category_theory.eq_to_hom | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

dc6c365e

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

34ee86e6

bump to nightly-2024-04-26-08

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

ab3b6a0f

Diff

@@ -225,10 +225,8 @@ theorem congr_inv_of_congr_hom (F G : C ⥤ D) {X Y : C} (e : X ≅ Y) (hX : F.o
 #align category_theory.functor.congr_inv_of_congr_hom CategoryTheory.Functor.congr_inv_of_congr_hom
 -/
 
-#print CategoryTheory.Functor.congr_map /-
 theorem congr_map (F : C ⥤ D) {X Y : C} {f g : X ⟶ Y} (h : f = g) : F.map f = F.map g := by rw [h]
 #align category_theory.functor.congr_map CategoryTheory.Functor.congr_map
--/
 
 section HEq

34ee86e6

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2018 Reid Barton. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Scott Morrison
 -/
-import Mathbin.CategoryTheory.Opposites
+import CategoryTheory.Opposites
 
 #align_import category_theory.eq_to_hom from "leanprover-community/mathlib"@"34ee86e6a59d911a8e4f89b68793ee7577ae79c7"

34ee86e6

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2018 Reid Barton. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.eq_to_hom
-! leanprover-community/mathlib commit 34ee86e6a59d911a8e4f89b68793ee7577ae79c7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Opposites
 
+#align_import category_theory.eq_to_hom from "leanprover-community/mathlib"@"34ee86e6a59d911a8e4f89b68793ee7577ae79c7"
+
 /-!
 # Morphisms from equations between objects.

34ee86e6

bump to nightly-2023-07-07-15

mathlib commit https://github.com/leanprover-community/mathlib/commit/8905e5ed90859939681a725b00f6063e65096d95

b75f01fb

Diff

@@ -190,18 +190,18 @@ theorem ext {F G : C ⥤ D} (h_obj : ∀ X, F.obj X = G.obj X)
 #align category_theory.functor.ext CategoryTheory.Functor.ext
 -/
 
-#print CategoryTheory.Functor.conj_eqToHom_iff_hEq /-
+#print CategoryTheory.Functor.conj_eqToHom_iff_heq /-
 /-- Two morphisms are conjugate via eq_to_hom if and only if they are heterogeneously equal. -/
-theorem conj_eqToHom_iff_hEq {W X Y Z : C} (f : W ⟶ X) (g : Y ⟶ Z) (h : W = Y) (h' : X = Z) :
+theorem conj_eqToHom_iff_heq {W X Y Z : C} (f : W ⟶ X) (g : Y ⟶ Z) (h : W = Y) (h' : X = Z) :
     f = eqToHom h ≫ g ≫ eqToHom h'.symm ↔ HEq f g := by cases h; cases h'; simp
-#align category_theory.functor.conj_eq_to_hom_iff_heq CategoryTheory.Functor.conj_eqToHom_iff_hEq
+#align category_theory.functor.conj_eq_to_hom_iff_heq CategoryTheory.Functor.conj_eqToHom_iff_heq
 -/
 
 #print CategoryTheory.Functor.hext /-
 /-- Proving equality between functors using heterogeneous equality. -/
 theorem hext {F G : C ⥤ D} (h_obj : ∀ X, F.obj X = G.obj X)
     (h_map : ∀ (X Y) (f : X ⟶ Y), HEq (F.map f) (G.map f)) : F = G :=
-  Functor.ext h_obj fun _ _ f => (conj_eqToHom_iff_hEq _ _ (h_obj _) (h_obj _)).2 <| h_map _ _ f
+  Functor.ext h_obj fun _ _ f => (conj_eqToHom_iff_heq _ _ (h_obj _) (h_obj _)).2 <| h_map _ _ f
 #align category_theory.functor.hext CategoryTheory.Functor.hext
 -/
 
@@ -238,38 +238,38 @@ section HEq
 -- Composition of functors and maps w.r.t. heq
 variable {E : Type u₃} [Category.{v₃} E] {F G : C ⥤ D} {X Y Z : C} {f : X ⟶ Y} {g : Y ⟶ Z}
 
-#print CategoryTheory.Functor.map_comp_hEq /-
-theorem map_comp_hEq (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y) (hz : F.obj Z = G.obj Z)
+#print CategoryTheory.Functor.map_comp_heq /-
+theorem map_comp_heq (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y) (hz : F.obj Z = G.obj Z)
     (hf : HEq (F.map f) (G.map f)) (hg : HEq (F.map g) (G.map g)) :
     HEq (F.map (f ≫ g)) (G.map (f ≫ g)) := by rw [F.map_comp, G.map_comp]; congr
-#align category_theory.functor.map_comp_heq CategoryTheory.Functor.map_comp_hEq
+#align category_theory.functor.map_comp_heq CategoryTheory.Functor.map_comp_heq
 -/
 
-#print CategoryTheory.Functor.map_comp_hEq' /-
-theorem map_comp_hEq' (hobj : ∀ X : C, F.obj X = G.obj X)
+#print CategoryTheory.Functor.map_comp_heq' /-
+theorem map_comp_heq' (hobj : ∀ X : C, F.obj X = G.obj X)
     (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) : HEq (F.map (f ≫ g)) (G.map (f ≫ g)) :=
   by rw [functor.hext hobj fun _ _ => hmap]
-#align category_theory.functor.map_comp_heq' CategoryTheory.Functor.map_comp_hEq'
+#align category_theory.functor.map_comp_heq' CategoryTheory.Functor.map_comp_heq'
 -/
 
-#print CategoryTheory.Functor.precomp_map_hEq /-
-theorem precomp_map_hEq (H : E ⥤ C) (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) {X Y : E}
+#print CategoryTheory.Functor.precomp_map_heq /-
+theorem precomp_map_heq (H : E ⥤ C) (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) {X Y : E}
     (f : X ⟶ Y) : HEq ((H ⋙ F).map f) ((H ⋙ G).map f) :=
   hmap _
-#align category_theory.functor.precomp_map_heq CategoryTheory.Functor.precomp_map_hEq
+#align category_theory.functor.precomp_map_heq CategoryTheory.Functor.precomp_map_heq
 -/
 
-#print CategoryTheory.Functor.postcomp_map_hEq /-
-theorem postcomp_map_hEq (H : D ⥤ E) (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y)
+#print CategoryTheory.Functor.postcomp_map_heq /-
+theorem postcomp_map_heq (H : D ⥤ E) (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y)
     (hmap : HEq (F.map f) (G.map f)) : HEq ((F ⋙ H).map f) ((G ⋙ H).map f) := by dsimp; congr
-#align category_theory.functor.postcomp_map_heq CategoryTheory.Functor.postcomp_map_hEq
+#align category_theory.functor.postcomp_map_heq CategoryTheory.Functor.postcomp_map_heq
 -/
 
-#print CategoryTheory.Functor.postcomp_map_hEq' /-
-theorem postcomp_map_hEq' (H : D ⥤ E) (hobj : ∀ X : C, F.obj X = G.obj X)
+#print CategoryTheory.Functor.postcomp_map_heq' /-
+theorem postcomp_map_heq' (H : D ⥤ E) (hobj : ∀ X : C, F.obj X = G.obj X)
     (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) : HEq ((F ⋙ H).map f) ((G ⋙ H).map f) :=
   by rw [functor.hext hobj fun _ _ => hmap]
-#align category_theory.functor.postcomp_map_heq' CategoryTheory.Functor.postcomp_map_hEq'
+#align category_theory.functor.postcomp_map_heq' CategoryTheory.Functor.postcomp_map_heq'
 -/
 
 #print CategoryTheory.Functor.hcongr_hom /-

34ee86e6

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -176,6 +176,7 @@ variable {D : Type u₂} [Category.{v₂} D]
 
 namespace Functor
 
+#print CategoryTheory.Functor.ext /-
 /-- Proving equality between functors. This isn't an extensionality lemma,
   because usually you don't really want to do this. -/
 theorem ext {F G : C ⥤ D} (h_obj : ∀ X, F.obj X = G.obj X)
@@ -187,6 +188,7 @@ theorem ext {F G : C ⥤ D} (h_obj : ∀ X, F.obj X = G.obj X)
   funext X Y f
   simpa using h_map X Y f
 #align category_theory.functor.ext CategoryTheory.Functor.ext
+-/
 
 #print CategoryTheory.Functor.conj_eqToHom_iff_hEq /-
 /-- Two morphisms are conjugate via eq_to_hom if and only if they are heterogeneously equal. -/
@@ -195,21 +197,28 @@ theorem conj_eqToHom_iff_hEq {W X Y Z : C} (f : W ⟶ X) (g : Y ⟶ Z) (h : W =
 #align category_theory.functor.conj_eq_to_hom_iff_heq CategoryTheory.Functor.conj_eqToHom_iff_hEq
 -/
 
+#print CategoryTheory.Functor.hext /-
 /-- Proving equality between functors using heterogeneous equality. -/
 theorem hext {F G : C ⥤ D} (h_obj : ∀ X, F.obj X = G.obj X)
     (h_map : ∀ (X Y) (f : X ⟶ Y), HEq (F.map f) (G.map f)) : F = G :=
   Functor.ext h_obj fun _ _ f => (conj_eqToHom_iff_hEq _ _ (h_obj _) (h_obj _)).2 <| h_map _ _ f
 #align category_theory.functor.hext CategoryTheory.Functor.hext
+-/
 
+#print CategoryTheory.Functor.congr_obj /-
 -- Using equalities between functors.
 theorem congr_obj {F G : C ⥤ D} (h : F = G) (X) : F.obj X = G.obj X := by subst h
 #align category_theory.functor.congr_obj CategoryTheory.Functor.congr_obj
+-/
 
+#print CategoryTheory.Functor.congr_hom /-
 theorem congr_hom {F G : C ⥤ D} (h : F = G) {X Y} (f : X ⟶ Y) :
     F.map f = eqToHom (congr_obj h X) ≫ G.map f ≫ eqToHom (congr_obj h Y).symm := by
   subst h <;> simp
 #align category_theory.functor.congr_hom CategoryTheory.Functor.congr_hom
+-/
 
+#print CategoryTheory.Functor.congr_inv_of_congr_hom /-
 theorem congr_inv_of_congr_hom (F G : C ⥤ D) {X Y : C} (e : X ≅ Y) (hX : F.obj X = G.obj X)
     (hY : F.obj Y = G.obj Y)
     (h₂ : F.map e.Hom = eqToHom (by rw [hX]) ≫ G.map e.Hom ≫ eqToHom (by rw [hY])) :
@@ -217,47 +226,63 @@ theorem congr_inv_of_congr_hom (F G : C ⥤ D) {X Y : C} (e : X ≅ Y) (hX : F.o
   simp only [← is_iso.iso.inv_hom e, functor.map_inv, h₂, is_iso.inv_comp, inv_eq_to_hom,
     category.assoc]
 #align category_theory.functor.congr_inv_of_congr_hom CategoryTheory.Functor.congr_inv_of_congr_hom
+-/
 
+#print CategoryTheory.Functor.congr_map /-
 theorem congr_map (F : C ⥤ D) {X Y : C} {f g : X ⟶ Y} (h : f = g) : F.map f = F.map g := by rw [h]
 #align category_theory.functor.congr_map CategoryTheory.Functor.congr_map
+-/
 
 section HEq
 
 -- Composition of functors and maps w.r.t. heq
 variable {E : Type u₃} [Category.{v₃} E] {F G : C ⥤ D} {X Y Z : C} {f : X ⟶ Y} {g : Y ⟶ Z}
 
+#print CategoryTheory.Functor.map_comp_hEq /-
 theorem map_comp_hEq (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y) (hz : F.obj Z = G.obj Z)
     (hf : HEq (F.map f) (G.map f)) (hg : HEq (F.map g) (G.map g)) :
     HEq (F.map (f ≫ g)) (G.map (f ≫ g)) := by rw [F.map_comp, G.map_comp]; congr
 #align category_theory.functor.map_comp_heq CategoryTheory.Functor.map_comp_hEq
+-/
 
+#print CategoryTheory.Functor.map_comp_hEq' /-
 theorem map_comp_hEq' (hobj : ∀ X : C, F.obj X = G.obj X)
     (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) : HEq (F.map (f ≫ g)) (G.map (f ≫ g)) :=
   by rw [functor.hext hobj fun _ _ => hmap]
 #align category_theory.functor.map_comp_heq' CategoryTheory.Functor.map_comp_hEq'
+-/
 
+#print CategoryTheory.Functor.precomp_map_hEq /-
 theorem precomp_map_hEq (H : E ⥤ C) (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) {X Y : E}
     (f : X ⟶ Y) : HEq ((H ⋙ F).map f) ((H ⋙ G).map f) :=
   hmap _
 #align category_theory.functor.precomp_map_heq CategoryTheory.Functor.precomp_map_hEq
+-/
 
+#print CategoryTheory.Functor.postcomp_map_hEq /-
 theorem postcomp_map_hEq (H : D ⥤ E) (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y)
     (hmap : HEq (F.map f) (G.map f)) : HEq ((F ⋙ H).map f) ((G ⋙ H).map f) := by dsimp; congr
 #align category_theory.functor.postcomp_map_heq CategoryTheory.Functor.postcomp_map_hEq
+-/
 
+#print CategoryTheory.Functor.postcomp_map_hEq' /-
 theorem postcomp_map_hEq' (H : D ⥤ E) (hobj : ∀ X : C, F.obj X = G.obj X)
     (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) : HEq ((F ⋙ H).map f) ((G ⋙ H).map f) :=
   by rw [functor.hext hobj fun _ _ => hmap]
 #align category_theory.functor.postcomp_map_heq' CategoryTheory.Functor.postcomp_map_hEq'
+-/
 
+#print CategoryTheory.Functor.hcongr_hom /-
 theorem hcongr_hom {F G : C ⥤ D} (h : F = G) {X Y} (f : X ⟶ Y) : HEq (F.map f) (G.map f) := by
   subst h
 #align category_theory.functor.hcongr_hom CategoryTheory.Functor.hcongr_hom
+-/
 
 end HEq
 
 end Functor
 
+#print CategoryTheory.eqToHom_map /-
 /-- This is not always a good idea as a `@[simp]` lemma,
 as we lose the ability to use results that interact with `F`,
 e.g. the naturality of a natural transformation.
@@ -267,22 +292,29 @@ In some files it may be appropriate to use `local attribute [simp] eq_to_hom_map
 theorem eqToHom_map (F : C ⥤ D) {X Y : C} (p : X = Y) :
     F.map (eqToHom p) = eqToHom (congr_arg F.obj p) := by cases p <;> simp
 #align category_theory.eq_to_hom_map CategoryTheory.eqToHom_map
+-/
 
+#print CategoryTheory.eqToIso_map /-
 /-- See the note on `eq_to_hom_map` regarding using this as a `simp` lemma.
 -/
 theorem eqToIso_map (F : C ⥤ D) {X Y : C} (p : X = Y) :
     F.mapIso (eqToIso p) = eqToIso (congr_arg F.obj p) := by ext <;> cases p <;> simp
 #align category_theory.eq_to_iso_map CategoryTheory.eqToIso_map
+-/
 
+#print CategoryTheory.eqToHom_app /-
 @[simp]
 theorem eqToHom_app {F G : C ⥤ D} (h : F = G) (X : C) :
     (eqToHom h : F ⟶ G).app X = eqToHom (Functor.congr_obj h X) := by subst h <;> rfl
 #align category_theory.eq_to_hom_app CategoryTheory.eqToHom_app
+-/
 
+#print CategoryTheory.NatTrans.congr /-
 theorem NatTrans.congr {F G : C ⥤ D} (α : F ⟶ G) {X Y : C} (h : X = Y) :
     α.app X = F.map (eqToHom h) ≫ α.app Y ≫ G.map (eqToHom h.symm) := by rw [α.naturality_assoc];
   simp [eq_to_hom_map]
 #align category_theory.nat_trans.congr CategoryTheory.NatTrans.congr
+-/
 
 #print CategoryTheory.eq_conj_eqToHom /-
 theorem eq_conj_eqToHom {X Y : C} (f : X ⟶ Y) : f = eqToHom rfl ≫ f ≫ eqToHom rfl := by
@@ -290,9 +322,11 @@ theorem eq_conj_eqToHom {X Y : C} (f : X ⟶ Y) : f = eqToHom rfl ≫ f ≫ eqTo
 #align category_theory.eq_conj_eq_to_hom CategoryTheory.eq_conj_eqToHom
 -/
 
+#print CategoryTheory.dcongr_arg /-
 theorem dcongr_arg {ι : Type _} {F G : ι → C} (α : ∀ i, F i ⟶ G i) {i j : ι} (h : i = j) :
     α i = eqToHom (congr_arg F h) ≫ α j ≫ eqToHom (congr_arg G h.symm) := by subst h; simp
 #align category_theory.dcongr_arg CategoryTheory.dcongr_arg
+-/
 
 end CategoryTheory

34ee86e6

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -176,12 +176,6 @@ variable {D : Type u₂} [Category.{v₂} D]
 
 namespace Functor
 
-/- warning: category_theory.functor.ext -> CategoryTheory.Functor.ext is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] {F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2} {G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2} (h_obj : forall (X : C), Eq.{succ u4} D (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X)), (forall (X : C) (Y : C) (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y)) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X Y f) (CategoryTheory.CategoryStruct.comp.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y) (CategoryTheory.eqToHom.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X) (h_obj X)) (CategoryTheory.CategoryStruct.comp.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G Y) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X Y f) (CategoryTheory.eqToHom.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G Y) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y) (Eq.symm.{succ u4} D (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G Y) (h_obj Y)))))) -> (Eq.{succ (max u1 u2 u3 u4)} (CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) F G)
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 /-- Proving equality between functors. This isn't an extensionality lemma,
   because usually you don't really want to do this. -/
 theorem ext {F G : C ⥤ D} (h_obj : ∀ X, F.obj X = G.obj X)
@@ -201,42 +195,21 @@ theorem conj_eqToHom_iff_hEq {W X Y Z : C} (f : W ⟶ X) (g : Y ⟶ Z) (h : W =
 #align category_theory.functor.conj_eq_to_hom_iff_heq CategoryTheory.Functor.conj_eqToHom_iff_hEq
 -/
 
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 /-- Proving equality between functors using heterogeneous equality. -/
 theorem hext {F G : C ⥤ D} (h_obj : ∀ X, F.obj X = G.obj X)
     (h_map : ∀ (X Y) (f : X ⟶ Y), HEq (F.map f) (G.map f)) : F = G :=
   Functor.ext h_obj fun _ _ f => (conj_eqToHom_iff_hEq _ _ (h_obj _) (h_obj _)).2 <| h_map _ _ f
 #align category_theory.functor.hext CategoryTheory.Functor.hext
 
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 -- Using equalities between functors.
 theorem congr_obj {F G : C ⥤ D} (h : F = G) (X) : F.obj X = G.obj X := by subst h
 #align category_theory.functor.congr_obj CategoryTheory.Functor.congr_obj
 
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 theorem congr_hom {F G : C ⥤ D} (h : F = G) {X Y} (f : X ⟶ Y) :
     F.map f = eqToHom (congr_obj h X) ≫ G.map f ≫ eqToHom (congr_obj h Y).symm := by
   subst h <;> simp
 #align category_theory.functor.congr_hom CategoryTheory.Functor.congr_hom
 
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-<too large>
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 theorem congr_inv_of_congr_hom (F G : C ⥤ D) {X Y : C} (e : X ≅ Y) (hX : F.obj X = G.obj X)
     (hY : F.obj Y = G.obj Y)
     (h₂ : F.map e.Hom = eqToHom (by rw [hX]) ≫ G.map e.Hom ≫ eqToHom (by rw [hY])) :
@@ -245,12 +218,6 @@ theorem congr_inv_of_congr_hom (F G : C ⥤ D) {X Y : C} (e : X ≅ Y) (hX : F.o
     category.assoc]
 #align category_theory.functor.congr_inv_of_congr_hom CategoryTheory.Functor.congr_inv_of_congr_hom
 
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 theorem congr_map (F : C ⥤ D) {X Y : C} {f g : X ⟶ Y} (h : f = g) : F.map f = F.map g := by rw [h]
 #align category_theory.functor.congr_map CategoryTheory.Functor.congr_map
 
@@ -259,57 +226,30 @@ section HEq
 -- Composition of functors and maps w.r.t. heq
 variable {E : Type u₃} [Category.{v₃} E] {F G : C ⥤ D} {X Y Z : C} {f : X ⟶ Y} {g : Y ⟶ Z}
 
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 theorem map_comp_hEq (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y) (hz : F.obj Z = G.obj Z)
     (hf : HEq (F.map f) (G.map f)) (hg : HEq (F.map g) (G.map g)) :
     HEq (F.map (f ≫ g)) (G.map (f ≫ g)) := by rw [F.map_comp, G.map_comp]; congr
 #align category_theory.functor.map_comp_heq CategoryTheory.Functor.map_comp_hEq
 
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 theorem map_comp_hEq' (hobj : ∀ X : C, F.obj X = G.obj X)
     (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) : HEq (F.map (f ≫ g)) (G.map (f ≫ g)) :=
   by rw [functor.hext hobj fun _ _ => hmap]
 #align category_theory.functor.map_comp_heq' CategoryTheory.Functor.map_comp_hEq'
 
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 theorem precomp_map_hEq (H : E ⥤ C) (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) {X Y : E}
     (f : X ⟶ Y) : HEq ((H ⋙ F).map f) ((H ⋙ G).map f) :=
   hmap _
 #align category_theory.functor.precomp_map_heq CategoryTheory.Functor.precomp_map_hEq
 
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 theorem postcomp_map_hEq (H : D ⥤ E) (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y)
     (hmap : HEq (F.map f) (G.map f)) : HEq ((F ⋙ H).map f) ((G ⋙ H).map f) := by dsimp; congr
 #align category_theory.functor.postcomp_map_heq CategoryTheory.Functor.postcomp_map_hEq
 
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 theorem postcomp_map_hEq' (H : D ⥤ E) (hobj : ∀ X : C, F.obj X = G.obj X)
     (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) : HEq ((F ⋙ H).map f) ((G ⋙ H).map f) :=
   by rw [functor.hext hobj fun _ _ => hmap]
 #align category_theory.functor.postcomp_map_heq' CategoryTheory.Functor.postcomp_map_hEq'
 
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 theorem hcongr_hom {F G : C ⥤ D} (h : F = G) {X Y} (f : X ⟶ Y) : HEq (F.map f) (G.map f) := by
   subst h
 #align category_theory.functor.hcongr_hom CategoryTheory.Functor.hcongr_hom
@@ -318,12 +258,6 @@ end HEq
 
 end Functor
 
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 /-- This is not always a good idea as a `@[simp]` lemma,
 as we lose the ability to use results that interact with `F`,
 e.g. the naturality of a natural transformation.
@@ -334,35 +268,17 @@ theorem eqToHom_map (F : C ⥤ D) {X Y : C} (p : X = Y) :
     F.map (eqToHom p) = eqToHom (congr_arg F.obj p) := by cases p <;> simp
 #align category_theory.eq_to_hom_map CategoryTheory.eqToHom_map
 
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 /-- See the note on `eq_to_hom_map` regarding using this as a `simp` lemma.
 -/
 theorem eqToIso_map (F : C ⥤ D) {X Y : C} (p : X = Y) :
     F.mapIso (eqToIso p) = eqToIso (congr_arg F.obj p) := by ext <;> cases p <;> simp
 #align category_theory.eq_to_iso_map CategoryTheory.eqToIso_map
 
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 @[simp]
 theorem eqToHom_app {F G : C ⥤ D} (h : F = G) (X : C) :
     (eqToHom h : F ⟶ G).app X = eqToHom (Functor.congr_obj h X) := by subst h <;> rfl
 #align category_theory.eq_to_hom_app CategoryTheory.eqToHom_app
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.nat_trans.congr CategoryTheory.NatTrans.congrₓ'. -/
 theorem NatTrans.congr {F G : C ⥤ D} (α : F ⟶ G) {X Y : C} (h : X = Y) :
     α.app X = F.map (eqToHom h) ≫ α.app Y ≫ G.map (eqToHom h.symm) := by rw [α.naturality_assoc];
   simp [eq_to_hom_map]
@@ -374,12 +290,6 @@ theorem eq_conj_eqToHom {X Y : C} (f : X ⟶ Y) : f = eqToHom rfl ≫ f ≫ eqTo
 #align category_theory.eq_conj_eq_to_hom CategoryTheory.eq_conj_eqToHom
 -/
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.dcongr_arg CategoryTheory.dcongr_argₓ'. -/
 theorem dcongr_arg {ι : Type _} {F G : ι → C} (α : ∀ i, F i ⟶ G i) {i j : ι} (h : i = j) :
     α i = eqToHom (congr_arg F h) ≫ α j ≫ eqToHom (congr_arg G h.symm) := by subst h; simp
 #align category_theory.dcongr_arg CategoryTheory.dcongr_arg

34ee86e6

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -62,11 +62,7 @@ theorem eqToHom_refl (X : C) (p : X = X) : eqToHom p = 𝟙 X :=
 #print CategoryTheory.eqToHom_trans /-
 @[simp, reassoc]
 theorem eqToHom_trans {X Y Z : C} (p : X = Y) (q : Y = Z) :
-    eqToHom p ≫ eqToHom q = eqToHom (p.trans q) :=
-  by
-  cases p
-  cases q
-  simp
+    eqToHom p ≫ eqToHom q = eqToHom (p.trans q) := by cases p; cases q; simp
 #align category_theory.eq_to_hom_trans CategoryTheory.eqToHom_trans
 -/
 
@@ -96,10 +92,7 @@ rather than relying on this lemma firing.
 -/
 @[simp]
 theorem congrArg_mpr_hom_left {X Y Z : C} (p : X = Y) (q : Y ⟶ Z) :
-    (congr_arg (fun W : C => W ⟶ Z) p).mpr q = eqToHom p ≫ q :=
-  by
-  cases p
-  simp
+    (congr_arg (fun W : C => W ⟶ Z) p).mpr q = eqToHom p ≫ q := by cases p; simp
 #align category_theory.congr_arg_mpr_hom_left CategoryTheory.congrArg_mpr_hom_left
 -/
 
@@ -113,10 +106,7 @@ rather than relying on this lemma firing.
 -/
 @[simp]
 theorem congrArg_mpr_hom_right {X Y Z : C} (p : X ⟶ Y) (q : Z = Y) :
-    (congr_arg (fun W : C => X ⟶ W) q).mpr p = p ≫ eqToHom q.symm :=
-  by
-  cases q
-  simp
+    (congr_arg (fun W : C => X ⟶ W) q).mpr p = p ≫ eqToHom q.symm := by cases q; simp
 #align category_theory.congr_arg_mpr_hom_right CategoryTheory.congrArg_mpr_hom_right
 -/
 
@@ -161,19 +151,15 @@ theorem eqToIso_trans {X Y Z : C} (p : X = Y) (q : Y = Z) :
 
 #print CategoryTheory.eqToHom_op /-
 @[simp]
-theorem eqToHom_op {X Y : C} (h : X = Y) : (eqToHom h).op = eqToHom (congr_arg op h.symm) :=
-  by
-  cases h
-  rfl
+theorem eqToHom_op {X Y : C} (h : X = Y) : (eqToHom h).op = eqToHom (congr_arg op h.symm) := by
+  cases h; rfl
 #align category_theory.eq_to_hom_op CategoryTheory.eqToHom_op
 -/
 
 #print CategoryTheory.eqToHom_unop /-
 @[simp]
 theorem eqToHom_unop {X Y : Cᵒᵖ} (h : X = Y) : (eqToHom h).unop = eqToHom (congr_arg unop h.symm) :=
-  by
-  cases h
-  rfl
+  by cases h; rfl
 #align category_theory.eq_to_hom_unop CategoryTheory.eqToHom_unop
 -/
 
@@ -182,10 +168,7 @@ instance {X Y : C} (h : X = Y) : IsIso (eqToHom h) :=
 
 #print CategoryTheory.inv_eqToHom /-
 @[simp]
-theorem inv_eqToHom {X Y : C} (h : X = Y) : inv (eqToHom h) = eqToHom h.symm :=
-  by
-  ext
-  simp
+theorem inv_eqToHom {X Y : C} (h : X = Y) : inv (eqToHom h) = eqToHom h.symm := by ext; simp
 #align category_theory.inv_eq_to_hom CategoryTheory.inv_eqToHom
 -/
 
@@ -204,11 +187,8 @@ Case conversion may be inaccurate. Consider using '#align category_theory.functo
 theorem ext {F G : C ⥤ D} (h_obj : ∀ X, F.obj X = G.obj X)
     (h_map : ∀ X Y f, F.map f = eqToHom (h_obj X) ≫ G.map f ≫ eqToHom (h_obj Y).symm) : F = G :=
   by
-  cases' F with F_obj _ _ _
-  cases' G with G_obj _ _ _
-  obtain rfl : F_obj = G_obj := by
-    ext X
-    apply h_obj
+  cases' F with F_obj _ _ _; cases' G with G_obj _ _ _
+  obtain rfl : F_obj = G_obj := by ext X; apply h_obj
   congr
   funext X Y f
   simpa using h_map X Y f
@@ -217,11 +197,7 @@ theorem ext {F G : C ⥤ D} (h_obj : ∀ X, F.obj X = G.obj X)
 #print CategoryTheory.Functor.conj_eqToHom_iff_hEq /-
 /-- Two morphisms are conjugate via eq_to_hom if and only if they are heterogeneously equal. -/
 theorem conj_eqToHom_iff_hEq {W X Y Z : C} (f : W ⟶ X) (g : Y ⟶ Z) (h : W = Y) (h' : X = Z) :
-    f = eqToHom h ≫ g ≫ eqToHom h'.symm ↔ HEq f g :=
-  by
-  cases h
-  cases h'
-  simp
+    f = eqToHom h ≫ g ≫ eqToHom h'.symm ↔ HEq f g := by cases h; cases h'; simp
 #align category_theory.functor.conj_eq_to_hom_iff_heq CategoryTheory.Functor.conj_eqToHom_iff_hEq
 -/
 
@@ -288,10 +264,7 @@ variable {E : Type u₃} [Category.{v₃} E] {F G : C ⥤ D} {X Y Z : C} {f : X
 Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_comp_heq CategoryTheory.Functor.map_comp_hEqₓ'. -/
 theorem map_comp_hEq (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y) (hz : F.obj Z = G.obj Z)
     (hf : HEq (F.map f) (G.map f)) (hg : HEq (F.map g) (G.map g)) :
-    HEq (F.map (f ≫ g)) (G.map (f ≫ g)) :=
-  by
-  rw [F.map_comp, G.map_comp]
-  congr
+    HEq (F.map (f ≫ g)) (G.map (f ≫ g)) := by rw [F.map_comp, G.map_comp]; congr
 #align category_theory.functor.map_comp_heq CategoryTheory.Functor.map_comp_hEq
 
 /- warning: category_theory.functor.map_comp_heq' -> CategoryTheory.Functor.map_comp_hEq' is a dubious translation:
@@ -320,10 +293,7 @@ theorem precomp_map_hEq (H : E ⥤ C) (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.ma
 <too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.functor.postcomp_map_heq CategoryTheory.Functor.postcomp_map_hEqₓ'. -/
 theorem postcomp_map_hEq (H : D ⥤ E) (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y)
-    (hmap : HEq (F.map f) (G.map f)) : HEq ((F ⋙ H).map f) ((G ⋙ H).map f) :=
-  by
-  dsimp
-  congr
+    (hmap : HEq (F.map f) (G.map f)) : HEq ((F ⋙ H).map f) ((G ⋙ H).map f) := by dsimp; congr
 #align category_theory.functor.postcomp_map_heq CategoryTheory.Functor.postcomp_map_hEq
 
 /- warning: category_theory.functor.postcomp_map_heq' -> CategoryTheory.Functor.postcomp_map_hEq' is a dubious translation:
@@ -394,9 +364,7 @@ but is expected to have type
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] {F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2} {G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2} (α : Quiver.Hom.{max (succ u3) (succ u2), max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u3 u2, max (max (max u3 u4) u1) u2} (CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u1, u2, u3, u4} C _inst_1 D _inst_2))) F G) {X : C} {Y : C} (h : Eq.{succ u3} C X Y), Eq.{succ u2} (Quiver.Hom.{succ u2, u4} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (Prefunctor.obj.{succ u1, succ u2, 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(CategoryTheory.eqToHom.{u1, u3} C _inst_1 Y X (Eq.symm.{succ u3} C X Y h)))))
 Case conversion may be inaccurate. Consider using '#align category_theory.nat_trans.congr CategoryTheory.NatTrans.congrₓ'. -/
 theorem NatTrans.congr {F G : C ⥤ D} (α : F ⟶ G) {X Y : C} (h : X = Y) :
-    α.app X = F.map (eqToHom h) ≫ α.app Y ≫ G.map (eqToHom h.symm) :=
-  by
-  rw [α.naturality_assoc]
+    α.app X = F.map (eqToHom h) ≫ α.app Y ≫ G.map (eqToHom h.symm) := by rw [α.naturality_assoc];
   simp [eq_to_hom_map]
 #align category_theory.nat_trans.congr CategoryTheory.NatTrans.congr
 
@@ -413,10 +381,7 @@ but is expected to have type
   forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u2, u3} C] {ι : Type.{u1}} {F : ι -> C} {G : ι -> C} (α : forall (i : ι), Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (F i) (G i)) {i : ι} {j : ι} (h : Eq.{succ u1} ι i j), Eq.{succ u2} (Quiver.Hom.{succ u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1)) (F i) (G i)) (α i) (CategoryTheory.CategoryStruct.comp.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (F i) (F j) (G i) (CategoryTheory.eqToHom.{u2, u3} C _inst_1 (F i) (F j) (congr_arg.{succ u1, succ u3} ι C i j F h)) (CategoryTheory.CategoryStruct.comp.{u2, u3} C (CategoryTheory.Category.toCategoryStruct.{u2, u3} C _inst_1) (F j) (G j) (G i) (α j) (CategoryTheory.eqToHom.{u2, u3} C _inst_1 (G j) (G i) (congr_arg.{succ u1, succ u3} ι C j i G (Eq.symm.{succ u1} ι i j h)))))
 Case conversion may be inaccurate. Consider using '#align category_theory.dcongr_arg CategoryTheory.dcongr_argₓ'. -/
 theorem dcongr_arg {ι : Type _} {F G : ι → C} (α : ∀ i, F i ⟶ G i) {i j : ι} (h : i = j) :
-    α i = eqToHom (congr_arg F h) ≫ α j ≫ eqToHom (congr_arg G h.symm) :=
-  by
-  subst h
-  simp
+    α i = eqToHom (congr_arg F h) ≫ α j ≫ eqToHom (congr_arg G h.symm) := by subst h; simp
 #align category_theory.dcongr_arg CategoryTheory.dcongr_arg
 
 end CategoryTheory

34ee86e6

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -259,10 +259,7 @@ theorem congr_hom {F G : C ⥤ D} (h : F = G) {X Y} (f : X ⟶ Y) :
 #align category_theory.functor.congr_hom CategoryTheory.Functor.congr_hom
 
 /- warning: category_theory.functor.congr_inv_of_congr_hom -> CategoryTheory.Functor.congr_inv_of_congr_hom is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.functor.congr_inv_of_congr_hom CategoryTheory.Functor.congr_inv_of_congr_homₓ'. -/
 theorem congr_inv_of_congr_hom (F G : C ⥤ D) {X Y : C} (e : X ≅ Y) (hX : F.obj X = G.obj X)
     (hY : F.obj Y = G.obj Y)
@@ -287,10 +284,7 @@ section HEq
 variable {E : Type u₃} [Category.{v₃} E] {F G : C ⥤ D} {X Y Z : C} {f : X ⟶ Y} {g : Y ⟶ Z}
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.functor.map_comp_heq CategoryTheory.Functor.map_comp_hEqₓ'. -/
 theorem map_comp_hEq (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y) (hz : F.obj Z = G.obj Z)
     (hf : HEq (F.map f) (G.map f)) (hg : HEq (F.map g) (G.map g)) :
@@ -323,10 +317,7 @@ theorem precomp_map_hEq (H : E ⥤ C) (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.ma
 #align category_theory.functor.precomp_map_heq CategoryTheory.Functor.precomp_map_hEq
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.functor.postcomp_map_heq CategoryTheory.Functor.postcomp_map_hEqₓ'. -/
 theorem postcomp_map_hEq (H : D ⥤ E) (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y)
     (hmap : HEq (F.map f) (G.map f)) : HEq ((F ⋙ H).map f) ((G ⋙ H).map f) :=
@@ -336,10 +327,7 @@ theorem postcomp_map_hEq (H : D ⥤ E) (hx : F.obj X = G.obj X) (hy : F.obj Y =
 #align category_theory.functor.postcomp_map_heq CategoryTheory.Functor.postcomp_map_hEq
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.functor.postcomp_map_heq' CategoryTheory.Functor.postcomp_map_hEq'ₓ'. -/
 theorem postcomp_map_hEq' (H : D ⥤ E) (hobj : ∀ X : C, F.obj X = G.obj X)
     (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) : HEq ((F ⋙ H).map f) ((G ⋙ H).map f) :=

34ee86e6

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -60,7 +60,7 @@ theorem eqToHom_refl (X : C) (p : X = X) : eqToHom p = 𝟙 X :=
 -/
 
 #print CategoryTheory.eqToHom_trans /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem eqToHom_trans {X Y Z : C} (p : X = Y) (q : Y = Z) :
     eqToHom p ≫ eqToHom q = eqToHom (p.trans q) :=
   by

34ee86e6

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

dc6c365e

feat(CategoryTheory/EqToHom): generalize Functor.congr_map to Prefunctor.congr_map (#12384)

cba2f37b

Diff

@@ -250,9 +250,6 @@ theorem congr_inv_of_congr_hom (F G : C ⥤ D) {X Y : C} (e : X ≅ Y) (hX : F.o
     Category.assoc]
 #align category_theory.functor.congr_inv_of_congr_hom CategoryTheory.Functor.congr_inv_of_congr_hom
 
-theorem congr_map (F : C ⥤ D) {X Y : C} {f g : X ⟶ Y} (h : f = g) : F.map f = F.map g := by rw [h]
-#align category_theory.functor.congr_map CategoryTheory.Functor.congr_map
-
 section HEq
 
 -- Composition of functors and maps w.r.t. heq

dc6c365e

chore: remove autoImplicit from more files (#11798)

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>

3bb1d613

Diff

@@ -26,9 +26,6 @@ This file introduces various `simp` lemmas which in favourable circumstances
 result in the various `eqToHom` morphisms to drop out at the appropriate moment!
 -/
 
-set_option autoImplicit true
-
-
 universe v₁ v₂ v₃ u₁ u₂ u₃
 
 -- morphism levels before object levels. See note [CategoryTheory universes].
@@ -71,6 +68,8 @@ theorem eqToHom_comp_iff {X X' Y : C} (p : X = X') (f : X ⟶ Y) (g : X' ⟶ Y)
     mpr := fun h => h ▸ by simp [whisker_eq _ h] }
 #align category_theory.eq_to_hom_comp_iff CategoryTheory.eqToHom_comp_iff
 
+variable {β : Sort*}
+
 /-- We can push `eqToHom` to the left through families of morphisms. -/
 -- The simpNF linter incorrectly claims that this will never apply.
 -- https://github.com/leanprover-community/mathlib4/issues/5049

dc6c365e

feat: safe variants of eqToHom_map (#10243)

eqToHom_map is notoriously not a good simp lemma, but these variants should be safe and already go a long way.

a55d6e57

Diff

@@ -306,12 +306,20 @@ theorem eqToHom_map (F : C ⥤ D) {X Y : C} (p : X = Y) :
     F.map (eqToHom p) = eqToHom (congr_arg F.obj p) := by cases p; simp
 #align category_theory.eq_to_hom_map CategoryTheory.eqToHom_map
 
+@[reassoc (attr := simp)]
+theorem eqToHom_map_comp (F : C ⥤ D) {X Y Z : C} (p : X = Y) (q : Y = Z) :
+    F.map (eqToHom p) ≫ F.map (eqToHom q) = F.map (eqToHom <| p.trans q) := by aesop_cat
+
 /-- See the note on `eqToHom_map` regarding using this as a `simp` lemma.
 -/
 theorem eqToIso_map (F : C ⥤ D) {X Y : C} (p : X = Y) :
     F.mapIso (eqToIso p) = eqToIso (congr_arg F.obj p) := by ext; cases p; simp
 #align category_theory.eq_to_iso_map CategoryTheory.eqToIso_map
 
+@[simp]
+theorem eqToIso_map_trans (F : C ⥤ D) {X Y Z : C} (p : X = Y) (q : Y = Z) :
+    F.mapIso (eqToIso p) ≪≫ F.mapIso (eqToIso q) = F.mapIso (eqToIso <| p.trans q) := by aesop_cat
+
 @[simp]
 theorem eqToHom_app {F G : C ⥤ D} (h : F = G) (X : C) :
     (eqToHom h : F ⟶ G).app X = eqToHom (Functor.congr_obj h X) := by subst h; rfl

dc6c365e

chore: fix some Lean-3-isms in comments (#10240)

96b716e8

Diff

@@ -300,7 +300,7 @@ end Functor
 as we lose the ability to use results that interact with `F`,
 e.g. the naturality of a natural transformation.
 
-In some files it may be appropriate to use `local attribute [simp] eqToHom_map`, however.
+In some files it may be appropriate to use `attribute [local simp] eqToHom_map`, however.
 -/
 theorem eqToHom_map (F : C ⥤ D) {X Y : C} (p : X = Y) :
     F.map (eqToHom p) = eqToHom (congr_arg F.obj p) := by cases p; simp

dc6c365e

fix: patch for std4#198 (more mul lemmas for Nat) (#6204)

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

2f63d25e

Diff

@@ -107,7 +107,7 @@ theorem congrArg_cast_hom_left {X Y Z : C} (p : X = Y) (q : Y ⟶ Z) :
   cases p
   simp
 
- /-- If we (perhaps unintentionally) perform equational rewriting on
+/-- If we (perhaps unintentionally) perform equational rewriting on
 the source object of a morphism,
 we can replace the resulting `_.mpr f` term by a composition with an `eqToHom`.

dc6c365e

feat(CategoryTheory): more extensionality properties for ComposableArrows (#8119)

d8165414

Diff

@@ -214,6 +214,12 @@ theorem ext {F G : C ⥤ D} (h_obj : ∀ X, F.obj X = G.obj X)
     simpa using h_map X Y f
 #align category_theory.functor.ext CategoryTheory.Functor.ext
 
+lemma ext_of_iso {F G : C ⥤ D} (e : F ≅ G) (hobj : ∀ X, F.obj X = G.obj X)
+    (happ : ∀ X, e.hom.app X = eqToHom (hobj X)) : F = G :=
+  Functor.ext hobj (fun X Y f => by
+    rw [← cancel_mono (e.hom.app Y), e.hom.naturality f, happ, happ, Category.assoc,
+    Category.assoc, eqToHom_trans, eqToHom_refl, Category.comp_id])
+
 /-- Two morphisms are conjugate via eqToHom if and only if they are heterogeneously equal. -/
 theorem conj_eqToHom_iff_heq {W X Y Z : C} (f : W ⟶ X) (g : Y ⟶ Z) (h : W = Y) (h' : X = Z) :
     f = eqToHom h ≫ g ≫ eqToHom h'.symm ↔ HEq f g := by

dc6c365e

fix: disable autoImplicit globally (#6528)

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.

0c24f831

Diff

@@ -26,6 +26,8 @@ This file introduces various `simp` lemmas which in favourable circumstances
 result in the various `eqToHom` morphisms to drop out at the appropriate moment!
 -/
 
+set_option autoImplicit true
+
 
 universe v₁ v₂ v₃ u₁ u₂ u₃

dc6c365e

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -319,7 +319,7 @@ theorem eq_conj_eqToHom {X Y : C} (f : X ⟶ Y) : f = eqToHom rfl ≫ f ≫ eqTo
   simp only [Category.id_comp, eqToHom_refl, Category.comp_id]
 #align category_theory.eq_conj_eq_to_hom CategoryTheory.eq_conj_eqToHom
 
-theorem dcongr_arg {ι : Type _} {F G : ι → C} (α : ∀ i, F i ⟶ G i) {i j : ι} (h : i = j) :
+theorem dcongr_arg {ι : Type*} {F G : ι → C} (α : ∀ i, F i ⟶ G i) {i j : ι} (h : i = j) :
     α i = eqToHom (congr_arg F h) ≫ α j ≫ eqToHom (congr_arg G h.symm) := by
   subst h
   simp

dc6c365e

feat: (co/bi/)products unchanged by reindexing and isomorphism of factors (#6259)

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

675f2fd9

Diff

@@ -69,8 +69,35 @@ theorem eqToHom_comp_iff {X X' Y : C} (p : X = X') (f : X ⟶ Y) (g : X' ⟶ Y)
     mpr := fun h => h ▸ by simp [whisker_eq _ h] }
 #align category_theory.eq_to_hom_comp_iff CategoryTheory.eqToHom_comp_iff
 
+/-- We can push `eqToHom` to the left through families of morphisms. -/
+-- The simpNF linter incorrectly claims that this will never apply.
+-- https://github.com/leanprover-community/mathlib4/issues/5049
+@[reassoc (attr := simp, nolint simpNF)]
+theorem eqToHom_naturality {f g : β → C} (z : ∀ b, f b ⟶ g b) {j j' : β} (w : j = j') :
+    z j ≫ eqToHom (by simp [w]) = eqToHom (by simp [w]) ≫ z j' := by
+  cases w
+  simp
+
+/-- A variant on `eqToHom_naturality` that helps Lean identify the families `f` and `g`. -/
+-- The simpNF linter incorrectly claims that this will never apply.
+-- https://github.com/leanprover-community/mathlib4/issues/5049
+@[reassoc (attr := simp, nolint simpNF)]
+theorem eqToHom_iso_hom_naturality {f g : β → C} (z : ∀ b, f b ≅ g b) {j j' : β} (w : j = j') :
+    (z j).hom ≫ eqToHom (by simp [w]) = eqToHom (by simp [w]) ≫ (z j').hom := by
+  cases w
+  simp
+
+/-- A variant on `eqToHom_naturality` that helps Lean identify the families `f` and `g`. -/
+-- The simpNF linter incorrectly claims that this will never apply.
+-- https://github.com/leanprover-community/mathlib4/issues/5049
+@[reassoc (attr := simp, nolint simpNF)]
+theorem eqToHom_iso_inv_naturality {f g : β → C} (z : ∀ b, f b ≅ g b) {j j' : β} (w : j = j') :
+    (z j).inv ≫ eqToHom (by simp [w]) = eqToHom (by simp [w]) ≫ (z j').inv := by
+  cases w
+  simp
+
 /- Porting note: simpNF complains about this not reducing but it is clearly used
-in `congrArg_mrp_hom_left`. It has been no-linted. -/
+in `congrArg_mpr_hom_left`. It has been no-linted. -/
 /-- Reducible form of congrArg_mpr_hom_left -/
 @[simp, nolint simpNF]
 theorem congrArg_cast_hom_left {X Y Z : C} (p : X = Y) (q : Y ⟶ Z) :

dc6c365e

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2018 Reid Barton. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Reid Barton, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.eq_to_hom
-! leanprover-community/mathlib commit dc6c365e751e34d100e80fe6e314c3c3e0fd2988
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Opposites
 
+#align_import category_theory.eq_to_hom from "leanprover-community/mathlib"@"dc6c365e751e34d100e80fe6e314c3c3e0fd2988"
+
 /-!
 # Morphisms from equations between objects.

dc6c365e

chore: cleanup whitespace (#5988)

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

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

12343aa5

Diff

@@ -76,8 +76,8 @@ theorem eqToHom_comp_iff {X X' Y : C} (p : X = X') (f : X ⟶ Y) (g : X' ⟶ Y)
 in `congrArg_mrp_hom_left`. It has been no-linted. -/
 /-- Reducible form of congrArg_mpr_hom_left -/
 @[simp, nolint simpNF]
-theorem congrArg_cast_hom_left {X Y Z : C} (p : X = Y) (q : Y ⟶  Z) :
-    cast (congrArg (fun W : C => W ⟶  Z) p.symm) q = eqToHom p ≫ q := by
+theorem congrArg_cast_hom_left {X Y Z : C} (p : X = Y) (q : Y ⟶ Z) :
+    cast (congrArg (fun W : C => W ⟶ Z) p.symm) q = eqToHom p ≫ q := by
   cases p
   simp
 
@@ -99,7 +99,7 @@ in `congrArg_mrp_hom_right`. It has been no-linted. -/
 /-- Reducible form of `congrArg_mpr_hom_right` -/
 @[simp, nolint simpNF]
 theorem congrArg_cast_hom_right {X Y Z : C} (p : X ⟶ Y) (q : Z = Y) :
-    cast (congrArg (fun W : C => X ⟶  W) q.symm) p = p ≫ eqToHom q.symm := by
+    cast (congrArg (fun W : C => X ⟶ W) q.symm) p = p ≫ eqToHom q.symm := by
   cases q
   simp

dc6c365e

feat: port AlgebraicTopology.FundamentalGroupoid.InducedMaps (#5756)

Co-authored-by: Johan Commelin <johan@commelin.net>

e5bc4385

Diff

@@ -189,17 +189,17 @@ theorem ext {F G : C ⥤ D} (h_obj : ∀ X, F.obj X = G.obj X)
 #align category_theory.functor.ext CategoryTheory.Functor.ext
 
 /-- Two morphisms are conjugate via eqToHom if and only if they are heterogeneously equal. -/
-theorem conj_eqToHom_iff_hEq {W X Y Z : C} (f : W ⟶ X) (g : Y ⟶ Z) (h : W = Y) (h' : X = Z) :
+theorem conj_eqToHom_iff_heq {W X Y Z : C} (f : W ⟶ X) (g : Y ⟶ Z) (h : W = Y) (h' : X = Z) :
     f = eqToHom h ≫ g ≫ eqToHom h'.symm ↔ HEq f g := by
   cases h
   cases h'
   simp
-#align category_theory.functor.conj_eq_to_hom_iff_heq CategoryTheory.Functor.conj_eqToHom_iff_hEq
+#align category_theory.functor.conj_eq_to_hom_iff_heq CategoryTheory.Functor.conj_eqToHom_iff_heq
 
 /-- Proving equality between functors using heterogeneous equality. -/
 theorem hext {F G : C ⥤ D} (h_obj : ∀ X, F.obj X = G.obj X)
     (h_map : ∀ (X Y) (f : X ⟶ Y), HEq (F.map f) (G.map f)) : F = G :=
-  Functor.ext h_obj fun _ _ f => (conj_eqToHom_iff_hEq _ _ (h_obj _) (h_obj _)).2 <| h_map _ _ f
+  Functor.ext h_obj fun _ _ f => (conj_eqToHom_iff_heq _ _ (h_obj _) (h_obj _)).2 <| h_map _ _ f
 #align category_theory.functor.hext CategoryTheory.Functor.hext
 
 -- Using equalities between functors.
@@ -227,34 +227,34 @@ section HEq
 -- Composition of functors and maps w.r.t. heq
 variable {E : Type u₃} [Category.{v₃} E] {F G : C ⥤ D} {X Y Z : C} {f : X ⟶ Y} {g : Y ⟶ Z}
 
-theorem map_comp_hEq (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y) (hz : F.obj Z = G.obj Z)
+theorem map_comp_heq (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y) (hz : F.obj Z = G.obj Z)
     (hf : HEq (F.map f) (G.map f)) (hg : HEq (F.map g) (G.map g)) :
     HEq (F.map (f ≫ g)) (G.map (f ≫ g)) := by
   rw [F.map_comp, G.map_comp]
   congr
-#align category_theory.functor.map_comp_heq CategoryTheory.Functor.map_comp_hEq
+#align category_theory.functor.map_comp_heq CategoryTheory.Functor.map_comp_heq
 
-theorem map_comp_hEq' (hobj : ∀ X : C, F.obj X = G.obj X)
+theorem map_comp_heq' (hobj : ∀ X : C, F.obj X = G.obj X)
     (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) :
     HEq (F.map (f ≫ g)) (G.map (f ≫ g)) := by
   rw [Functor.hext hobj fun _ _ => hmap]
-#align category_theory.functor.map_comp_heq' CategoryTheory.Functor.map_comp_hEq'
+#align category_theory.functor.map_comp_heq' CategoryTheory.Functor.map_comp_heq'
 
-theorem precomp_map_hEq (H : E ⥤ C) (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) {X Y : E}
+theorem precomp_map_heq (H : E ⥤ C) (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) {X Y : E}
     (f : X ⟶ Y) : HEq ((H ⋙ F).map f) ((H ⋙ G).map f) :=
   hmap _
-#align category_theory.functor.precomp_map_heq CategoryTheory.Functor.precomp_map_hEq
+#align category_theory.functor.precomp_map_heq CategoryTheory.Functor.precomp_map_heq
 
-theorem postcomp_map_hEq (H : D ⥤ E) (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y)
+theorem postcomp_map_heq (H : D ⥤ E) (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y)
     (hmap : HEq (F.map f) (G.map f)) : HEq ((F ⋙ H).map f) ((G ⋙ H).map f) := by
   dsimp
   congr
-#align category_theory.functor.postcomp_map_heq CategoryTheory.Functor.postcomp_map_hEq
+#align category_theory.functor.postcomp_map_heq CategoryTheory.Functor.postcomp_map_heq
 
-theorem postcomp_map_hEq' (H : D ⥤ E) (hobj : ∀ X : C, F.obj X = G.obj X)
+theorem postcomp_map_heq' (H : D ⥤ E) (hobj : ∀ X : C, F.obj X = G.obj X)
     (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) : HEq ((F ⋙ H).map f) ((G ⋙ H).map f) :=
   by rw [Functor.hext hobj fun _ _ => hmap]
-#align category_theory.functor.postcomp_map_heq' CategoryTheory.Functor.postcomp_map_hEq'
+#align category_theory.functor.postcomp_map_heq' CategoryTheory.Functor.postcomp_map_heq'
 
 theorem hcongr_hom {F G : C ⥤ D} (h : F = G) {X Y} (f : X ⟶ Y) : HEq (F.map f) (G.map f) := by
   rw [h]

dc6c365e

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

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

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

5b958613

Diff

@@ -173,7 +173,8 @@ namespace Functor
 /-- Proving equality between functors. This isn't an extensionality lemma,
   because usually you don't really want to do this. -/
 theorem ext {F G : C ⥤ D} (h_obj : ∀ X, F.obj X = G.obj X)
-    (h_map : ∀ X Y f, F.map f = eqToHom (h_obj X) ≫ G.map f ≫ eqToHom (h_obj Y).symm) :
+    (h_map : ∀ X Y f,
+      F.map f = eqToHom (h_obj X) ≫ G.map f ≫ eqToHom (h_obj Y).symm := by aesop_cat) :
     F = G := by
   match F, G with
   | mk F_pre _ _ , mk G_pre _ _ =>

dc6c365e

chore: fix typos (#4518)

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

92beef58

Diff

@@ -72,7 +72,7 @@ theorem eqToHom_comp_iff {X X' Y : C} (p : X = X') (f : X ⟶ Y) (g : X' ⟶ Y)
     mpr := fun h => h ▸ by simp [whisker_eq _ h] }
 #align category_theory.eq_to_hom_comp_iff CategoryTheory.eqToHom_comp_iff
 
-/- Porting note: simpNF complains about thsi not reducing but it is clearly used
+/- Porting note: simpNF complains about this not reducing but it is clearly used
 in `congrArg_mrp_hom_left`. It has been no-linted. -/
 /-- Reducible form of congrArg_mpr_hom_left -/
 @[simp, nolint simpNF]
@@ -94,7 +94,7 @@ theorem congrArg_mpr_hom_left {X Y Z : C} (p : X = Y) (q : Y ⟶ Z) :
   simp
 #align category_theory.congr_arg_mpr_hom_left CategoryTheory.congrArg_mpr_hom_left
 
-/- Porting note: simpNF complains about thsi not reducing but it is clearly used
+/- Porting note: simpNF complains about this not reducing but it is clearly used
 in `congrArg_mrp_hom_right`. It has been no-linted. -/
 /-- Reducible form of `congrArg_mpr_hom_right` -/
 @[simp, nolint simpNF]

dc6c365e

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

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

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

14167e48

Diff

@@ -54,8 +54,7 @@ theorem eqToHom_refl (X : C) (p : X = X) : eqToHom p = 𝟙 X :=
 
 @[reassoc (attr := simp)]
 theorem eqToHom_trans {X Y Z : C} (p : X = Y) (q : Y = Z) :
-    eqToHom p ≫ eqToHom q = eqToHom (p.trans q) :=
-  by
+    eqToHom p ≫ eqToHom q = eqToHom (p.trans q) := by
   cases p
   cases q
   simp

dc6c365e

fix: category_theory -> CategoryTheory in note (#2357)

This changes the name of a library_note from "category_theory universes" to "CategoryTheory universes" to be more in line with the new naming conventions.

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

1640c545

Diff

@@ -32,7 +32,7 @@ result in the various `eqToHom` morphisms to drop out at the appropriate moment!
 
 universe v₁ v₂ v₃ u₁ u₂ u₃
 
--- morphism levels before object levels. See note [category_theory universes].
+-- morphism levels before object levels. See note [CategoryTheory universes].
 namespace CategoryTheory
 
 open Opposite

dc6c365e

chore: tidy various files (#2251)

0a70c6a6

Diff

@@ -73,14 +73,14 @@ theorem eqToHom_comp_iff {X X' Y : C} (p : X = X') (f : X ⟶ Y) (g : X' ⟶ Y)
     mpr := fun h => h ▸ by simp [whisker_eq _ h] }
 #align category_theory.eq_to_hom_comp_iff CategoryTheory.eqToHom_comp_iff
 
-/- Porting note: simpNF complains about thsi not reducing but it is clearly used 
+/- Porting note: simpNF complains about thsi not reducing but it is clearly used
 in `congrArg_mrp_hom_left`. It has been no-linted. -/
 /-- Reducible form of congrArg_mpr_hom_left -/
 @[simp, nolint simpNF]
-theorem congrArg_cast_hom_left {X Y Z : C} (p : X = Y) (q : Y ⟶  Z) : 
-     cast (congrArg (fun W : C => W ⟶  Z) p.symm) q = eqToHom p ≫ q := by 
-  cases p 
-  simp 
+theorem congrArg_cast_hom_left {X Y Z : C} (p : X = Y) (q : Y ⟶  Z) :
+    cast (congrArg (fun W : C => W ⟶  Z) p.symm) q = eqToHom p ≫ q := by
+  cases p
+  simp
 
  /-- If we (perhaps unintentionally) perform equational rewriting on
 the source object of a morphism,
@@ -88,22 +88,21 @@ we can replace the resulting `_.mpr f` term by a composition with an `eqToHom`.
 
 It may be advisable to introduce any necessary `eqToHom` morphisms manually,
 rather than relying on this lemma firing.
--/  
+-/
 theorem congrArg_mpr_hom_left {X Y Z : C} (p : X = Y) (q : Y ⟶ Z) :
-    (congrArg (fun W : C => W ⟶ Z) p).mpr q = eqToHom p ≫ q :=
-  by
+    (congrArg (fun W : C => W ⟶ Z) p).mpr q = eqToHom p ≫ q := by
   cases p
   simp
 #align category_theory.congr_arg_mpr_hom_left CategoryTheory.congrArg_mpr_hom_left
 
-/- Porting note: simpNF complains about thsi not reducing but it is clearly used 
+/- Porting note: simpNF complains about thsi not reducing but it is clearly used
 in `congrArg_mrp_hom_right`. It has been no-linted. -/
 /-- Reducible form of `congrArg_mpr_hom_right` -/
 @[simp, nolint simpNF]
 theorem congrArg_cast_hom_right {X Y Z : C} (p : X ⟶ Y) (q : Z = Y) :
-    cast (congrArg (fun W : C => X ⟶  W) q.symm) p = p ≫ eqToHom q.symm := by 
-  cases q 
-  simp 
+    cast (congrArg (fun W : C => X ⟶  W) q.symm) p = p ≫ eqToHom q.symm := by
+  cases q
+  simp
 
 /-- If we (perhaps unintentionally) perform equational rewriting on
 the target object of a morphism,
@@ -113,8 +112,7 @@ It may be advisable to introduce any necessary `eqToHom` morphisms manually,
 rather than relying on this lemma firing.
 -/
 theorem congrArg_mpr_hom_right {X Y Z : C} (p : X ⟶ Y) (q : Z = Y) :
-    (congrArg (fun W : C => X ⟶ W) q).mpr p = p ≫ eqToHom q.symm :=
-  by
+    (congrArg (fun W : C => X ⟶ W) q).mpr p = p ≫ eqToHom q.symm := by
   cases q
   simp
 #align category_theory.congr_arg_mpr_hom_right CategoryTheory.congrArg_mpr_hom_right
@@ -149,15 +147,14 @@ theorem eqToIso_trans {X Y Z : C} (p : X = Y) (q : Y = Z) :
 #align category_theory.eq_to_iso_trans CategoryTheory.eqToIso_trans
 
 @[simp]
-theorem eqToHom_op {X Y : C} (h : X = Y) : (eqToHom h).op = eqToHom (congr_arg op h.symm) :=
-  by
+theorem eqToHom_op {X Y : C} (h : X = Y) : (eqToHom h).op = eqToHom (congr_arg op h.symm) := by
   cases h
   rfl
 #align category_theory.eq_to_hom_op CategoryTheory.eqToHom_op
 
 @[simp]
-theorem eqToHom_unop {X Y : Cᵒᵖ} (h : X = Y) : (eqToHom h).unop = eqToHom (congr_arg unop h.symm) :=
-  by
+theorem eqToHom_unop {X Y : Cᵒᵖ} (h : X = Y) :
+    (eqToHom h).unop = eqToHom (congr_arg unop h.symm) := by
   cases h
   rfl
 #align category_theory.eq_to_hom_unop CategoryTheory.eqToHom_unop
@@ -166,8 +163,7 @@ instance {X Y : C} (h : X = Y) : IsIso (eqToHom h) :=
   IsIso.of_iso (eqToIso h)
 
 @[simp]
-theorem inv_eqToHom {X Y : C} (h : X = Y) : inv (eqToHom h) = eqToHom h.symm :=
-  by
+theorem inv_eqToHom {X Y : C} (h : X = Y) : inv (eqToHom h) = eqToHom h.symm := by
   aesop_cat
 #align category_theory.inv_eq_to_hom CategoryTheory.inv_eqToHom
 
@@ -178,12 +174,12 @@ namespace Functor
 /-- Proving equality between functors. This isn't an extensionality lemma,
   because usually you don't really want to do this. -/
 theorem ext {F G : C ⥤ D} (h_obj : ∀ X, F.obj X = G.obj X)
-    (h_map : ∀ X Y f, F.map f = eqToHom (h_obj X) ≫ G.map f ≫ eqToHom (h_obj Y).symm) : F = G :=
-  by
-  match F, G with 
+    (h_map : ∀ X Y f, F.map f = eqToHom (h_obj X) ≫ G.map f ≫ eqToHom (h_obj Y).symm) :
+    F = G := by
+  match F, G with
   | mk F_pre _ _ , mk G_pre _ _ =>
     match F_pre, G_pre with  -- Porting note: did not unfold the Prefunctor unlike Lean3
-    | Prefunctor.mk F_obj _ , Prefunctor.mk G_obj _ =>  
+    | Prefunctor.mk F_obj _ , Prefunctor.mk G_obj _ =>
     obtain rfl : F_obj = G_obj := by
       ext X
       apply h_obj
@@ -194,8 +190,7 @@ theorem ext {F G : C ⥤ D} (h_obj : ∀ X, F.obj X = G.obj X)
 
 /-- Two morphisms are conjugate via eqToHom if and only if they are heterogeneously equal. -/
 theorem conj_eqToHom_iff_hEq {W X Y Z : C} (f : W ⟶ X) (g : Y ⟶ Z) (h : W = Y) (h' : X = Z) :
-    f = eqToHom h ≫ g ≫ eqToHom h'.symm ↔ HEq f g :=
-  by
+    f = eqToHom h ≫ g ≫ eqToHom h'.symm ↔ HEq f g := by
   cases h
   cases h'
   simp
@@ -234,16 +229,16 @@ variable {E : Type u₃} [Category.{v₃} E] {F G : C ⥤ D} {X Y Z : C} {f : X
 
 theorem map_comp_hEq (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y) (hz : F.obj Z = G.obj Z)
     (hf : HEq (F.map f) (G.map f)) (hg : HEq (F.map g) (G.map g)) :
-    HEq (F.map (f ≫ g)) (G.map (f ≫ g)) :=
-  by
+    HEq (F.map (f ≫ g)) (G.map (f ≫ g)) := by
   rw [F.map_comp, G.map_comp]
   congr
 #align category_theory.functor.map_comp_heq CategoryTheory.Functor.map_comp_hEq
 
-theorem map_comp_heq' (hobj : ∀ X : C, F.obj X = G.obj X)
-    (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) : HEq (F.map (f ≫ g)) (G.map (f ≫ g)) :=
-  by rw [Functor.hext hobj fun _ _ => hmap]
-#align category_theory.functor.map_comp_heq' CategoryTheory.Functor.map_comp_heq'
+theorem map_comp_hEq' (hobj : ∀ X : C, F.obj X = G.obj X)
+    (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) :
+    HEq (F.map (f ≫ g)) (G.map (f ≫ g)) := by
+  rw [Functor.hext hobj fun _ _ => hmap]
+#align category_theory.functor.map_comp_heq' CategoryTheory.Functor.map_comp_hEq'
 
 theorem precomp_map_hEq (H : E ⥤ C) (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) {X Y : E}
     (f : X ⟶ Y) : HEq ((H ⋙ F).map f) ((H ⋙ G).map f) :=
@@ -251,19 +246,18 @@ theorem precomp_map_hEq (H : E ⥤ C) (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.ma
 #align category_theory.functor.precomp_map_heq CategoryTheory.Functor.precomp_map_hEq
 
 theorem postcomp_map_hEq (H : D ⥤ E) (hx : F.obj X = G.obj X) (hy : F.obj Y = G.obj Y)
-    (hmap : HEq (F.map f) (G.map f)) : HEq ((F ⋙ H).map f) ((G ⋙ H).map f) :=
-  by
+    (hmap : HEq (F.map f) (G.map f)) : HEq ((F ⋙ H).map f) ((G ⋙ H).map f) := by
   dsimp
   congr
 #align category_theory.functor.postcomp_map_heq CategoryTheory.Functor.postcomp_map_hEq
 
-theorem postcomp_map_heq' (H : D ⥤ E) (hobj : ∀ X : C, F.obj X = G.obj X)
+theorem postcomp_map_hEq' (H : D ⥤ E) (hobj : ∀ X : C, F.obj X = G.obj X)
     (hmap : ∀ {X Y} (f : X ⟶ Y), HEq (F.map f) (G.map f)) : HEq ((F ⋙ H).map f) ((G ⋙ H).map f) :=
   by rw [Functor.hext hobj fun _ _ => hmap]
-#align category_theory.functor.postcomp_map_heq' CategoryTheory.Functor.postcomp_map_heq'
+#align category_theory.functor.postcomp_map_heq' CategoryTheory.Functor.postcomp_map_hEq'
 
 theorem hcongr_hom {F G : C ⥤ D} (h : F = G) {X Y} (f : X ⟶ Y) : HEq (F.map f) (G.map f) := by
-  rw [h] 
+  rw [h]
 #align category_theory.functor.hcongr_hom CategoryTheory.Functor.hcongr_hom
 
 end HEq
@@ -292,8 +286,7 @@ theorem eqToHom_app {F G : C ⥤ D} (h : F = G) (X : C) :
 #align category_theory.eq_to_hom_app CategoryTheory.eqToHom_app
 
 theorem NatTrans.congr {F G : C ⥤ D} (α : F ⟶ G) {X Y : C} (h : X = Y) :
-    α.app X = F.map (eqToHom h) ≫ α.app Y ≫ G.map (eqToHom h.symm) :=
-  by
+    α.app X = F.map (eqToHom h) ≫ α.app Y ≫ G.map (eqToHom h.symm) := by
   rw [α.naturality_assoc]
   simp [eqToHom_map]
 #align category_theory.nat_trans.congr CategoryTheory.NatTrans.congr
@@ -303,8 +296,7 @@ theorem eq_conj_eqToHom {X Y : C} (f : X ⟶ Y) : f = eqToHom rfl ≫ f ≫ eqTo
 #align category_theory.eq_conj_eq_to_hom CategoryTheory.eq_conj_eqToHom
 
 theorem dcongr_arg {ι : Type _} {F G : ι → C} (α : ∀ i, F i ⟶ G i) {i j : ι} (h : i = j) :
-    α i = eqToHom (congr_arg F h) ≫ α j ≫ eqToHom (congr_arg G h.symm) :=
-  by
+    α i = eqToHom (congr_arg F h) ≫ α j ≫ eqToHom (congr_arg G h.symm) := by
   subst h
   simp
 #align category_theory.dcongr_arg CategoryTheory.dcongr_arg

dc6c365e

feat port/CategoryTheory.EqToHom (#2207)

ef02d663

`category_theory.eq_to_hom` ⟷ `Mathlib.CategoryTheory.EqToHom`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 11

category_theory.eq_to_hom ⟷ Mathlib.CategoryTheory.EqToHom

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 11

`category_theory.eq_to_hom` ⟷ `Mathlib.CategoryTheory.EqToHom`