f.app X f = (F.corepr_f.app F.corepr_X ≫ F.map f) (𝟙 F.corepr_X)
@@ -296,6 +327,7 @@ theorem coreprW_app_hom (X : C) (f : F.coreprX ⟶ X) : (F.coreprW.app X).Hom f
   dsimp
   simp
 #align category_theory.functor.corepr_w_app_hom CategoryTheory.Functor.coreprW_app_hom
+-/
 
 end Corepresentable
 
@@ -346,12 +378,14 @@ def yonedaEvaluation : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁) ⥤ Type max u₁ v₁
 #align category_theory.yoneda_evaluation CategoryTheory.yonedaEvaluation
 -/
 
+#print CategoryTheory.yonedaEvaluation_map_down /-
 @[simp]
 theorem yonedaEvaluation_map_down (P Q : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁)) (α : P ⟶ Q)
     (x : (yonedaEvaluation C).obj P) :
     ((yonedaEvaluation C).map α x).down = α.2.app Q.1 (P.2.map α.1 x.down) :=
   rfl
 #align category_theory.yoneda_evaluation_map_down CategoryTheory.yonedaEvaluation_map_down
+-/
 
 #print CategoryTheory.yonedaPairing /-
 /-- The "Yoneda pairing" functor, which sends `X : Cᵒᵖ` and `F : Cᵒᵖ ⥤ Type`
@@ -362,11 +396,13 @@ def yonedaPairing : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁) ⥤ Type max u₁ v₁ :=
 #align category_theory.yoneda_pairing CategoryTheory.yonedaPairing
 -/
 
+#print CategoryTheory.yonedaPairing_map /-
 @[simp]
 theorem yonedaPairing_map (P Q : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁)) (α : P ⟶ Q) (β : (yonedaPairing C).obj P) :
     (yonedaPairing C).map α β = yoneda.map α.1.unop ≫ β ≫ α.2 :=
   rfl
 #align category_theory.yoneda_pairing_map CategoryTheory.yonedaPairing_map
+-/
 
 #print CategoryTheory.yonedaLemma /-
 /-- The Yoneda lemma asserts that that the Yoneda pairing
@@ -405,6 +441,7 @@ def yonedaLemma : yonedaPairing C ≅ yonedaEvaluation C
 
 variable {C}
 
+#print CategoryTheory.yonedaSections /-
 /-- The isomorphism between `yoneda.obj X ⟶ F` and `F.obj (op X)`
 (we need to insert a `ulift` to get the universes right!)
 given by the Yoneda lemma.
@@ -413,26 +450,34 @@ given by the Yoneda lemma.
 def yonedaSections (X : C) (F : Cᵒᵖ ⥤ Type v₁) : (yoneda.obj X ⟶ F) ≅ ULift.{u₁} (F.obj (op X)) :=
   (yonedaLemma C).app (op X, F)
 #align category_theory.yoneda_sections CategoryTheory.yonedaSections
+-/
 
+#print CategoryTheory.yonedaEquiv /-
 /-- We have a type-level equivalence between natural transformations from the yoneda embedding
 and elements of `F.obj X`, without any universe switching.
 -/
 def yonedaEquiv {X : C} {F : Cᵒᵖ ⥤ Type v₁} : (yoneda.obj X ⟶ F) ≃ F.obj (op X) :=
   (yonedaSections X F).toEquiv.trans Equiv.ulift
 #align category_theory.yoneda_equiv CategoryTheory.yonedaEquiv
+-/
 
+#print CategoryTheory.yonedaEquiv_apply /-
 @[simp]
 theorem yonedaEquiv_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda.obj X ⟶ F) :
     yonedaEquiv f = f.app (op X) (𝟙 X) :=
   rfl
 #align category_theory.yoneda_equiv_apply CategoryTheory.yonedaEquiv_apply
+-/
 
+#print CategoryTheory.yonedaEquiv_symm_app_apply /-
 @[simp]
 theorem yonedaEquiv_symm_app_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (x : F.obj (op X)) (Y : Cᵒᵖ)
     (f : Y.unop ⟶ X) : (yonedaEquiv.symm x).app Y f = F.map f.op x :=
   rfl
 #align category_theory.yoneda_equiv_symm_app_apply CategoryTheory.yonedaEquiv_symm_app_apply
+-/
 
+#print CategoryTheory.yonedaEquiv_naturality /-
 theorem yonedaEquiv_naturality {X Y : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda.obj X ⟶ F) (g : Y ⟶ X) :
     F.map g.op (yonedaEquiv f) = yonedaEquiv (yoneda.map g ≫ f) :=
   by
@@ -441,7 +486,9 @@ theorem yonedaEquiv_naturality {X Y : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda
   dsimp
   simp
 #align category_theory.yoneda_equiv_naturality CategoryTheory.yonedaEquiv_naturality
+-/
 
+#print CategoryTheory.yonedaSectionsSmall /-
 /-- When `C` is a small category, we can restate the isomorphism from `yoneda_sections`
 without having to change universes.
 -/
@@ -449,19 +496,24 @@ def yonedaSectionsSmall {C : Type u₁} [SmallCategory C] (X : C) (F : Cᵒᵖ 
     (yoneda.obj X ⟶ F) ≅ F.obj (op X) :=
   yonedaSections X F ≪≫ uliftTrivial _
 #align category_theory.yoneda_sections_small CategoryTheory.yonedaSectionsSmall
+-/
 
+#print CategoryTheory.yonedaSectionsSmall_hom /-
 @[simp]
 theorem yonedaSectionsSmall_hom {C : Type u₁} [SmallCategory C] (X : C) (F : Cᵒᵖ ⥤ Type u₁)
     (f : yoneda.obj X ⟶ F) : (yonedaSectionsSmall X F).Hom f = f.app _ (𝟙 _) :=
   rfl
 #align category_theory.yoneda_sections_small_hom CategoryTheory.yonedaSectionsSmall_hom
+-/
 
+#print CategoryTheory.yonedaSectionsSmall_inv_app_apply /-
 @[simp]
 theorem yonedaSectionsSmall_inv_app_apply {C : Type u₁} [SmallCategory C] (X : C)
     (F : Cᵒᵖ ⥤ Type u₁) (t : F.obj (op X)) (Y : Cᵒᵖ) (f : Y.unop ⟶ X) :
     ((yonedaSectionsSmall X F).inv t).app Y f = F.map f.op t :=
   rfl
 #align category_theory.yoneda_sections_small_inv_app_apply CategoryTheory.yonedaSectionsSmall_inv_app_apply
+-/
 
 attribute [local ext] Functor.ext
 
@@ -476,6 +528,7 @@ def curriedYonedaLemma {C : Type u₁} [SmallCategory C] :
 #align category_theory.curried_yoneda_lemma CategoryTheory.curriedYonedaLemma
 -/
 
+#print CategoryTheory.curriedYonedaLemma' /-
 /-- The curried version of yoneda lemma when `C` is small. -/
 def curriedYonedaLemma' {C : Type u₁} [SmallCategory C] :
     yoneda ⋙ (whiskeringLeft Cᵒᵖ (Cᵒᵖ ⥤ Type u₁)ᵒᵖ (Type u₁)).obj yoneda.op ≅ 𝟭 (Cᵒᵖ ⥤ Type u₁) :=
@@ -486,6 +539,7 @@ def curriedYonedaLemma' {C : Type u₁} [SmallCategory C] :
             _)) ≪≫
       eqToIso (by tidy)
 #align category_theory.curried_yoneda_lemma' CategoryTheory.curriedYonedaLemma'
+-/
 
 end CategoryTheory
 

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

@@ -182,7 +182,7 @@ namespace Functor
 See <https://stacks.math.columbia.edu/tag/001Q>.
 -/
 class Representable (F : Cᵒᵖ ⥤ Type v₁) : Prop where
-  has_representation : ∃ (X : _)(f : yoneda.obj X ⟶ F), IsIso f
+  has_representation : ∃ (X : _) (f : yoneda.obj X ⟶ F), IsIso f
 #align category_theory.functor.representable CategoryTheory.Functor.Representable
 -/
 
@@ -194,7 +194,7 @@ instance {X : C} : Representable (yoneda.obj X) where has_representation := ⟨X
 See <https://stacks.math.columbia.edu/tag/001Q>.
 -/
 class Corepresentable (F : C ⥤ Type v₁) : Prop where
-  has_corepresentation : ∃ (X : _)(f : coyoneda.obj X ⟶ F), IsIso f
+  has_corepresentation : ∃ (X : _) (f : coyoneda.obj X ⟶ F), IsIso f
 #align category_theory.functor.corepresentable CategoryTheory.Functor.Corepresentable
 -/
 
@@ -212,7 +212,7 @@ variable [F.Representable]
 #print CategoryTheory.Functor.reprX /-
 /-- The representing object for the representable functor `F`. -/
 noncomputable def reprX : C :=
-  (Representable.has_representation : ∃ (X : _)(f : _ ⟶ F), _).some
+  (Representable.has_representation : ∃ (X : _) (f : _ ⟶ F), _).some
 #align category_theory.functor.repr_X CategoryTheory.Functor.reprX
 -/
 
@@ -263,7 +263,7 @@ variable [F.Corepresentable]
 #print CategoryTheory.Functor.coreprX /-
 /-- The representing object for the corepresentable functor `F`. -/
 noncomputable def coreprX : C :=
-  (Corepresentable.has_corepresentation : ∃ (X : _)(f : _ ⟶ F), _).some.unop
+  (Corepresentable.has_corepresentation : ∃ (X : _) (f : _ ⟶ F), _).some.unop
 #align category_theory.functor.corepr_X CategoryTheory.Functor.coreprX
 -/
 

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

@@ -69,16 +69,10 @@ def coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁
 
 namespace Yoneda
 
-/- warning: category_theory.yoneda.obj_map_id -> CategoryTheory.Yoneda.obj_map_id is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.yoneda.obj_map_id CategoryTheory.Yoneda.obj_map_idₓ'. -/
 theorem obj_map_id {X Y : C} (f : op X ⟶ op Y) :
     (yoneda.obj X).map f (𝟙 X) = (yoneda.map f.unop).app (op Y) (𝟙 Y) := by dsimp; simp
 #align category_theory.yoneda.obj_map_id CategoryTheory.Yoneda.obj_map_id
 
-/- warning: category_theory.yoneda.naturality -> CategoryTheory.Yoneda.naturality is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.yoneda.naturality CategoryTheory.Yoneda.naturalityₓ'. -/
 @[simp]
 theorem naturality {X Y : C} (α : yoneda.obj X ⟶ yoneda.obj Y) {Z Z' : C} (f : Z ⟶ Z')
     (h : Z' ⟶ X) : f ≫ α.app (op Z') h = α.app (op Z) (f ≫ h) :=
@@ -126,12 +120,6 @@ def ext (X Y : C) (p : ∀ {Z : C}, (Z ⟶ X) → (Z ⟶ Y)) (q : ∀ {Z : C}, (
 #align category_theory.yoneda.ext CategoryTheory.Yoneda.ext
 -/
 
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 /-- If `yoneda.map f` is an isomorphism, so was `f`.
 -/
 theorem isIso {X Y : C} (f : X ⟶ Y) [IsIso (yoneda.map f)] : IsIso f :=
@@ -142,9 +130,6 @@ end Yoneda
 
 namespace Coyoneda
 
-/- warning: category_theory.coyoneda.naturality -> CategoryTheory.Coyoneda.naturality is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.coyoneda.naturality CategoryTheory.Coyoneda.naturalityₓ'. -/
 @[simp]
 theorem naturality {X Y : Cᵒᵖ} (α : coyoneda.obj X ⟶ coyoneda.obj Y) {Z Z' : C} (f : Z' ⟶ Z)
     (h : unop X ⟶ Z') : α.app Z' h ≫ f = α.app Z (h ≫ f) :=
@@ -166,24 +151,12 @@ instance coyoneda_faithful : Faithful (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁)
 #align category_theory.coyoneda.coyoneda_faithful CategoryTheory.Coyoneda.coyoneda_faithful
 -/
 
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 /-- If `coyoneda.map f` is an isomorphism, so was `f`.
 -/
 theorem isIso {X Y : Cᵒᵖ} (f : X ⟶ Y) [IsIso (coyoneda.map f)] : IsIso f :=
   isIso_of_fully_faithful coyoneda f
 #align category_theory.coyoneda.is_iso CategoryTheory.Coyoneda.isIso
 
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 /-- The identity functor on `Type` is isomorphic to the coyoneda functor coming from `punit`. -/
 def punitIso : coyoneda.obj (Opposite.op PUnit) ≅ 𝟭 (Type v₁) :=
   NatIso.ofComponents
@@ -193,12 +166,6 @@ def punitIso : coyoneda.obj (Opposite.op PUnit) ≅ 𝟭 (Type v₁) :=
     (by tidy)
 #align category_theory.coyoneda.punit_iso CategoryTheory.Coyoneda.punitIso
 
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 /-- Taking the `unop` of morphisms is a natural isomorphism. -/
 @[simps]
 def objOpOp (X : C) : coyoneda.obj (op (op X)) ≅ yoneda.obj X :=
@@ -249,23 +216,11 @@ noncomputable def reprX : C :=
 #align category_theory.functor.repr_X CategoryTheory.Functor.reprX
 -/
 
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 /-- The (forward direction of the) isomorphism witnessing `F` is representable. -/
 noncomputable def reprF : yoneda.obj F.reprX ⟶ F :=
   Representable.has_representation.choose_spec.some
 #align category_theory.functor.repr_f CategoryTheory.Functor.reprF
 
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 /-- The representing element for the representable functor `F`, sometimes called the universal
 element of the functor.
 -/
@@ -276,12 +231,6 @@ noncomputable def reprx : F.obj (op F.reprX) :=
 instance : IsIso F.reprF :=
   Representable.has_representation.choose_spec.choose_spec
 
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 /-- An isomorphism between `F` and a functor of the form `C(-, F.repr_X)`.  Note the components
 `F.repr_w.app X` definitionally have type `(X.unop ⟶ F.repr_X) ≅ F.obj X`.
 -/
@@ -289,23 +238,11 @@ noncomputable def reprW : yoneda.obj F.reprX ≅ F :=
   asIso F.reprF
 #align category_theory.functor.repr_w CategoryTheory.Functor.reprW
 
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 @[simp]
 theorem reprW_hom : F.reprW.Hom = F.reprF :=
   rfl
 #align category_theory.functor.repr_w_hom CategoryTheory.Functor.reprW_hom
 
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 theorem reprW_app_hom (X : Cᵒᵖ) (f : unop X ⟶ F.reprX) :
     (F.reprW.app X).Hom f = F.map f.op F.reprx :=
   by
@@ -330,23 +267,11 @@ noncomputable def coreprX : C :=
 #align category_theory.functor.corepr_X CategoryTheory.Functor.coreprX
 -/
 
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 /-- The (forward direction of the) isomorphism witnessing `F` is corepresentable. -/
 noncomputable def coreprF : coyoneda.obj (op F.coreprX) ⟶ F :=
   Corepresentable.has_corepresentation.choose_spec.some
 #align category_theory.functor.corepr_f CategoryTheory.Functor.coreprF
 
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 /-- The representing element for the corepresentable functor `F`, sometimes called the universal
 element of the functor.
 -/
@@ -357,12 +282,6 @@ noncomputable def coreprx : F.obj F.coreprX :=
 instance : IsIso F.coreprF :=
   Corepresentable.has_corepresentation.choose_spec.choose_spec
 
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 /-- An isomorphism between `F` and a functor of the form `C(F.corepr X, -)`. Note the components
 `F.corepr_w.app X` definitionally have type `F.corepr_X ⟶ X ≅ F.obj X`.
 -/
@@ -370,12 +289,6 @@ noncomputable def coreprW : coyoneda.obj (op F.coreprX) ≅ F :=
   asIso F.coreprF
 #align category_theory.functor.corepr_w CategoryTheory.Functor.coreprW
 
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 theorem coreprW_app_hom (X : C) (f : F.coreprX ⟶ X) : (F.coreprW.app X).Hom f = F.map f F.coreprx :=
   by
   change F.corepr_f.app X f = (F.corepr_f.app F.corepr_X ≫ F.map f) (𝟙 F.corepr_X)
@@ -433,9 +346,6 @@ def yonedaEvaluation : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁) ⥤ Type max u₁ v₁
 #align category_theory.yoneda_evaluation CategoryTheory.yonedaEvaluation
 -/
 
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 @[simp]
 theorem yonedaEvaluation_map_down (P Q : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁)) (α : P ⟶ Q)
     (x : (yonedaEvaluation C).obj P) :
@@ -452,9 +362,6 @@ def yonedaPairing : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁) ⥤ Type max u₁ v₁ :=
 #align category_theory.yoneda_pairing CategoryTheory.yonedaPairing
 -/
 
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 @[simp]
 theorem yonedaPairing_map (P Q : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁)) (α : P ⟶ Q) (β : (yonedaPairing C).obj P) :
     (yonedaPairing C).map α β = yoneda.map α.1.unop ≫ β ≫ α.2 :=
@@ -498,12 +405,6 @@ def yonedaLemma : yonedaPairing C ≅ yonedaEvaluation C
 
 variable {C}
 
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 /-- The isomorphism between `yoneda.obj X ⟶ F` and `F.obj (op X)`
 (we need to insert a `ulift` to get the universes right!)
 given by the Yoneda lemma.
@@ -513,12 +414,6 @@ def yonedaSections (X : C) (F : Cᵒᵖ ⥤ Type v₁) : (yoneda.obj X ⟶ F) 
   (yonedaLemma C).app (op X, F)
 #align category_theory.yoneda_sections CategoryTheory.yonedaSections
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.yoneda_equiv CategoryTheory.yonedaEquivₓ'. -/
 /-- We have a type-level equivalence between natural transformations from the yoneda embedding
 and elements of `F.obj X`, without any universe switching.
 -/
@@ -526,27 +421,18 @@ def yonedaEquiv {X : C} {F : Cᵒᵖ ⥤ Type v₁} : (yoneda.obj X ⟶ F) ≃ F
   (yonedaSections X F).toEquiv.trans Equiv.ulift
 #align category_theory.yoneda_equiv CategoryTheory.yonedaEquiv
 
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 @[simp]
 theorem yonedaEquiv_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda.obj X ⟶ F) :
     yonedaEquiv f = f.app (op X) (𝟙 X) :=
   rfl
 #align category_theory.yoneda_equiv_apply CategoryTheory.yonedaEquiv_apply
 
-/- warning: category_theory.yoneda_equiv_symm_app_apply -> CategoryTheory.yonedaEquiv_symm_app_apply is a dubious translation:
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 @[simp]
 theorem yonedaEquiv_symm_app_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (x : F.obj (op X)) (Y : Cᵒᵖ)
     (f : Y.unop ⟶ X) : (yonedaEquiv.symm x).app Y f = F.map f.op x :=
   rfl
 #align category_theory.yoneda_equiv_symm_app_apply CategoryTheory.yonedaEquiv_symm_app_apply
 
-/- warning: category_theory.yoneda_equiv_naturality -> CategoryTheory.yonedaEquiv_naturality is a dubious translation:
-<too large>
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 theorem yonedaEquiv_naturality {X Y : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda.obj X ⟶ F) (g : Y ⟶ X) :
     F.map g.op (yonedaEquiv f) = yonedaEquiv (yoneda.map g ≫ f) :=
   by
@@ -556,12 +442,6 @@ theorem yonedaEquiv_naturality {X Y : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda
   simp
 #align category_theory.yoneda_equiv_naturality CategoryTheory.yonedaEquiv_naturality
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.yoneda_sections_small CategoryTheory.yonedaSectionsSmallₓ'. -/
 /-- When `C` is a small category, we can restate the isomorphism from `yoneda_sections`
 without having to change universes.
 -/
@@ -570,18 +450,12 @@ def yonedaSectionsSmall {C : Type u₁} [SmallCategory C] (X : C) (F : Cᵒᵖ 
   yonedaSections X F ≪≫ uliftTrivial _
 #align category_theory.yoneda_sections_small CategoryTheory.yonedaSectionsSmall
 
-/- warning: category_theory.yoneda_sections_small_hom -> CategoryTheory.yonedaSectionsSmall_hom is a dubious translation:
-<too large>
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 @[simp]
 theorem yonedaSectionsSmall_hom {C : Type u₁} [SmallCategory C] (X : C) (F : Cᵒᵖ ⥤ Type u₁)
     (f : yoneda.obj X ⟶ F) : (yonedaSectionsSmall X F).Hom f = f.app _ (𝟙 _) :=
   rfl
 #align category_theory.yoneda_sections_small_hom CategoryTheory.yonedaSectionsSmall_hom
 
-/- warning: category_theory.yoneda_sections_small_inv_app_apply -> CategoryTheory.yonedaSectionsSmall_inv_app_apply is a dubious translation:
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 @[simp]
 theorem yonedaSectionsSmall_inv_app_apply {C : Type u₁} [SmallCategory C] (X : C)
     (F : Cᵒᵖ ⥤ Type u₁) (t : F.obj (op X)) (Y : Cᵒᵖ) (f : Y.unop ⟶ X) :
@@ -602,9 +476,6 @@ def curriedYonedaLemma {C : Type u₁} [SmallCategory C] :
 #align category_theory.curried_yoneda_lemma CategoryTheory.curriedYonedaLemma
 -/
 
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-<too large>
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 /-- The curried version of yoneda lemma when `C` is small. -/
 def curriedYonedaLemma' {C : Type u₁} [SmallCategory C] :
     yoneda ⋙ (whiskeringLeft Cᵒᵖ (Cᵒᵖ ⥤ Type u₁)ᵒᵖ (Type u₁)).obj yoneda.op ≅ 𝟭 (Cᵒᵖ ⥤ Type u₁) :=

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

@@ -73,10 +73,7 @@ namespace Yoneda
 <too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda.obj_map_id CategoryTheory.Yoneda.obj_map_idₓ'. -/
 theorem obj_map_id {X Y : C} (f : op X ⟶ op Y) :
-    (yoneda.obj X).map f (𝟙 X) = (yoneda.map f.unop).app (op Y) (𝟙 Y) :=
-  by
-  dsimp
-  simp
+    (yoneda.obj X).map f (𝟙 X) = (yoneda.map f.unop).app (op Y) (𝟙 Y) := by dsimp; simp
 #align category_theory.yoneda.obj_map_id CategoryTheory.Yoneda.obj_map_id
 
 /- warning: category_theory.yoneda.naturality -> CategoryTheory.Yoneda.naturality is a dubious translation:

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

@@ -70,10 +70,7 @@ def coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁
 namespace Yoneda
 
 /- warning: category_theory.yoneda.obj_map_id -> CategoryTheory.Yoneda.obj_map_id is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda.obj_map_id CategoryTheory.Yoneda.obj_map_idₓ'. -/
 theorem obj_map_id {X Y : C} (f : op X ⟶ op Y) :
     (yoneda.obj X).map f (𝟙 X) = (yoneda.map f.unop).app (op Y) (𝟙 Y) :=
@@ -83,10 +80,7 @@ theorem obj_map_id {X Y : C} (f : op X ⟶ op Y) :
 #align category_theory.yoneda.obj_map_id CategoryTheory.Yoneda.obj_map_id
 
 /- warning: category_theory.yoneda.naturality -> CategoryTheory.Yoneda.naturality is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda.naturality CategoryTheory.Yoneda.naturalityₓ'. -/
 @[simp]
 theorem naturality {X Y : C} (α : yoneda.obj X ⟶ yoneda.obj Y) {Z Z' : C} (f : Z ⟶ Z')
@@ -152,10 +146,7 @@ end Yoneda
 namespace Coyoneda
 
 /- warning: category_theory.coyoneda.naturality -> CategoryTheory.Coyoneda.naturality is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.coyoneda.naturality CategoryTheory.Coyoneda.naturalityₓ'. -/
 @[simp]
 theorem naturality {X Y : Cᵒᵖ} (α : coyoneda.obj X ⟶ coyoneda.obj Y) {Z Z' : C} (f : Z' ⟶ Z)
@@ -446,10 +437,7 @@ def yonedaEvaluation : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁) ⥤ Type max u₁ v₁
 -/
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda_evaluation_map_down CategoryTheory.yonedaEvaluation_map_downₓ'. -/
 @[simp]
 theorem yonedaEvaluation_map_down (P Q : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁)) (α : P ⟶ Q)
@@ -468,10 +456,7 @@ def yonedaPairing : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁) ⥤ Type max u₁ v₁ :=
 -/
 
 /- warning: category_theory.yoneda_pairing_map -> CategoryTheory.yonedaPairing_map is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda_pairing_map CategoryTheory.yonedaPairing_mapₓ'. -/
 @[simp]
 theorem yonedaPairing_map (P Q : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁)) (α : P ⟶ Q) (β : (yonedaPairing C).obj P) :
@@ -545,10 +530,7 @@ def yonedaEquiv {X : C} {F : Cᵒᵖ ⥤ Type v₁} : (yoneda.obj X ⟶ F) ≃ F
 #align category_theory.yoneda_equiv CategoryTheory.yonedaEquiv
 
 /- warning: category_theory.yoneda_equiv_apply -> CategoryTheory.yonedaEquiv_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda_equiv_apply CategoryTheory.yonedaEquiv_applyₓ'. -/
 @[simp]
 theorem yonedaEquiv_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda.obj X ⟶ F) :
@@ -557,10 +539,7 @@ theorem yonedaEquiv_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda.obj X
 #align category_theory.yoneda_equiv_apply CategoryTheory.yonedaEquiv_apply
 
 /- warning: category_theory.yoneda_equiv_symm_app_apply -> CategoryTheory.yonedaEquiv_symm_app_apply is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda_equiv_symm_app_apply CategoryTheory.yonedaEquiv_symm_app_applyₓ'. -/
 @[simp]
 theorem yonedaEquiv_symm_app_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (x : F.obj (op X)) (Y : Cᵒᵖ)
@@ -569,10 +548,7 @@ theorem yonedaEquiv_symm_app_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (x : F.ob
 #align category_theory.yoneda_equiv_symm_app_apply CategoryTheory.yonedaEquiv_symm_app_apply
 
 /- warning: category_theory.yoneda_equiv_naturality -> CategoryTheory.yonedaEquiv_naturality is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda_equiv_naturality CategoryTheory.yonedaEquiv_naturalityₓ'. -/
 theorem yonedaEquiv_naturality {X Y : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda.obj X ⟶ F) (g : Y ⟶ X) :
     F.map g.op (yonedaEquiv f) = yonedaEquiv (yoneda.map g ≫ f) :=
@@ -598,10 +574,7 @@ def yonedaSectionsSmall {C : Type u₁} [SmallCategory C] (X : C) (F : Cᵒᵖ 
 #align category_theory.yoneda_sections_small CategoryTheory.yonedaSectionsSmall
 
 /- warning: category_theory.yoneda_sections_small_hom -> CategoryTheory.yonedaSectionsSmall_hom is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda_sections_small_hom CategoryTheory.yonedaSectionsSmall_homₓ'. -/
 @[simp]
 theorem yonedaSectionsSmall_hom {C : Type u₁} [SmallCategory C] (X : C) (F : Cᵒᵖ ⥤ Type u₁)
@@ -610,10 +583,7 @@ theorem yonedaSectionsSmall_hom {C : Type u₁} [SmallCategory C] (X : C) (F : C
 #align category_theory.yoneda_sections_small_hom CategoryTheory.yonedaSectionsSmall_hom
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda_sections_small_inv_app_apply CategoryTheory.yonedaSectionsSmall_inv_app_applyₓ'. -/
 @[simp]
 theorem yonedaSectionsSmall_inv_app_apply {C : Type u₁} [SmallCategory C] (X : C)
@@ -636,10 +606,7 @@ def curriedYonedaLemma {C : Type u₁} [SmallCategory C] :
 -/
 
 /- warning: category_theory.curried_yoneda_lemma' -> CategoryTheory.curriedYonedaLemma' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.curried_yoneda_lemma' CategoryTheory.curriedYonedaLemma'ₓ'. -/
 /-- The curried version of yoneda lemma when `C` is small. -/
 def curriedYonedaLemma' {C : Type u₁} [SmallCategory C] :

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

@@ -548,7 +548,7 @@ def yonedaEquiv {X : C} {F : Cᵒᵖ ⥤ Type v₁} : (yoneda.obj X ⟶ F) ≃ F
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda_equiv_apply CategoryTheory.yonedaEquiv_applyₓ'. -/
 @[simp]
 theorem yonedaEquiv_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda.obj X ⟶ F) :
@@ -560,7 +560,7 @@ theorem yonedaEquiv_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda.obj X
 lean 3 declaration is
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(CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1} F) (Opposite.op.{succ u2} C X) (Opposite.op.{succ u2} C (Opposite.unop.{succ u2} C Y)) (Quiver.Hom.op.{u2, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Opposite.unop.{succ u2} C Y) X f) x)
 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda_equiv_symm_app_apply CategoryTheory.yonedaEquiv_symm_app_applyₓ'. -/
 @[simp]
 theorem yonedaEquiv_symm_app_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (x : F.obj (op X)) (Y : Cᵒᵖ)
@@ -572,7 +572,7 @@ theorem yonedaEquiv_symm_app_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (x : F.ob
 lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda_equiv_naturality CategoryTheory.yonedaEquiv_naturalityₓ'. -/
 theorem yonedaEquiv_naturality {X Y : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda.obj X ⟶ F) (g : Y ⟶ X) :
     F.map g.op (yonedaEquiv f) = yonedaEquiv (yoneda.map g ≫ f) :=

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

@@ -601,7 +601,7 @@ def yonedaSectionsSmall {C : Type u₁} [SmallCategory C] (X : C) (F : Cᵒᵖ 
 lean 3 declaration is
   forall {C : Type.{u1}} [_inst_2 : CategoryTheory.SmallCategory.{u1} C] (X : C) (F : CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (f : Quiver.Hom.{succ u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Functor.obj.{u1, u1, u1, succ u1} C _inst_2 (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u1} C _inst_2) X) F), Eq.{succ u1} (CategoryTheory.Functor.obj.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1} F (Opposite.op.{succ u1} C X)) (CategoryTheory.Iso.hom.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} (Quiver.Hom.{succ u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Functor.obj.{u1, u1, u1, succ u1} C _inst_2 (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u1} C _inst_2) X) F) (CategoryTheory.Functor.obj.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1} F (Opposite.op.{succ u1} C X)) (CategoryTheory.yonedaSectionsSmall.{u1} C _inst_2 X F) f) (CategoryTheory.NatTrans.app.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1} (CategoryTheory.Functor.obj.{u1, u1, u1, succ u1} C _inst_2 (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u1} C _inst_2) X) F f (Opposite.op.{succ u1} C X) (CategoryTheory.CategoryStruct.id.{u1, u1} C (CategoryTheory.Category.toCategoryStruct.{u1, u1} C _inst_2) (Opposite.unop.{succ u1} C (Opposite.op.{succ u1} C X))))
 but is expected to have type
-  forall {C : Type.{u1}} [_inst_2 : CategoryTheory.SmallCategory.{u1} C] (X : C) (F : CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (f : Quiver.Hom.{succ u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}))) (Prefunctor.obj.{succ u1, succ u1, u1, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} C (CategoryTheory.Category.toCategoryStruct.{u1, u1} C _inst_2)) (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, succ u1} C _inst_2 (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u1} C _inst_2)) X) F), Eq.{succ u1} (Prefunctor.obj.{succ u1, succ u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} C) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2))) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1} F) (Opposite.op.{succ u1} C X)) (CategoryTheory.Iso.hom.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} (Quiver.Hom.{succ u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}))) (Prefunctor.obj.{succ u1, succ u1, u1, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} C (CategoryTheory.Category.toCategoryStruct.{u1, u1} C _inst_2)) (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, succ u1} C _inst_2 (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u1} C _inst_2)) X) F) (Prefunctor.obj.{succ u1, succ u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} C) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2))) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1} F) (Opposite.op.{succ u1} C X)) (CategoryTheory.yonedaSectionsSmall.{u1} C _inst_2 X F) f) (CategoryTheory.NatTrans.app.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1} (Prefunctor.obj.{succ u1, succ u1, u1, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} C (CategoryTheory.Category.toCategoryStruct.{u1, u1} C _inst_2)) (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, succ u1} C _inst_2 (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u1} C _inst_2)) X) F f X (CategoryTheory.CategoryStruct.id.{u1, u1} C (CategoryTheory.Category.toCategoryStruct.{u1, u1} C _inst_2) (Opposite.unop.{succ u1} C X)))
+  forall {C : Type.{u1}} [_inst_2 : CategoryTheory.SmallCategory.{u1} C] (X : C) (F : CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (f : Quiver.Hom.{succ u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}))) (Prefunctor.obj.{succ u1, succ u1, u1, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} C (CategoryTheory.Category.toCategoryStruct.{u1, u1} C _inst_2)) (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, succ u1} C _inst_2 (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u1} C _inst_2)) X) F), Eq.{succ u1} (Prefunctor.obj.{succ u1, succ u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} C) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2))) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1} F) (Opposite.op.{succ u1} C X)) (CategoryTheory.Iso.hom.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1} (Quiver.Hom.{succ u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}))) (Prefunctor.obj.{succ u1, succ u1, u1, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} C (CategoryTheory.Category.toCategoryStruct.{u1, u1} C _inst_2)) (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, succ u1} C _inst_2 (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u1} C _inst_2)) X) F) (Prefunctor.obj.{succ u1, succ u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} (Opposite.{succ u1} C) (CategoryTheory.Category.toCategoryStruct.{u1, u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2))) Type.{u1} (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} Type.{u1} (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} Type.{u1} CategoryTheory.types.{u1})) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1} F) (Opposite.op.{succ u1} C X)) (CategoryTheory.yonedaSectionsSmall.{u1} C _inst_2 X F) f) (CategoryTheory.NatTrans.app.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1} (Prefunctor.obj.{succ u1, succ u1, u1, succ u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u1} C (CategoryTheory.Category.toCategoryStruct.{u1, u1} C _inst_2)) (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{u1, succ u1} (CategoryTheory.Functor.{u1, u1, u1, succ u1} (Opposite.{succ u1} C) (CategoryTheory.Category.opposite.{u1, u1} C _inst_2) Type.{u1} 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 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda_sections_small_hom CategoryTheory.yonedaSectionsSmall_homₓ'. -/
 @[simp]
 theorem yonedaSectionsSmall_hom {C : Type u₁} [SmallCategory C] (X : C) (F : Cᵒᵖ ⥤ Type u₁)

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -548,7 +548,7 @@ def yonedaEquiv {X : C} {F : Cᵒᵖ ⥤ Type v₁} : (yoneda.obj X ⟶ F) ≃ F
 lean 3 declaration is
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 but is expected to have type
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(CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.yoneda.{u1, u2} C _inst_1)) X) F f (Opposite.op.{succ u2} C X) (CategoryTheory.CategoryStruct.id.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) X))
 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda_equiv_apply CategoryTheory.yonedaEquiv_applyₓ'. -/
 @[simp]
 theorem yonedaEquiv_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda.obj X ⟶ F) :
@@ -560,7 +560,7 @@ theorem yonedaEquiv_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda.obj X
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {F : CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}} (x : CategoryTheory.Functor.obj.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1} F (Opposite.op.{succ u2} C X)) (Y : Opposite.{succ u2} C) (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Opposite.unop.{succ u2} C Y) X), Eq.{succ u1} (CategoryTheory.Functor.obj.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1} F Y) (CategoryTheory.NatTrans.app.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1} 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda_equiv_symm_app_apply CategoryTheory.yonedaEquiv_symm_app_applyₓ'. -/
 @[simp]
 theorem yonedaEquiv_symm_app_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (x : F.obj (op X)) (Y : Cᵒᵖ)
@@ -572,7 +572,7 @@ theorem yonedaEquiv_symm_app_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (x : F.ob
 lean 3 declaration is
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} {F : CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}} (f : Quiver.Hom.{succ (max u2 u1), max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u1 u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) Type.{u1} CategoryTheory.types.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} 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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.yoneda_equiv_naturality CategoryTheory.yonedaEquiv_naturalityₓ'. -/
 theorem yonedaEquiv_naturality {X Y : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda.obj X ⟶ F) (g : Y ⟶ X) :
     F.map g.op (yonedaEquiv f) = yonedaEquiv (yoneda.map g ≫ f) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/3ade05ac9447ae31a22d2ea5423435e054131240

@@ -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 category_theory.yoneda
-! leanprover-community/mathlib commit 85cd3e6032af192374e4f5b44ae128971489e347
+! leanprover-community/mathlib commit 23aa88e32dcc9d2a24cca7bc23268567ed4cd7d6
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.CategoryTheory.Products.Basic
 /-!
 # The Yoneda embedding
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The Yoneda embedding as a functor `yoneda : C ⥤ (Cᵒᵖ ⥤ Type v₁)`,
 along with an instance that it is `fully_faithful`.
 

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

Before this PR, Functor.Full contained the data of the preimage of maps by a full functor F. This PR makes Functor.Full a proposition. This is to prevent any diamond to appear.

The lemma Functor.image_preimage is also renamed Functor.map_preimage.

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

@@ -68,13 +68,24 @@ theorem naturality {X Y : C} (α : yoneda.obj X ⟶ yoneda.obj Y) {Z Z' : C} (f
   (FunctorToTypes.naturality _ _ α f.op h).symm
 #align category_theory.yoneda.naturality CategoryTheory.Yoneda.naturality
 
+/-- The morphism `X ⟶ Y` corresponding to a natural transformation
+`yoneda.obj X ⟶ yoneda.obj Y`. -/
+def preimage {X Y : C} (f : yoneda.obj X ⟶ yoneda.obj Y) : X ⟶ Y :=
+  f.app (op X) (𝟙 X)
+
+@[simp]
+lemma map_preimage {X Y : C} (f : yoneda.obj X ⟶ yoneda.obj Y) :
+    yoneda.map (preimage f) = f := by
+  dsimp only [preimage]
+  aesop_cat
+
 /-- The Yoneda embedding is full.
 
 See <https://stacks.math.columbia.edu/tag/001P>.
 -/
-instance yonedaFull : (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁).Full where
-  preimage {X} {Y} f := f.app (op X) (𝟙 X)
-#align category_theory.yoneda.yoneda_full CategoryTheory.Yoneda.yonedaFull
+instance yoneda_full : (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁).Full where
+  map_surjective f := ⟨preimage f, by simp⟩
+#align category_theory.yoneda.yoneda_full CategoryTheory.Yoneda.yoneda_full
 
 /-- The Yoneda embedding is faithful.
 
@@ -85,6 +96,15 @@ instance yoneda_faithful : (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁).Faithful where
     convert congr_fun (congr_app p (op X)) (𝟙 X) using 1 <;> dsimp <;> simp
 #align category_theory.yoneda.yoneda_faithful CategoryTheory.Yoneda.yoneda_faithful
 
+/-- The isomorphism `X ≅ Y` corresponding to a natural isomorphism
+`yoneda.obj X ≅ yoneda.obj Y`. -/
+@[simps]
+def preimageIso {X Y : C} (e : yoneda.obj X ≅ yoneda.obj Y) : X ≅ Y where
+  hom := preimage e.hom
+  inv := preimage e.inv
+  hom_inv_id := yoneda.map_injective (by simp)
+  inv_hom_id := yoneda.map_injective (by simp)
+
 /-- Extensionality via Yoneda. The typical usage would be
 ```
 -- Goal is `X ≅ Y`
@@ -93,10 +113,11 @@ apply yoneda.ext,
 -- functions are inverses and natural in `Z`.
 ```
 -/
-def ext (X Y : C) (p : ∀ {Z : C}, (Z ⟶ X) → (Z ⟶ Y)) (q : ∀ {Z : C}, (Z ⟶ Y) → (Z ⟶ X))
+def ext (X Y : C) (p : ∀ {Z : C}, (Z ⟶ X) → (Z ⟶ Y))
+    (q : ∀ {Z : C}, (Z ⟶ Y) → (Z ⟶ X))
     (h₁ : ∀ {Z : C} (f : Z ⟶ X), q (p f) = f) (h₂ : ∀ {Z : C} (f : Z ⟶ Y), p (q f) = f)
     (n : ∀ {Z Z' : C} (f : Z' ⟶ Z) (g : Z ⟶ X), p (f ≫ g) = f ≫ p g) : X ≅ Y :=
-  yoneda.preimageIso
+  preimageIso
     (NatIso.ofComponents fun Z =>
       { hom := p
         inv := q })
@@ -118,10 +139,20 @@ theorem naturality {X Y : Cᵒᵖ} (α : coyoneda.obj X ⟶ coyoneda.obj Y) {Z Z
   (FunctorToTypes.naturality _ _ α f h).symm
 #align category_theory.coyoneda.naturality CategoryTheory.Coyoneda.naturality
 
-instance coyonedaFull : (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁).Full where
-  preimage {X} _ f := (f.app _ (𝟙 X.unop)).op
-  witness {X} {Y} f := by simp only [coyoneda]; aesop_cat
-#align category_theory.coyoneda.coyoneda_full CategoryTheory.Coyoneda.coyonedaFull
+/-- The morphism `X ⟶ Y` corresponding to a natural transformation
+`coyoneda.obj X ⟶ coyoneda.obj Y`. -/
+def preimage {X Y : Cᵒᵖ} (f : coyoneda.obj X ⟶ coyoneda.obj Y) : X ⟶ Y :=
+  (f.app _ (𝟙 X.unop)).op
+
+@[simp]
+lemma map_preimage {X Y : Cᵒᵖ} (f : coyoneda.obj X ⟶ coyoneda.obj Y) :
+    coyoneda.map (preimage f) = f := by
+  dsimp [preimage]
+  aesop_cat
+
+instance coyoneda_full : (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁).Full where
+  map_surjective f := ⟨preimage f, by simp⟩
+#align category_theory.coyoneda.coyoneda_full CategoryTheory.Coyoneda.coyoneda_full
 
 instance coyoneda_faithful : (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁).Faithful where
   map_injective {X} _ _ _ p := by
@@ -129,6 +160,39 @@ instance coyoneda_faithful : (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁).Faithful w
     simpa using congr_arg Quiver.Hom.op t
 #align category_theory.coyoneda.coyoneda_faithful CategoryTheory.Coyoneda.coyoneda_faithful
 
+/-- The isomorphism `X ≅ Y` corresponding to a natural isomorphism
+`coyoneda.obj X ≅ coyoneda.obj Y`. -/
+@[simps]
+def preimageIso {X Y : Cᵒᵖ} (e : coyoneda.obj X ≅ coyoneda.obj Y) : X ≅ Y where
+  hom := preimage e.hom
+  inv := preimage e.inv
+  hom_inv_id := coyoneda.map_injective (by simp)
+  inv_hom_id := coyoneda.map_injective (by simp)
+
+section
+
+variable {D : Type*} [Category D] {F G : D ⥤ Cᵒᵖ}
+
+/-- The natural transformation `F ⟶ G` corresponding to a natural transformation
+`F ⋙ coyoneda ⟶ G ⋙ coyoneda`. -/
+@[simps]
+def preimageNatTrans (f : F ⋙ coyoneda ⟶ G ⋙ coyoneda) : F ⟶ G where
+  app X := preimage (f.app X)
+  naturality X Y g := coyoneda.map_injective (by
+    simp only [Functor.map_comp, map_preimage]
+    exact f.naturality g)
+
+/-- The natural isomorphism `F ≅ G` corresponding to a natural transformation
+`F ⋙ coyoneda ≅ G ⋙ coyoneda`. -/
+@[simps]
+def preimageNatIso (e : F ⋙ coyoneda ≅ G ⋙ coyoneda) : F ≅ G where
+  hom := preimageNatTrans e.hom
+  inv := preimageNatTrans e.inv
+  hom_inv_id := by ext X; apply coyoneda.map_injective; simp
+  inv_hom_id := by ext X; apply coyoneda.map_injective; simp
+
+end
+
 /-- If `coyoneda.map f` is an isomorphism, so was `f`.
 -/
 theorem isIso {X Y : Cᵒᵖ} (f : X ⟶ Y) [IsIso (coyoneda.map f)] : IsIso f :=

It is shown in this PR that the forget functor from commutative groups to groups preserves all limits (regardless of the universe parameters of the index category). It is also shown that a functor F : J ⥤ CommGroupCat (or F : J ⥤ GroupCat) has a limit iff the type (F ⋙ forget _).sections is small. This is related to the fact that the forget functor CommGroupCat.{u} ⥤ Type u is corepresentable (by ULift ℤ).

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

@@ -158,10 +158,10 @@ See <https://stacks.math.columbia.edu/tag/001Q>.
 -/
 class Representable (F : Cᵒᵖ ⥤ Type v₁) : Prop where
   /-- `Hom(-,X) ≅ F` via `f` -/
-  has_representation : ∃ (X : _) (f : yoneda.obj X ⟶ F), IsIso f
+  has_representation : ∃ (X : _), Nonempty (yoneda.obj X ≅ F)
 #align category_theory.functor.representable CategoryTheory.Functor.Representable
 
-instance {X : C} : Representable (yoneda.obj X) where has_representation := ⟨X, 𝟙 _, inferInstance⟩
+instance {X : C} : Representable (yoneda.obj X) where has_representation := ⟨X, ⟨Iso.refl _⟩⟩
 
 /-- A functor `F : C ⥤ Type v₁` is corepresentable if there is object `X` so `F ≅ coyoneda.obj X`.
 
@@ -169,58 +169,43 @@ See <https://stacks.math.columbia.edu/tag/001Q>.
 -/
 class Corepresentable (F : C ⥤ Type v₁) : Prop where
   /-- `Hom(X,-) ≅ F` via `f` -/
-  has_corepresentation : ∃ (X : _) (f : coyoneda.obj X ⟶ F), IsIso f
+  has_corepresentation : ∃ (X : _), Nonempty (coyoneda.obj X ≅ F)
 #align category_theory.functor.corepresentable CategoryTheory.Functor.Corepresentable
 
 instance {X : Cᵒᵖ} : Corepresentable (coyoneda.obj X) where
-  has_corepresentation := ⟨X, 𝟙 _, inferInstance⟩
+  has_corepresentation := ⟨X, ⟨Iso.refl _⟩⟩
 
 -- instance : corepresentable (𝟭 (Type v₁)) :=
 -- corepresentable_of_nat_iso (op punit) coyoneda.punit_iso
 section Representable
 
 variable (F : Cᵒᵖ ⥤ Type v₁)
-variable [F.Representable]
+variable [hF : F.Representable]
 
 /-- The representing object for the representable functor `F`. -/
-noncomputable def reprX : C :=
-  (Representable.has_representation : ∃ (_ : _) (_ : _ ⟶ F), _).choose
+noncomputable def reprX : C := hF.has_representation.choose
 set_option linter.uppercaseLean3 false
 #align category_theory.functor.repr_X CategoryTheory.Functor.reprX
 
-/-- The (forward direction of the) isomorphism witnessing `F` is representable. -/
-noncomputable def reprF : yoneda.obj F.reprX ⟶ F :=
-  Representable.has_representation.choose_spec.choose
-#align category_theory.functor.repr_f CategoryTheory.Functor.reprF
+/-- An isomorphism between a representable `F` and a functor of the
+form `C(-, F.reprX)`.  Note the components `F.reprW.app X`
+definitionally have type `(X.unop ⟶ F.repr_X) ≅ F.obj X`.
+-/
+noncomputable def reprW : yoneda.obj F.reprX ≅ F :=
+  Representable.has_representation.choose_spec.some
+#align category_theory.functor.repr_f CategoryTheory.Functor.reprW
 
 /-- The representing element for the representable functor `F`, sometimes called the universal
 element of the functor.
 -/
 noncomputable def reprx : F.obj (op F.reprX) :=
-  F.reprF.app (op F.reprX) (𝟙 F.reprX)
+  F.reprW.hom.app (op F.reprX) (𝟙 F.reprX)
 #align category_theory.functor.repr_x CategoryTheory.Functor.reprx
 
-instance : IsIso F.reprF :=
-  Representable.has_representation.choose_spec.choose_spec
-
-/-- An isomorphism between `F` and a functor of the form `C(-, F.repr_X)`.  Note the components
-`F.repr_w.app X` definitionally have type `(X.unop ⟶ F.repr_X) ≅ F.obj X`.
--/
-noncomputable def reprW : yoneda.obj F.reprX ≅ F :=
-  asIso F.reprF
-#align category_theory.functor.repr_w CategoryTheory.Functor.reprW
-
-@[simp]
-theorem reprW_hom : F.reprW.hom = F.reprF :=
-  rfl
-#align category_theory.functor.repr_w_hom CategoryTheory.Functor.reprW_hom
-
 theorem reprW_app_hom (X : Cᵒᵖ) (f : unop X ⟶ F.reprX) :
     (F.reprW.app X).hom f = F.map f.op F.reprx := by
-  change F.reprF.app X f = (F.reprF.app (op F.reprX) ≫ F.map f.op) (𝟙 F.reprX)
-  rw [← F.reprF.naturality]
-  dsimp
-  simp
+  simp only [yoneda_obj_obj, Iso.app_hom, op_unop, reprx, ← FunctorToTypes.naturality,
+    yoneda_obj_map, unop_op, Quiver.Hom.unop_op, Category.comp_id]
 #align category_theory.functor.repr_w_app_hom CategoryTheory.Functor.reprW_app_hom
 
 end Representable
@@ -228,60 +213,51 @@ end Representable
 section Corepresentable
 
 variable (F : C ⥤ Type v₁)
-variable [F.Corepresentable]
+variable [hF : F.Corepresentable]
 
 /-- The representing object for the corepresentable functor `F`. -/
 noncomputable def coreprX : C :=
-  (Corepresentable.has_corepresentation : ∃ (_ : _) (_ : _ ⟶ F), _).choose.unop
+  hF.has_corepresentation.choose.unop
 set_option linter.uppercaseLean3 false
 #align category_theory.functor.corepr_X CategoryTheory.Functor.coreprX
 
-/-- The (forward direction of the) isomorphism witnessing `F` is corepresentable. -/
-noncomputable def coreprF : coyoneda.obj (op F.coreprX) ⟶ F :=
-  Corepresentable.has_corepresentation.choose_spec.choose
-#align category_theory.functor.corepr_f CategoryTheory.Functor.coreprF
+/-- An isomorphism between a corepresnetable `F` and a functor of the form
+`C(F.corepr X, -)`. Note the components `F.coreprW.app X`
+definitionally have type `F.corepr_X ⟶ X ≅ F.obj X`.
+-/
+noncomputable def coreprW : coyoneda.obj (op F.coreprX) ≅ F :=
+  hF.has_corepresentation.choose_spec.some
+#align category_theory.functor.corepr_f CategoryTheory.Functor.coreprW
 
 /-- The representing element for the corepresentable functor `F`, sometimes called the universal
 element of the functor.
 -/
 noncomputable def coreprx : F.obj F.coreprX :=
-  F.coreprF.app F.coreprX (𝟙 F.coreprX)
+  F.coreprW.hom.app F.coreprX (𝟙 F.coreprX)
 #align category_theory.functor.corepr_x CategoryTheory.Functor.coreprx
 
-instance : IsIso F.coreprF :=
-  Corepresentable.has_corepresentation.choose_spec.choose_spec
-
-/-- An isomorphism between `F` and a functor of the form `C(F.corepr X, -)`. Note the components
-`F.corepr_w.app X` definitionally have type `F.corepr_X ⟶ X ≅ F.obj X`.
--/
-noncomputable def coreprW : coyoneda.obj (op F.coreprX) ≅ F :=
-  asIso F.coreprF
-#align category_theory.functor.corepr_w CategoryTheory.Functor.coreprW
-
 theorem coreprW_app_hom (X : C) (f : F.coreprX ⟶ X) :
     (F.coreprW.app X).hom f = F.map f F.coreprx := by
-  change F.coreprF.app X f = (F.coreprF.app F.coreprX ≫ F.map f) (𝟙 F.coreprX)
-  rw [← F.coreprF.naturality]
-  dsimp
-  simp
+  simp only [coyoneda_obj_obj, unop_op, Iso.app_hom, coreprx, ← FunctorToTypes.naturality,
+    coyoneda_obj_map, Category.id_comp]
 #align category_theory.functor.corepr_w_app_hom CategoryTheory.Functor.coreprW_app_hom
 
 end Corepresentable
 
 end Functor
 
-theorem representable_of_nat_iso (F : Cᵒᵖ ⥤ Type v₁) {G} (i : F ≅ G) [F.Representable] :
+theorem representable_of_natIso (F : Cᵒᵖ ⥤ Type v₁) {G} (i : F ≅ G) [F.Representable] :
     G.Representable :=
-  { has_representation := ⟨F.reprX, F.reprF ≫ i.hom, inferInstance⟩ }
-#align category_theory.representable_of_nat_iso CategoryTheory.representable_of_nat_iso
+  { has_representation := ⟨F.reprX, ⟨F.reprW ≪≫ i⟩⟩ }
+#align category_theory.representable_of_nat_iso CategoryTheory.representable_of_natIso
 
-theorem corepresentable_of_nat_iso (F : C ⥤ Type v₁) {G} (i : F ≅ G) [F.Corepresentable] :
+theorem corepresentable_of_natIso (F : C ⥤ Type v₁) {G} (i : F ≅ G) [F.Corepresentable] :
     G.Corepresentable :=
-  { has_corepresentation := ⟨op F.coreprX, F.coreprF ≫ i.hom, inferInstance⟩ }
-#align category_theory.corepresentable_of_nat_iso CategoryTheory.corepresentable_of_nat_iso
+  { has_corepresentation := ⟨op F.coreprX, ⟨F.coreprW ≪≫ i⟩⟩ }
+#align category_theory.corepresentable_of_nat_iso CategoryTheory.corepresentable_of_natIso
 
 instance : Functor.Corepresentable (𝟭 (Type v₁)) :=
-  corepresentable_of_nat_iso (coyoneda.obj (op PUnit)) Coyoneda.punitIso
+  corepresentable_of_natIso (coyoneda.obj (op PUnit)) Coyoneda.punitIso
 
 open Opposite
 

and reduce its scope in a few other instances. Mostly in CategoryTheory and Data this time; some Combinatorics also.

Co-authored-by: Richard Osborn <richardosborn@mac.com>

@@ -21,9 +21,6 @@ Also the Yoneda lemma, `yonedaLemma : (yoneda_pairing C) ≅ (yoneda_evaluation
 * [Stacks: Opposite Categories and the Yoneda Lemma](https://stacks.math.columbia.edu/tag/001L)
 -/
 
-set_option autoImplicit true
-
-
 namespace CategoryTheory
 
 open Opposite
@@ -326,7 +323,8 @@ def yonedaPairing : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁) ⥤ Type max u₁ v₁ :=
 -- as `ext` will not look through the definition.
 -- See https://github.com/leanprover-community/mathlib4/issues/5229
 @[ext]
-lemma yonedaPairingExt {x y : (yonedaPairing C).obj X} (w : ∀ Y, x.app Y = y.app Y) : x = y :=
+lemma yonedaPairingExt {X : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁)} {x y : (yonedaPairing C).obj X}
+    (w : ∀ Y, x.app Y = y.app Y) : x = y :=
   NatTrans.ext _ _ (funext w)
 
 @[simp]
@@ -335,6 +333,7 @@ theorem yonedaPairing_map (P Q : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁)) (α : P ⟶
   rfl
 #align category_theory.yoneda_pairing_map CategoryTheory.yonedaPairing_map
 
+universe w in
 variable {C} in
 /-- A bijection `(yoneda.obj X ⋙ uliftFunctor ⟶ F) ≃ F.obj (op X)` which is a variant
 of `yonedaEquiv` with heterogeneous universes. -/

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

@@ -75,7 +75,7 @@ theorem naturality {X Y : C} (α : yoneda.obj X ⟶ yoneda.obj Y) {Z Z' : C} (f
 
 See <https://stacks.math.columbia.edu/tag/001P>.
 -/
-instance yonedaFull : Full (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁) where
+instance yonedaFull : (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁).Full where
   preimage {X} {Y} f := f.app (op X) (𝟙 X)
 #align category_theory.yoneda.yoneda_full CategoryTheory.Yoneda.yonedaFull
 
@@ -83,7 +83,7 @@ instance yonedaFull : Full (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁) where
 
 See <https://stacks.math.columbia.edu/tag/001P>.
 -/
-instance yoneda_faithful : Faithful (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁) where
+instance yoneda_faithful : (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁).Faithful where
   map_injective {X} {Y} f g p := by
     convert congr_fun (congr_app p (op X)) (𝟙 X) using 1 <;> dsimp <;> simp
 #align category_theory.yoneda.yoneda_faithful CategoryTheory.Yoneda.yoneda_faithful
@@ -121,12 +121,12 @@ theorem naturality {X Y : Cᵒᵖ} (α : coyoneda.obj X ⟶ coyoneda.obj Y) {Z Z
   (FunctorToTypes.naturality _ _ α f h).symm
 #align category_theory.coyoneda.naturality CategoryTheory.Coyoneda.naturality
 
-instance coyonedaFull : Full (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁) where
+instance coyonedaFull : (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁).Full where
   preimage {X} _ f := (f.app _ (𝟙 X.unop)).op
   witness {X} {Y} f := by simp only [coyoneda]; aesop_cat
 #align category_theory.coyoneda.coyoneda_full CategoryTheory.Coyoneda.coyonedaFull
 
-instance coyoneda_faithful : Faithful (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁) where
+instance coyoneda_faithful : (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁).Faithful where
   map_injective {X} _ _ _ p := by
     have t := congr_fun (congr_app p X.unop) (𝟙 _)
     simpa using congr_arg Quiver.Hom.op t

A few miscellaneous directories: RingTheory, SetTheory, Combinatorics and CategoryTheory.

Co-authored-by: Scott Morrison <scott@tqft.net>

@@ -138,7 +138,7 @@ theorem isIso {X Y : Cᵒᵖ} (f : X ⟶ Y) [IsIso (coyoneda.map f)] : IsIso f :
   isIso_of_fully_faithful coyoneda f
 #align category_theory.coyoneda.is_iso CategoryTheory.Coyoneda.isIso
 
-/-- The identity functor on `Type` is isomorphic to the coyoneda functor coming from `punit`. -/
+/-- The identity functor on `Type` is isomorphic to the coyoneda functor coming from `PUnit`. -/
 def punitIso : coyoneda.obj (Opposite.op PUnit) ≅ 𝟭 (Type v₁) :=
   NatIso.ofComponents fun X =>
     { hom := fun f => f ⟨⟩
@@ -383,7 +383,7 @@ def yonedaLemma : yonedaPairing C ≅ yonedaEvaluation C where
 variable {C}
 
 /-- The isomorphism between `yoneda.obj X ⟶ F` and `F.obj (op X)`
-(we need to insert a `ulift` to get the universes right!)
+(we need to insert a `ULift` to get the universes right!)
 given by the Yoneda lemma.
 -/
 @[simps!]

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

@@ -183,7 +183,6 @@ instance {X : Cᵒᵖ} : Corepresentable (coyoneda.obj X) where
 section Representable
 
 variable (F : Cᵒᵖ ⥤ Type v₁)
-
 variable [F.Representable]
 
 /-- The representing object for the representable functor `F`. -/
@@ -232,7 +231,6 @@ end Representable
 section Corepresentable
 
 variable (F : C ⥤ Type v₁)
-
 variable [F.Corepresentable]
 
 /-- The representing object for the corepresentable functor `F`. -/

@@ -400,7 +400,6 @@ def yonedaEquiv {X : C} {F : Cᵒᵖ ⥤ Type v₁} : (yoneda.obj X ⟶ F) ≃ F
   (yonedaSections X F).toEquiv.trans Equiv.ulift
 #align category_theory.yoneda_equiv CategoryTheory.yonedaEquiv
 
-@[simp]
 theorem yonedaEquiv_apply {X : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda.obj X ⟶ F) :
     yonedaEquiv f = f.app (op X) (𝟙 X) :=
   rfl

While thinking about simp lemmas for opposite categories (for the sake of comonoid objects, for the sake of group objects, for the sake of reductive groups), noticed some of the Yoneda lemma proofs can be golfed.

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

@@ -365,35 +365,21 @@ def yonedaLemma : yonedaPairing C ≅ yonedaEvaluation C where
     { app := fun F x => ULift.up ((x.app F.1) (𝟙 (unop F.1)))
       naturality := by
         intro X Y f
-        simp only [yonedaEvaluation]
         ext
-        dsimp
-        erw [Category.id_comp, ← FunctorToTypes.naturality]
-        simp only [Category.comp_id, yoneda_obj_map] }
+        simp [yonedaEvaluation, ← FunctorToTypes.naturality] }
   inv :=
     { app := fun F x =>
-        { app := fun X a => (F.2.map a.op) x.down
-          naturality := by
-            intro X Y f
-            ext
-            dsimp
-            rw [FunctorToTypes.map_comp_apply] }
+        { app := fun X a => (F.2.map a.op) x.down }
       naturality := by
         intro X Y f
-        simp only [yoneda]
         ext
-        dsimp
-        rw [← FunctorToTypes.naturality X.snd Y.snd f.snd, FunctorToTypes.map_comp_apply] }
+        simp [yoneda, ← FunctorToTypes.naturality] }
   hom_inv_id := by
     ext
-    dsimp
-    erw [← FunctorToTypes.naturality, obj_map_id]
-    simp only [yoneda_map_app, Quiver.Hom.unop_op]
-    erw [Category.id_comp]
+    simp [← FunctorToTypes.naturality]
   inv_hom_id := by
     ext
-    dsimp
-    rw [FunctorToTypes.map_id_apply, ULift.up_down]
+    simp [ULift.up_down]
 #align category_theory.yoneda_lemma CategoryTheory.yonedaLemma
 
 variable {C}

The PR generalizes universes for standardSimplex, which is now a functor SimplexCategory ⥤ SSet.{u} for any universe u.

@@ -337,6 +337,23 @@ theorem yonedaPairing_map (P Q : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁)) (α : P ⟶
   rfl
 #align category_theory.yoneda_pairing_map CategoryTheory.yonedaPairing_map
 
+variable {C} in
+/-- A bijection `(yoneda.obj X ⋙ uliftFunctor ⟶ F) ≃ F.obj (op X)` which is a variant
+of `yonedaEquiv` with heterogeneous universes. -/
+def yonedaCompUliftFunctorEquiv (F : Cᵒᵖ ⥤ Type max v₁ w) (X : C) :
+    (yoneda.obj X ⋙ uliftFunctor.{w} ⟶ F) ≃ F.obj (op X) where
+  toFun φ := φ.app (op X) (ULift.up (𝟙 _))
+  invFun f :=
+    { app := fun Y x => F.map (ULift.down x).op f }
+  left_inv φ := by
+    ext Y f
+    dsimp
+    rw [← FunctorToTypes.naturality]
+    dsimp
+    rw [Category.comp_id]
+    rfl
+  right_inv f := by aesop_cat
+
 /-- The Yoneda lemma asserts that the Yoneda pairing
 `(X : Cᵒᵖ, F : Cᵒᵖ ⥤ Type) ↦ (yoneda.obj (unop X) ⟶ F)`
 is naturally isomorphic to the evaluation `(X, F) ↦ F.obj X`.

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

@@ -351,7 +351,7 @@ def yonedaLemma : yonedaPairing C ≅ yonedaEvaluation C where
         simp only [yonedaEvaluation]
         ext
         dsimp
-        erw [Category.id_comp, ←FunctorToTypes.naturality]
+        erw [Category.id_comp, ← FunctorToTypes.naturality]
         simp only [Category.comp_id, yoneda_obj_map] }
   inv :=
     { app := fun F x =>
@@ -366,7 +366,7 @@ def yonedaLemma : yonedaPairing C ≅ yonedaEvaluation C where
         simp only [yoneda]
         ext
         dsimp
-        rw [←FunctorToTypes.naturality X.snd Y.snd f.snd, FunctorToTypes.map_comp_apply] }
+        rw [← FunctorToTypes.naturality X.snd Y.snd f.snd, FunctorToTypes.map_comp_apply] }
   hom_inv_id := by
     ext
     dsimp

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

@@ -421,11 +421,11 @@ lemma yonedaEquiv_naturality' {X Y : Cᵒᵖ} {F : Cᵒᵖ ⥤ Type v₁} (f : y
     (g : X ⟶ Y) : F.map g (yonedaEquiv f) = yonedaEquiv (yoneda.map g.unop ≫ f) :=
   yonedaEquiv_naturality _ _
 
-lemma yonedaEquiv_comp {X : C} {F G : Cᵒᵖ ⥤ Type v₁} (α : yoneda.obj X ⟶ F) (β : F ⟶ G)  :
+lemma yonedaEquiv_comp {X : C} {F G : Cᵒᵖ ⥤ Type v₁} (α : yoneda.obj X ⟶ F) (β : F ⟶ G) :
     yonedaEquiv (α ≫ β) = β.app _ (yonedaEquiv α) :=
   rfl
 
-lemma yonedaEquiv_comp' {X : Cᵒᵖ} {F G : Cᵒᵖ ⥤ Type v₁} (α : yoneda.obj (unop X) ⟶ F) (β : F ⟶ G)  :
+lemma yonedaEquiv_comp' {X : Cᵒᵖ} {F G : Cᵒᵖ ⥤ Type v₁} (α : yoneda.obj (unop X) ⟶ F) (β : F ⟶ G) :
     yonedaEquiv (α ≫ β) = β.app X (yonedaEquiv α) :=
   rfl
 

This reverts commit f3695eb2.

@@ -429,7 +429,8 @@ lemma yonedaEquiv_comp' {X : Cᵒᵖ} {F G : Cᵒᵖ ⥤ Type v₁} (α : yoneda
     yonedaEquiv (α ≫ β) = β.app X (yonedaEquiv α) :=
   rfl
 
-@[simp]
+-- This lemma has always been bad, but leanprover/lean4#2644 made `simp` start noticing
+@[simp, nolint simpNF]
 lemma yonedaEquiv_yoneda_map {X Y : C} (f : X ⟶ Y) : yonedaEquiv (yoneda.map f) = f := by
   rw [yonedaEquiv_apply]
   simp

This reverts commit 26eb2b0a.

@@ -429,8 +429,7 @@ lemma yonedaEquiv_comp' {X : Cᵒᵖ} {F G : Cᵒᵖ ⥤ Type v₁} (α : yoneda
     yonedaEquiv (α ≫ β) = β.app X (yonedaEquiv α) :=
   rfl
 
--- This lemma has always been bad, but leanprover/lean4#2644 made `simp` start noticing
-@[simp, nolint simpNF]
+@[simp]
 lemma yonedaEquiv_yoneda_map {X Y : C} (f : X ⟶ Y) : yonedaEquiv (yoneda.map f) = f := by
   rw [yonedaEquiv_apply]
   simp

This includes all the changes from #7606.

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

@@ -429,7 +429,8 @@ lemma yonedaEquiv_comp' {X : Cᵒᵖ} {F G : Cᵒᵖ ⥤ Type v₁} (α : yoneda
     yonedaEquiv (α ≫ β) = β.app X (yonedaEquiv α) :=
   rfl
 
-@[simp]
+-- This lemma has always been bad, but leanprover/lean4#2644 made `simp` start noticing
+@[simp, nolint simpNF]
 lemma yonedaEquiv_yoneda_map {X Y : C} (f : X ⟶ Y) : yonedaEquiv (yoneda.map f) = f := by
   rw [yonedaEquiv_apply]
   simp

In this PR, it is shown that the shift of a distinguished triangle is a distinguished triangle. It is also shown that in a morphism between distinguished triangles, if two morphisms are isomorphisms, so is the third.

@@ -497,4 +497,10 @@ def curriedYonedaLemma' {C : Type u₁} [SmallCategory C] :
     · aesop_cat
 #align category_theory.curried_yoneda_lemma' CategoryTheory.curriedYonedaLemma'
 
+lemma isIso_of_yoneda_map_bijective {X Y : C} (f : X ⟶ Y)
+    (hf : ∀ (T : C), Function.Bijective (fun (x : T ⟶ X) => x ≫ f)) :
+    IsIso f := by
+  obtain ⟨g, hg : g ≫ f = 𝟙 Y⟩ := (hf Y).2 (𝟙 Y)
+  exact ⟨g, (hf _).1 (by aesop_cat), hg⟩
+
 end CategoryTheory

A linter that throws on seeing a colon at the start of a line, according to the style guideline that says these operators should go before linebreaks.

@@ -485,8 +485,8 @@ def curriedYonedaLemma {C : Type u₁} [SmallCategory C] :
 
 /-- The curried version of yoneda lemma when `C` is small. -/
 def curriedYonedaLemma' {C : Type u₁} [SmallCategory C] :
-    yoneda ⋙ (whiskeringLeft Cᵒᵖ (Cᵒᵖ ⥤ Type u₁)ᵒᵖ (Type u₁)).obj yoneda.op ≅ 𝟭 (Cᵒᵖ ⥤ Type u₁)
-    := by
+    yoneda ⋙ (whiskeringLeft Cᵒᵖ (Cᵒᵖ ⥤ Type u₁)ᵒᵖ (Type u₁)).obj yoneda.op
+      ≅ 𝟭 (Cᵒᵖ ⥤ Type u₁) := by
   refine eqToIso ?_ ≪≫ curry.mapIso (isoWhiskerLeft (Prod.swap _ _)
     (yonedaLemma C ≪≫ isoWhiskerLeft (evaluationUncurried Cᵒᵖ (Type u₁)) uliftFunctorTrivial :_))
     ≪≫ eqToIso ?_

Autoimplicits are highly controversial and also defeat the performance-improving work in #6474.

The intent of this PR is to make autoImplicit opt-in on a per-file basis, by disabling it in the lakefile and enabling it again with set_option autoImplicit true in the few files that rely on it.

That also keeps this PR small, as opposed to attempting to "fix" files to not need it any more.

I claim that many of the uses of autoImplicit in these files are accidental; situations such as:

• Assuming variables are in scope, but pasting the lemma in the wrong section
• Pasting in a lemma from a scratch file without checking to see if the variable names are consistent with the rest of the file
• Making a copy-paste error between lemmas and forgetting to add an explicit arguments.

Having set_option autoImplicit false as the default prevents these types of mistake being made in the 90% of files where autoImplicits are not used at all, and causes them to be caught by CI during review.

I think there were various points during the port where we encouraged porters to delete the universes u v lines; I think having autoparams for universe variables only would cover a lot of the cases we actually use them, while avoiding any real shortcomings.

A Zulip poll (after combining overlapping votes accordingly) was in favor of this change with 5:5:18 as the no:dontcare:yes vote ratio.

While this PR was being reviewed, a handful of files gained some more likely-accidental autoImplicits. In these places, set_option autoImplicit true has been placed locally within a section, rather than at the top of the file.

@@ -21,6 +21,8 @@ Also the Yoneda lemma, `yonedaLemma : (yoneda_pairing C) ≅ (yoneda_evaluation
 * [Stacks: Opposite Categories and the Yoneda Lemma](https://stacks.math.columbia.edu/tag/001L)
 -/
 
+set_option autoImplicit true
+
 
 namespace CategoryTheory
 

@@ -415,6 +415,28 @@ theorem yonedaEquiv_naturality {X Y : C} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda
   simp
 #align category_theory.yoneda_equiv_naturality CategoryTheory.yonedaEquiv_naturality
 
+lemma yonedaEquiv_naturality' {X Y : Cᵒᵖ} {F : Cᵒᵖ ⥤ Type v₁} (f : yoneda.obj (unop X) ⟶ F)
+    (g : X ⟶ Y) : F.map g (yonedaEquiv f) = yonedaEquiv (yoneda.map g.unop ≫ f) :=
+  yonedaEquiv_naturality _ _
+
+lemma yonedaEquiv_comp {X : C} {F G : Cᵒᵖ ⥤ Type v₁} (α : yoneda.obj X ⟶ F) (β : F ⟶ G)  :
+    yonedaEquiv (α ≫ β) = β.app _ (yonedaEquiv α) :=
+  rfl
+
+lemma yonedaEquiv_comp' {X : Cᵒᵖ} {F G : Cᵒᵖ ⥤ Type v₁} (α : yoneda.obj (unop X) ⟶ F) (β : F ⟶ G)  :
+    yonedaEquiv (α ≫ β) = β.app X (yonedaEquiv α) :=
+  rfl
+
+@[simp]
+lemma yonedaEquiv_yoneda_map {X Y : C} (f : X ⟶ Y) : yonedaEquiv (yoneda.map f) = f := by
+  rw [yonedaEquiv_apply]
+  simp
+
+lemma yonedaEquiv_symm_map {X Y : Cᵒᵖ} (f : X ⟶ Y) {F : Cᵒᵖ ⥤ Type v₁} (t : F.obj X) :
+    yonedaEquiv.symm (F.map f t) = yoneda.map f.unop ≫ yonedaEquiv.symm t := by
+  obtain ⟨u, rfl⟩ := yonedaEquiv.surjective t
+  rw [yonedaEquiv_naturality', Equiv.symm_apply_apply, Equiv.symm_apply_apply]
+
 /-- When `C` is a small category, we can restate the isomorphism from `yoneda_sections`
 without having to change universes.
 -/

@@ -335,7 +335,7 @@ theorem yonedaPairing_map (P Q : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁)) (α : P ⟶
   rfl
 #align category_theory.yoneda_pairing_map CategoryTheory.yonedaPairing_map
 
-/-- The Yoneda lemma asserts that that the Yoneda pairing
+/-- The Yoneda lemma asserts that the Yoneda pairing
 `(X : Cᵒᵖ, F : Cᵒᵖ ⥤ Type) ↦ (yoneda.obj (unop X) ⟶ F)`
 is naturally isomorphic to the evaluation `(X, F) ↦ F.obj X`.
 

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2017 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 category_theory.yoneda
-! leanprover-community/mathlib commit 369525b73f229ccd76a6ec0e0e0bf2be57599768
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Functor.Hom
 import Mathlib.CategoryTheory.Functor.Currying
 import Mathlib.CategoryTheory.Products.Basic
 
+#align_import category_theory.yoneda from "leanprover-community/mathlib"@"369525b73f229ccd76a6ec0e0e0bf2be57599768"
+
 /-!
 # The Yoneda embedding
 

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

@@ -325,6 +325,13 @@ def yonedaPairing : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁) ⥤ Type max u₁ v₁ :=
   Functor.prod yoneda.op (𝟭 (Cᵒᵖ ⥤ Type v₁)) ⋙ Functor.hom (Cᵒᵖ ⥤ Type v₁)
 #align category_theory.yoneda_pairing CategoryTheory.yonedaPairing
 
+-- Porting note: we need to provide this `@[ext]` lemma separately,
+-- as `ext` will not look through the definition.
+-- See https://github.com/leanprover-community/mathlib4/issues/5229
+@[ext]
+lemma yonedaPairingExt {x y : (yonedaPairing C).obj X} (w : ∀ Y, x.app Y = y.app Y) : x = y :=
+  NatTrans.ext _ _ (funext w)
+
 @[simp]
 theorem yonedaPairing_map (P Q : Cᵒᵖ × (Cᵒᵖ ⥤ Type v₁)) (α : P ⟶ Q) (β : (yonedaPairing C).obj P) :
     (yonedaPairing C).map α β = yoneda.map α.1.unop ≫ β ≫ α.2 :=
@@ -341,26 +348,35 @@ def yonedaLemma : yonedaPairing C ≅ yonedaEvaluation C where
   hom :=
     { app := fun F x => ULift.up ((x.app F.1) (𝟙 (unop F.1)))
       naturality := by
-        intro X Y f; simp only [yonedaEvaluation]; funext; dsimp
+        intro X Y f
+        simp only [yonedaEvaluation]
+        ext
+        dsimp
         erw [Category.id_comp, ←FunctorToTypes.naturality]
         simp only [Category.comp_id, yoneda_obj_map] }
   inv :=
     { app := fun F x =>
         { app := fun X a => (F.2.map a.op) x.down
           naturality := by
-            intro X Y f; funext; dsimp
+            intro X Y f
+            ext
+            dsimp
             rw [FunctorToTypes.map_comp_apply] }
       naturality := by
-        intro X Y f; simp only [yoneda]; funext; apply NatTrans.ext; funext; funext; dsimp
+        intro X Y f
+        simp only [yoneda]
+        ext
+        dsimp
         rw [←FunctorToTypes.naturality X.snd Y.snd f.snd, FunctorToTypes.map_comp_apply] }
   hom_inv_id := by
-    apply NatTrans.ext; funext; funext;
-    apply NatTrans.ext; funext; funext; dsimp
+    ext
+    dsimp
     erw [← FunctorToTypes.naturality, obj_map_id]
     simp only [yoneda_map_app, Quiver.Hom.unop_op]
     erw [Category.id_comp]
   inv_hom_id := by
-    apply NatTrans.ext; funext; funext; dsimp
+    ext
+    dsimp
     rw [FunctorToTypes.map_id_apply, ULift.up_down]
 #align category_theory.yoneda_lemma CategoryTheory.yonedaLemma
 
@@ -434,23 +450,12 @@ def curriedYonedaLemma {C : Type u₁} [SmallCategory C] :
     eqToIso ?_
   · apply Functor.ext
     · intro X Y f
-      simp only [curry, yoneda, coyoneda, curryObj, yonedaPairing]
-      dsimp
-      apply NatTrans.ext
-      dsimp at *
-      funext F g
-      apply NatTrans.ext
+      ext
       simp
-    · intro X
-      simp only [curry, yoneda, coyoneda, curryObj, yonedaPairing]
-      aesop_cat
+    · aesop_cat
   · apply Functor.ext
     · intro X Y f
-      simp only [curry, yoneda, coyoneda, curryObj, yonedaPairing]
-      dsimp
-      apply NatTrans.ext
-      dsimp at *
-      funext F g
+      ext
       simp
     · intro X
       simp only [curry, yoneda, coyoneda, curryObj, yonedaPairing]
@@ -466,11 +471,9 @@ def curriedYonedaLemma' {C : Type u₁} [SmallCategory C] :
     ≪≫ eqToIso ?_
   · apply Functor.ext
     · intro X Y f
-      simp only [curry, yoneda, coyoneda, curryObj, yonedaPairing]
       aesop_cat
   · apply Functor.ext
-    · intro X Y f
-      aesop_cat
+    · aesop_cat
 #align category_theory.curried_yoneda_lemma' CategoryTheory.curriedYonedaLemma'
 
 end CategoryTheory

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

@@ -162,7 +162,7 @@ See <https://stacks.math.columbia.edu/tag/001Q>.
 -/
 class Representable (F : Cᵒᵖ ⥤ Type v₁) : Prop where
   /-- `Hom(-,X) ≅ F` via `f` -/
-  has_representation : ∃ (X : _)(f : yoneda.obj X ⟶ F), IsIso f
+  has_representation : ∃ (X : _) (f : yoneda.obj X ⟶ F), IsIso f
 #align category_theory.functor.representable CategoryTheory.Functor.Representable
 
 instance {X : C} : Representable (yoneda.obj X) where has_representation := ⟨X, 𝟙 _, inferInstance⟩
@@ -173,7 +173,7 @@ See <https://stacks.math.columbia.edu/tag/001Q>.
 -/
 class Corepresentable (F : C ⥤ Type v₁) : Prop where
   /-- `Hom(X,-) ≅ F` via `f` -/
-  has_corepresentation : ∃ (X : _)(f : coyoneda.obj X ⟶ F), IsIso f
+  has_corepresentation : ∃ (X : _) (f : coyoneda.obj X ⟶ F), IsIso f
 #align category_theory.functor.corepresentable CategoryTheory.Functor.Corepresentable
 
 instance {X : Cᵒᵖ} : Corepresentable (coyoneda.obj X) where
@@ -189,7 +189,7 @@ variable [F.Representable]
 
 /-- The representing object for the representable functor `F`. -/
 noncomputable def reprX : C :=
-  (Representable.has_representation : ∃ (_ : _)(_ : _ ⟶ F), _).choose
+  (Representable.has_representation : ∃ (_ : _) (_ : _ ⟶ F), _).choose
 set_option linter.uppercaseLean3 false
 #align category_theory.functor.repr_X CategoryTheory.Functor.reprX
 
@@ -238,7 +238,7 @@ variable [F.Corepresentable]
 
 /-- The representing object for the corepresentable functor `F`. -/
 noncomputable def coreprX : C :=
-  (Corepresentable.has_corepresentation : ∃ (_ : _)(_ : _ ⟶ F), _).choose.unop
+  (Corepresentable.has_corepresentation : ∃ (_ : _) (_ : _ ⟶ F), _).choose.unop
 set_option linter.uppercaseLean3 false
 #align category_theory.functor.corepr_X CategoryTheory.Functor.coreprX
 

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

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

@@ -42,14 +42,9 @@ See <https://stacks.math.columbia.edu/tag/001O>.
 def yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁ where
   obj X :=
     { obj := fun Y => unop Y ⟶ X
-      map := fun f g => f.unop ≫ g
-      map_comp := fun f g => by funext; dsimp; erw [Category.assoc]
-      map_id := fun Y => by funext; dsimp; erw [Category.id_comp] }
+      map := fun f g => f.unop ≫ g }
   map f :=
-    { app := fun Y g => g ≫ f
-      naturality := fun Y Y' g => by funext Z; aesop_cat }
-  map_id := by aesop_cat
-  map_comp f g := by ext Y; dsimp; rw [Category.assoc]
+    { app := fun Y g => g ≫ f }
 #align category_theory.yoneda CategoryTheory.yoneda
 
 /-- The co-Yoneda embedding, as a functor from `Cᵒᵖ` into co-presheaves on `C`.
@@ -58,12 +53,9 @@ def yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁ where
 def coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁ where
   obj X :=
     { obj := fun Y => unop X ⟶ Y
-      map := fun f g => g ≫ f
-      map_comp := fun f g => by funext; dsimp; erw [Category.assoc]
-      map_id := fun Y => by funext; dsimp; erw [Category.comp_id] }
+      map := fun f g => g ≫ f }
   map f :=
-    { app := fun Y g => f.unop ≫ g
-      naturality := fun Y Y' g => by funext Z; aesop_cat }
+    { app := fun Y g => f.unop ≫ g }
 #align category_theory.coyoneda CategoryTheory.coyoneda
 
 namespace Yoneda
@@ -86,7 +78,6 @@ See <https://stacks.math.columbia.edu/tag/001P>.
 -/
 instance yonedaFull : Full (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁) where
   preimage {X} {Y} f := f.app (op X) (𝟙 X)
-  witness {X} {Y} f := by simp only [yoneda]; aesop_cat
 #align category_theory.yoneda.yoneda_full CategoryTheory.Yoneda.yonedaFull
 
 /-- The Yoneda embedding is faithful.
@@ -110,13 +101,9 @@ def ext (X Y : C) (p : ∀ {Z : C}, (Z ⟶ X) → (Z ⟶ Y)) (q : ∀ {Z : C}, (
     (h₁ : ∀ {Z : C} (f : Z ⟶ X), q (p f) = f) (h₂ : ∀ {Z : C} (f : Z ⟶ Y), p (q f) = f)
     (n : ∀ {Z Z' : C} (f : Z' ⟶ Z) (g : Z ⟶ X), p (f ≫ g) = f ≫ p g) : X ≅ Y :=
   yoneda.preimageIso
-    (NatIso.ofComponents
-      (fun Z =>
-        { hom := p
-          inv := q
-          hom_inv_id := by simp only [yoneda]; funext; apply h₁
-          inv_hom_id := by simp only [yoneda]; funext; apply h₂ })
-      (fun f => by simp only [yoneda]; funext; apply n))
+    (NatIso.ofComponents fun Z =>
+      { hom := p
+        inv := q })
 #align category_theory.yoneda.ext CategoryTheory.Yoneda.ext
 
 /-- If `yoneda.map f` is an isomorphism, so was `f`.
@@ -154,17 +141,15 @@ theorem isIso {X Y : Cᵒᵖ} (f : X ⟶ Y) [IsIso (coyoneda.map f)] : IsIso f :
 
 /-- The identity functor on `Type` is isomorphic to the coyoneda functor coming from `punit`. -/
 def punitIso : coyoneda.obj (Opposite.op PUnit) ≅ 𝟭 (Type v₁) :=
-  NatIso.ofComponents
-    (fun X =>
-      { hom := fun f => f ⟨⟩
-        inv := fun x _ => x })
-    (by aesop_cat)
+  NatIso.ofComponents fun X =>
+    { hom := fun f => f ⟨⟩
+      inv := fun x _ => x }
 #align category_theory.coyoneda.punit_iso CategoryTheory.Coyoneda.punitIso
 
 /-- Taking the `unop` of morphisms is a natural isomorphism. -/
 @[simps!]
 def objOpOp (X : C) : coyoneda.obj (op (op X)) ≅ yoneda.obj X :=
-  NatIso.ofComponents (fun _ => (opEquiv _ _).toIso) fun _ {_Y} _f => rfl
+  NatIso.ofComponents fun _ => (opEquiv _ _).toIso
 #align category_theory.coyoneda.obj_op_op CategoryTheory.Coyoneda.objOpOp
 
 end Coyoneda

Co-authored-by: Wojciech Nawrocki <wjnawrocki@protonmail.com>

@@ -103,7 +103,7 @@ instance yoneda_faithful : Faithful (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁) where
 -- Goal is `X ≅ Y`
 apply yoneda.ext,
 -- Goals are now functions `(Z ⟶ X) → (Z ⟶ Y)`, `(Z ⟶ Y) → (Z ⟶ X)`, and the fact that these
-functions are inverses and natural in `Z`.
+-- functions are inverses and natural in `Z`.
 ```
 -/
 def ext (X Y : C) (p : ∀ {Z : C}, (Z ⟶ X) → (Z ⟶ Y)) (q : ∀ {Z : C}, (Z ⟶ Y) → (Z ⟶ X))

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

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

@@ -279,8 +279,8 @@ noncomputable def coreprW : coyoneda.obj (op F.coreprX) ≅ F :=
   asIso F.coreprF
 #align category_theory.functor.corepr_w CategoryTheory.Functor.coreprW
 
-theorem coreprW_app_hom (X : C) (f : F.coreprX ⟶ X) : (F.coreprW.app X).hom f = F.map f F.coreprx :=
-  by
+theorem coreprW_app_hom (X : C) (f : F.coreprX ⟶ X) :
+    (F.coreprW.app X).hom f = F.map f F.coreprx := by
   change F.coreprF.app X f = (F.coreprF.app F.coreprX ≫ F.map f) (𝟙 F.coreprX)
   rw [← F.coreprF.naturality]
   dsimp

@@ -39,8 +39,7 @@ variable {C : Type u₁} [Category.{v₁} C]
 See <https://stacks.math.columbia.edu/tag/001O>.
 -/
 @[simps]
-def yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁
-    where
+def yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁ where
   obj X :=
     { obj := fun Y => unop Y ⟶ X
       map := fun f g => f.unop ≫ g
@@ -50,14 +49,13 @@ def yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁
     { app := fun Y g => g ≫ f
       naturality := fun Y Y' g => by funext Z; aesop_cat }
   map_id := by aesop_cat
-  map_comp := fun f g => by ext Y; dsimp; rw [Category.assoc];
+  map_comp f g := by ext Y; dsimp; rw [Category.assoc]
 #align category_theory.yoneda CategoryTheory.yoneda
 
 /-- The co-Yoneda embedding, as a functor from `Cᵒᵖ` into co-presheaves on `C`.
 -/
 @[simps]
-def coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁
-    where
+def coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁ where
   obj X :=
     { obj := fun Y => unop X ⟶ Y
       map := fun f g => g ≫ f
@@ -137,10 +135,9 @@ theorem naturality {X Y : Cᵒᵖ} (α : coyoneda.obj X ⟶ coyoneda.obj Y) {Z Z
   (FunctorToTypes.naturality _ _ α f h).symm
 #align category_theory.coyoneda.naturality CategoryTheory.Coyoneda.naturality
 
-instance coyonedaFull : Full (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁)
-    where
-      preimage {X} _ f := (f.app _ (𝟙 X.unop)).op
-      witness {X} {Y} f := by simp only [coyoneda]; aesop_cat
+instance coyonedaFull : Full (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁) where
+  preimage {X} _ f := (f.app _ (𝟙 X.unop)).op
+  witness {X} {Y} f := by simp only [coyoneda]; aesop_cat
 #align category_theory.coyoneda.coyoneda_full CategoryTheory.Coyoneda.coyonedaFull
 
 instance coyoneda_faithful : Faithful (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁) where
@@ -194,8 +191,8 @@ class Corepresentable (F : C ⥤ Type v₁) : Prop where
   has_corepresentation : ∃ (X : _)(f : coyoneda.obj X ⟶ F), IsIso f
 #align category_theory.functor.corepresentable CategoryTheory.Functor.Corepresentable
 
-instance {X : Cᵒᵖ} : Corepresentable (coyoneda.obj X)
-    where has_corepresentation := ⟨X, 𝟙 _, inferInstance⟩
+instance {X : Cᵒᵖ} : Corepresentable (coyoneda.obj X) where
+  has_corepresentation := ⟨X, 𝟙 _, inferInstance⟩
 
 -- instance : corepresentable (𝟭 (Type v₁)) :=
 -- corepresentable_of_nat_iso (op punit) coyoneda.punit_iso
@@ -355,8 +352,7 @@ is naturally isomorphic to the evaluation `(X, F) ↦ F.obj X`.
 
 See <https://stacks.math.columbia.edu/tag/001P>.
 -/
-def yonedaLemma : yonedaPairing C ≅ yonedaEvaluation C
-    where
+def yonedaLemma : yonedaPairing C ≅ yonedaEvaluation C where
   hom :=
     { app := fun F x => ULift.up ((x.app F.1) (𝟙 (unop F.1)))
       naturality := by

This lemma, which was not needed in mathlib3, simplifies several proofs (back to the state they were in in mathlib3).

Note on what's going on here: Lean 3 ext would fall back on "try all ext lemmas" if it failed, and thus it could see through lots of definitional equalities. Lean 4 ext doesn't do this (because it's inefficient) and so we need to add more ext lemmas in order to recover Lean 3 functionality.

@@ -50,7 +50,7 @@ def yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁
     { app := fun Y g => g ≫ f
       naturality := fun Y Y' g => by funext Z; aesop_cat }
   map_id := by aesop_cat
-  map_comp := fun f g => by ext Y; dsimp; funext f; simp
+  map_comp := fun f g => by ext Y; dsimp; rw [Category.assoc];
 #align category_theory.yoneda CategoryTheory.yoneda
 
 /-- The co-Yoneda embedding, as a functor from `Cᵒᵖ` into co-presheaves on `C`.

• There is now configuration for congr!, convert, and convert_to to control parts of the congruence algorithm, in particular transparency settings when applying congruence lemmas.
• congr! now applies congruence lemmas with reducible transparency by default. This prevents it from unfolding definitions when applying congruence lemmas. It also now tries both the LHS-biased and RHS-biased simp congruence lemmas, with a configuration option to set which it should try first.
• There is now a new HEq congruence lemma generator that gives each hypothesis access to the proofs of previous hypotheses. This means that if you have an equality ⊢ ⟨a, x⟩ = ⟨b, y⟩ of sigma types, congr! turns this into goals ⊢ a = b and ⊢ a = b → HEq x y (note that congr! will also auto-introduce a = b for you in the second goal). This congruence lemma generator applies to more cases than the simp congruence lemma generator does.
• congr! (and hence convert) are more careful about applying lemmas that don't force definitions to unfold. There were a number of cases in mathlib where the implementation of congr was being abused to unfold definitions.
• With set_option trace.congr! true you can see what congr! sees when it is deciding on congruence lemmas.
• There is also a bug fix in convert_to to do using 1 when there is no using clause, to match its documentation.

Note that congr! is more capable than congr at finding a way to equate left-hand sides and right-hand sides, so you will frequently need to limit its depth with a using clause. However, there is also a new heuristic to prevent considering unlikely-to-be-provable type equalities (controlled by the typeEqs option), which can help limit the depth automatically.

There is also a predefined configuration that you can invoke with, for example, convert (config := .unfoldSameFun) h, that causes it to behave more like congr, including using default transparency when unfolding.

@@ -95,10 +95,9 @@ instance yonedaFull : Full (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁) where
 
 See <https://stacks.math.columbia.edu/tag/001P>.
 -/
-instance yoneda_faithful : Faithful (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁)
-    where
-      map_injective {X} {Y} f g p := by
-        convert congr_fun (congr_app p (op X)) (𝟙 X) <;> dsimp <;> simp
+instance yoneda_faithful : Faithful (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁) where
+  map_injective {X} {Y} f g p := by
+    convert congr_fun (congr_app p (op X)) (𝟙 X) using 1 <;> dsimp <;> simp
 #align category_theory.yoneda.yoneda_faithful CategoryTheory.Yoneda.yoneda_faithful
 
 /-- Extensionality via Yoneda. The typical usage would be

vscode is already configured by .vscode/settings.json to trim these on save. It's not clear how they've managed to stick around.

By doing this all in one PR now, it avoids getting random whitespace diffs in PRs later.

This was done with a regex search in vscode,

@@ -46,11 +46,11 @@ def yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁
       map := fun f g => f.unop ≫ g
       map_comp := fun f g => by funext; dsimp; erw [Category.assoc]
       map_id := fun Y => by funext; dsimp; erw [Category.id_comp] }
-  map f := 
-    { app := fun Y g => g ≫ f 
+  map f :=
+    { app := fun Y g => g ≫ f
       naturality := fun Y Y' g => by funext Z; aesop_cat }
-  map_id := by aesop_cat 
-  map_comp := fun f g => by ext Y; dsimp; funext f; simp 
+  map_id := by aesop_cat
+  map_comp := fun f g => by ext Y; dsimp; funext f; simp
 #align category_theory.yoneda CategoryTheory.yoneda
 
 /-- The co-Yoneda embedding, as a functor from `Cᵒᵖ` into co-presheaves on `C`.
@@ -60,11 +60,11 @@ def coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁
     where
   obj X :=
     { obj := fun Y => unop X ⟶ Y
-      map := fun f g => g ≫ f 
-      map_comp := fun f g => by funext; dsimp; erw [Category.assoc]  
+      map := fun f g => g ≫ f
+      map_comp := fun f g => by funext; dsimp; erw [Category.assoc]
       map_id := fun Y => by funext; dsimp; erw [Category.comp_id] }
-  map f := 
-    { app := fun Y g => f.unop ≫ g 
+  map f :=
+    { app := fun Y g => f.unop ≫ g
       naturality := fun Y Y' g => by funext Z; aesop_cat }
 #align category_theory.coyoneda CategoryTheory.coyoneda
 
@@ -86,9 +86,9 @@ theorem naturality {X Y : C} (α : yoneda.obj X ⟶ yoneda.obj Y) {Z Z' : C} (f
 
 See <https://stacks.math.columbia.edu/tag/001P>.
 -/
-instance yonedaFull : Full (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁) where 
+instance yonedaFull : Full (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁) where
   preimage {X} {Y} f := f.app (op X) (𝟙 X)
-  witness {X} {Y} f := by simp only [yoneda]; aesop_cat 
+  witness {X} {Y} f := by simp only [yoneda]; aesop_cat
 #align category_theory.yoneda.yoneda_full CategoryTheory.Yoneda.yonedaFull
 
 /-- The Yoneda embedding is faithful.
@@ -96,7 +96,7 @@ instance yonedaFull : Full (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁) where
 See <https://stacks.math.columbia.edu/tag/001P>.
 -/
 instance yoneda_faithful : Faithful (yoneda : C ⥤ Cᵒᵖ ⥤ Type v₁)
-    where 
+    where
       map_injective {X} {Y} f g p := by
         convert congr_fun (congr_app p (op X)) (𝟙 X) <;> dsimp <;> simp
 #align category_theory.yoneda.yoneda_faithful CategoryTheory.Yoneda.yoneda_faithful
@@ -117,8 +117,8 @@ def ext (X Y : C) (p : ∀ {Z : C}, (Z ⟶ X) → (Z ⟶ Y)) (q : ∀ {Z : C}, (
       (fun Z =>
         { hom := p
           inv := q
-          hom_inv_id := by simp only [yoneda]; funext; apply h₁ 
-          inv_hom_id := by simp only [yoneda]; funext; apply h₂ }) 
+          hom_inv_id := by simp only [yoneda]; funext; apply h₁
+          inv_hom_id := by simp only [yoneda]; funext; apply h₂ })
       (fun f => by simp only [yoneda]; funext; apply n))
 #align category_theory.yoneda.ext CategoryTheory.Yoneda.ext
 
@@ -139,12 +139,12 @@ theorem naturality {X Y : Cᵒᵖ} (α : coyoneda.obj X ⟶ coyoneda.obj Y) {Z Z
 #align category_theory.coyoneda.naturality CategoryTheory.Coyoneda.naturality
 
 instance coyonedaFull : Full (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁)
-    where 
+    where
       preimage {X} _ f := (f.app _ (𝟙 X.unop)).op
       witness {X} {Y} f := by simp only [coyoneda]; aesop_cat
 #align category_theory.coyoneda.coyoneda_full CategoryTheory.Coyoneda.coyonedaFull
 
-instance coyoneda_faithful : Faithful (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁) where 
+instance coyoneda_faithful : Faithful (coyoneda : Cᵒᵖ ⥤ C ⥤ Type v₁) where
   map_injective {X} _ _ _ p := by
     have t := congr_fun (congr_app p X.unop) (𝟙 _)
     simpa using congr_arg Quiver.Hom.op t
@@ -209,7 +209,7 @@ variable [F.Representable]
 /-- The representing object for the representable functor `F`. -/
 noncomputable def reprX : C :=
   (Representable.has_representation : ∃ (_ : _)(_ : _ ⟶ F), _).choose
-set_option linter.uppercaseLean3 false 
+set_option linter.uppercaseLean3 false
 #align category_theory.functor.repr_X CategoryTheory.Functor.reprX
 
 /-- The (forward direction of the) isomorphism witnessing `F` is representable. -/
@@ -258,7 +258,7 @@ variable [F.Corepresentable]
 /-- The representing object for the corepresentable functor `F`. -/
 noncomputable def coreprX : C :=
   (Corepresentable.has_corepresentation : ∃ (_ : _)(_ : _ ⟶ F), _).choose.unop
-set_option linter.uppercaseLean3 false 
+set_option linter.uppercaseLean3 false
 #align category_theory.functor.corepr_X CategoryTheory.Functor.coreprX
 
 /-- The (forward direction of the) isomorphism witnessing `F` is corepresentable. -/
@@ -361,7 +361,7 @@ def yonedaLemma : yonedaPairing C ≅ yonedaEvaluation C
   hom :=
     { app := fun F x => ULift.up ((x.app F.1) (𝟙 (unop F.1)))
       naturality := by
-        intro X Y f; simp only [yonedaEvaluation]; funext; dsimp 
+        intro X Y f; simp only [yonedaEvaluation]; funext; dsimp
         erw [Category.id_comp, ←FunctorToTypes.naturality]
         simp only [Category.comp_id, yoneda_obj_map] }
   inv :=
@@ -374,7 +374,7 @@ def yonedaLemma : yonedaPairing C ≅ yonedaEvaluation C
         intro X Y f; simp only [yoneda]; funext; apply NatTrans.ext; funext; funext; dsimp
         rw [←FunctorToTypes.naturality X.snd Y.snd f.snd, FunctorToTypes.map_comp_apply] }
   hom_inv_id := by
-    apply NatTrans.ext; funext; funext; 
+    apply NatTrans.ext; funext; funext;
     apply NatTrans.ext; funext; funext; dsimp
     erw [← FunctorToTypes.naturality, obj_map_id]
     simp only [yoneda_map_app, Quiver.Hom.unop_op]
@@ -448,50 +448,49 @@ attribute [local ext] Functor.ext
 /- Porting note: this used to be two calls to `tidy` -/
 /-- The curried version of yoneda lemma when `C` is small. -/
 def curriedYonedaLemma {C : Type u₁} [SmallCategory C] :
-    (yoneda.op ⋙ coyoneda : Cᵒᵖ ⥤ (Cᵒᵖ ⥤ Type u₁) ⥤ Type u₁) ≅ evaluation Cᵒᵖ (Type u₁) := by 
-  refine eqToIso ?_ ≪≫ curry.mapIso 
+    (yoneda.op ⋙ coyoneda : Cᵒᵖ ⥤ (Cᵒᵖ ⥤ Type u₁) ⥤ Type u₁) ≅ evaluation Cᵒᵖ (Type u₁) := by
+  refine eqToIso ?_ ≪≫ curry.mapIso
     (yonedaLemma C ≪≫ isoWhiskerLeft (evaluationUncurried Cᵒᵖ (Type u₁)) uliftFunctorTrivial) ≪≫
     eqToIso ?_
-  · apply Functor.ext 
-    · intro X Y f 
+  · apply Functor.ext
+    · intro X Y f
       simp only [curry, yoneda, coyoneda, curryObj, yonedaPairing]
-      dsimp 
-      apply NatTrans.ext 
+      dsimp
+      apply NatTrans.ext
       dsimp at *
-      funext F g 
-      apply NatTrans.ext 
-      simp 
-    · intro X 
+      funext F g
+      apply NatTrans.ext
+      simp
+    · intro X
       simp only [curry, yoneda, coyoneda, curryObj, yonedaPairing]
       aesop_cat
   · apply Functor.ext
-    · intro X Y f 
+    · intro X Y f
       simp only [curry, yoneda, coyoneda, curryObj, yonedaPairing]
-      dsimp 
-      apply NatTrans.ext 
+      dsimp
+      apply NatTrans.ext
       dsimp at *
-      funext F g 
-      simp 
-    · intro X 
+      funext F g
+      simp
+    · intro X
       simp only [curry, yoneda, coyoneda, curryObj, yonedaPairing]
-      aesop_cat 
+      aesop_cat
 #align category_theory.curried_yoneda_lemma CategoryTheory.curriedYonedaLemma
 
 /-- The curried version of yoneda lemma when `C` is small. -/
 def curriedYonedaLemma' {C : Type u₁} [SmallCategory C] :
-    yoneda ⋙ (whiskeringLeft Cᵒᵖ (Cᵒᵖ ⥤ Type u₁)ᵒᵖ (Type u₁)).obj yoneda.op ≅ 𝟭 (Cᵒᵖ ⥤ Type u₁) 
-    := by 
+    yoneda ⋙ (whiskeringLeft Cᵒᵖ (Cᵒᵖ ⥤ Type u₁)ᵒᵖ (Type u₁)).obj yoneda.op ≅ 𝟭 (Cᵒᵖ ⥤ Type u₁)
+    := by
   refine eqToIso ?_ ≪≫ curry.mapIso (isoWhiskerLeft (Prod.swap _ _)
-    (yonedaLemma C ≪≫ isoWhiskerLeft (evaluationUncurried Cᵒᵖ (Type u₁)) uliftFunctorTrivial :_)) 
+    (yonedaLemma C ≪≫ isoWhiskerLeft (evaluationUncurried Cᵒᵖ (Type u₁)) uliftFunctorTrivial :_))
     ≪≫ eqToIso ?_
-  · apply Functor.ext 
-    · intro X Y f 
+  · apply Functor.ext
+    · intro X Y f
       simp only [curry, yoneda, coyoneda, curryObj, yonedaPairing]
       aesop_cat
   · apply Functor.ext
-    · intro X Y f 
+    · intro X Y f
       aesop_cat
 #align category_theory.curried_yoneda_lemma' CategoryTheory.curriedYonedaLemma'
 
 end CategoryTheory
-