category_theory.endofunctor.algebra | 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

70fd9563

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

2ed2c631

bump to nightly-2024-04-14-09

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

f736ea6b

Diff

@@ -164,12 +164,13 @@ theorem iso_of_iso (f : A₀ ⟶ A₁) [IsIso f.1] : IsIso f :=
 -/
 
 #print CategoryTheory.Endofunctor.Algebra.forget_reflects_iso /-
-instance forget_reflects_iso : ReflectsIsomorphisms (forget F) where reflects A B := iso_of_iso
+instance forget_reflects_iso : CategoryTheory.Functor.ReflectsIsomorphisms (forget F)
+    where reflects A B := iso_of_iso
 #align category_theory.endofunctor.algebra.forget_reflects_iso CategoryTheory.Endofunctor.Algebra.forget_reflects_iso
 -/
 
 #print CategoryTheory.Endofunctor.Algebra.forget_faithful /-
-instance forget_faithful : Faithful (forget F) where
+instance forget_faithful : CategoryTheory.Functor.Faithful (forget F) where
 #align category_theory.endofunctor.algebra.forget_faithful CategoryTheory.Endofunctor.Algebra.forget_faithful
 -/
 
@@ -427,12 +428,13 @@ theorem iso_of_iso (f : V₀ ⟶ V₁) [IsIso f.1] : IsIso f :=
 -/
 
 #print CategoryTheory.Endofunctor.Coalgebra.forget_reflects_iso /-
-instance forget_reflects_iso : ReflectsIsomorphisms (forget F) where reflects A B := iso_of_iso
+instance forget_reflects_iso : CategoryTheory.Functor.ReflectsIsomorphisms (forget F)
+    where reflects A B := iso_of_iso
 #align category_theory.endofunctor.coalgebra.forget_reflects_iso CategoryTheory.Endofunctor.Coalgebra.forget_reflects_iso
 -/
 
 #print CategoryTheory.Endofunctor.Coalgebra.forget_faithful /-
-instance forget_faithful : Faithful (forget F) where
+instance forget_faithful : CategoryTheory.Functor.Faithful (forget F) where
 #align category_theory.endofunctor.coalgebra.forget_faithful CategoryTheory.Endofunctor.Coalgebra.forget_faithful
 -/

2ed2c631

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2022 Joseph Hua. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Bhavik Mehta, Johan Commelin, Reid Barton, Rob Lewis, Joseph Hua
 -/
-import CategoryTheory.Functor.ReflectsIsomorphisms
+import CategoryTheory.Functor.ReflectsIso
 import CategoryTheory.Limits.Shapes.Terminal
 
 #align_import category_theory.endofunctor.algebra from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"

2ed2c631

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2022 Joseph Hua. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Bhavik Mehta, Johan Commelin, Reid Barton, Rob Lewis, Joseph Hua
 -/
-import Mathbin.CategoryTheory.Functor.ReflectsIsomorphisms
-import Mathbin.CategoryTheory.Limits.Shapes.Terminal
+import CategoryTheory.Functor.ReflectsIsomorphisms
+import CategoryTheory.Limits.Shapes.Terminal
 
 #align_import category_theory.endofunctor.algebra from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"

2ed2c631

bump to nightly-2023-09-06-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

f3106448

Diff

@@ -72,8 +72,6 @@ structure Hom (A₀ A₁ : Algebra F) where
 #align category_theory.endofunctor.algebra.hom CategoryTheory.Endofunctor.Algebra.Hom
 -/
 
-restate_axiom hom.h'
-
 attribute [simp, reassoc] hom.h
 
 namespace Hom
@@ -333,8 +331,6 @@ structure Hom (V₀ V₁ : Coalgebra F) where
 #align category_theory.endofunctor.coalgebra.hom CategoryTheory.Endofunctor.Coalgebra.Hom
 -/
 
-restate_axiom hom.h'
-
 attribute [simp, reassoc] hom.h
 
 namespace Hom

2ed2c631

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Joseph Hua. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Bhavik Mehta, Johan Commelin, Reid Barton, Rob Lewis, Joseph Hua
-
-! This file was ported from Lean 3 source module category_theory.endofunctor.algebra
-! leanprover-community/mathlib commit 2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Functor.ReflectsIsomorphisms
 import Mathbin.CategoryTheory.Limits.Shapes.Terminal
 
+#align_import category_theory.endofunctor.algebra from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"
+
 /-!
 
 # Algebras of endofunctors

2ed2c631

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -137,6 +137,7 @@ theorem comp_f : (f ≫ g).1 = f.1 ≫ g.1 :=
 /-- Algebras of an endofunctor `F` form a category -/
 instance (F : C ⥤ C) : Category (Algebra F) where
 
+#print CategoryTheory.Endofunctor.Algebra.isoMk /-
 /-- To construct an isomorphism of algebras, it suffices to give an isomorphism of the As which
 commutes with the structure morphisms.
 -/
@@ -148,6 +149,7 @@ def isoMk (h : A₀.1 ≅ A₁.1) (w : F.map h.Hom ≫ A₁.str = A₀.str ≫ h
     { f := h.inv
       h' := by rw [h.eq_comp_inv, category.assoc, ← w, ← functor.map_comp_assoc]; simp }
 #align category_theory.endofunctor.algebra.iso_mk CategoryTheory.Endofunctor.Algebra.isoMk
+-/
 
 #print CategoryTheory.Endofunctor.Algebra.forget /-
 /-- The forgetful functor from the category of algebras, forgetting the algebraic structure. -/
@@ -238,6 +240,7 @@ def functorOfNatTransEq {F G : C ⥤ C} {α β : F ⟶ G} (h : α = β) :
 #align category_theory.endofunctor.algebra.functor_of_nat_trans_eq CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq
 -/
 
+#print CategoryTheory.Endofunctor.Algebra.equivOfNatIso /-
 /-- Naturally isomorphic endofunctors give equivalent categories of algebras.
 Furthermore, they are equivalent as categories over `C`, that is,
 we have `equiv_of_nat_iso h ⋙ forget = forget`.
@@ -251,37 +254,48 @@ def equivOfNatIso {F G : C ⥤ C} (α : F ≅ G) : Algebra F ≌ Algebra G
   counitIso :=
     (functorOfNatTransComp _ _).symm ≪≫ functorOfNatTransEq (by simp) ≪≫ functorOfNatTransId
 #align category_theory.endofunctor.algebra.equiv_of_nat_iso CategoryTheory.Endofunctor.Algebra.equivOfNatIso
+-/
 
 namespace Initial
 
 variable {A} (h : Limits.IsInitial A)
 
+#print CategoryTheory.Endofunctor.Algebra.Initial.strInv /-
 /-- The inverse of the structure map of an initial algebra -/
 @[simp]
 def strInv : A.1 ⟶ F.obj A.1 :=
   (h.to ⟨F.obj A.1, F.map A.str⟩).1
 #align category_theory.endofunctor.algebra.initial.str_inv CategoryTheory.Endofunctor.Algebra.Initial.strInv
+-/
 
+#print CategoryTheory.Endofunctor.Algebra.Initial.left_inv' /-
 theorem left_inv' : (⟨strInv h ≫ A.str⟩ : A ⟶ A) = 𝟙 A :=
   Limits.IsInitial.hom_ext h _ (𝟙 A)
 #align category_theory.endofunctor.algebra.initial.left_inv' CategoryTheory.Endofunctor.Algebra.Initial.left_inv'
+-/
 
+#print CategoryTheory.Endofunctor.Algebra.Initial.left_inv /-
 theorem left_inv : strInv h ≫ A.str = 𝟙 _ :=
   congr_arg Hom.f (left_inv' h)
 #align category_theory.endofunctor.algebra.initial.left_inv CategoryTheory.Endofunctor.Algebra.Initial.left_inv
+-/
 
+#print CategoryTheory.Endofunctor.Algebra.Initial.right_inv /-
 theorem right_inv : A.str ≫ strInv h = 𝟙 _ :=
   by
   rw [str_inv, ← (h.to ⟨F.obj A.1, F.map A.str⟩).h, ← F.map_id, ← F.map_comp]
   congr; exact left_inv h
 #align category_theory.endofunctor.algebra.initial.right_inv CategoryTheory.Endofunctor.Algebra.Initial.right_inv
+-/
 
+#print CategoryTheory.Endofunctor.Algebra.Initial.str_isIso /-
 /-- The structure map of the inital algebra is an isomorphism,
 hence endofunctors preserve their initial algebras
 -/
 theorem str_isIso (h : Limits.IsInitial A) : IsIso A.str :=
   { out := ⟨strInv h, right_inv _, left_inv _⟩ }
 #align category_theory.endofunctor.algebra.initial.str_is_iso CategoryTheory.Endofunctor.Algebra.Initial.str_isIso
+-/
 
 end Initial
 
@@ -384,6 +398,7 @@ theorem comp_f : (f ≫ g).1 = f.1 ≫ g.1 :=
 /-- Coalgebras of an endofunctor `F` form a category -/
 instance (F : C ⥤ C) : Category (Coalgebra F) where
 
+#print CategoryTheory.Endofunctor.Coalgebra.isoMk /-
 /-- To construct an isomorphism of coalgebras, it suffices to give an isomorphism of the Vs which
 commutes with the structure morphisms.
 -/
@@ -397,6 +412,7 @@ def isoMk (h : V₀.1 ≅ V₁.1) (w : V₀.str ≫ F.map h.Hom = h.Hom ≫ V₁
         rw [h.eq_inv_comp, ← category.assoc, ← w, category.assoc, ← functor.map_comp]
         simp only [iso.hom_inv_id, Functor.map_id, category.comp_id] }
 #align category_theory.endofunctor.coalgebra.iso_mk CategoryTheory.Endofunctor.Coalgebra.isoMk
+-/
 
 #print CategoryTheory.Endofunctor.Coalgebra.forget /-
 /-- The forgetful functor from the category of coalgebras, forgetting the coalgebraic structure. -/
@@ -490,6 +506,7 @@ def functorOfNatTransEq {F G : C ⥤ C} {α β : F ⟶ G} (h : α = β) :
 #align category_theory.endofunctor.coalgebra.functor_of_nat_trans_eq CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq
 -/
 
+#print CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso /-
 /-- Naturally isomorphic endofunctors give equivalent categories of coalgebras.
 Furthermore, they are equivalent as categories over `C`, that is,
 we have `equiv_of_nat_iso h ⋙ forget = forget`.
@@ -503,6 +520,7 @@ def equivOfNatIso {F G : C ⥤ C} (α : F ≅ G) : Coalgebra F ≌ Coalgebra G
   counitIso :=
     (functorOfNatTransComp _ _).symm ≪≫ functorOfNatTransEq (by simp) ≪≫ functorOfNatTransId
 #align category_theory.endofunctor.coalgebra.equiv_of_nat_iso CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso
+-/
 
 end Coalgebra
 
@@ -510,17 +528,21 @@ namespace Adjunction
 
 variable {F : C ⥤ C} {G : C ⥤ C}
 
+#print CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_str /-
 theorem Algebra.homEquiv_naturality_str (adj : F ⊣ G) (A₁ A₂ : Algebra F) (f : A₁ ⟶ A₂) :
     (adj.homEquiv A₁.a A₁.a) A₁.str ≫ G.map f.f = f.f ≫ (adj.homEquiv A₂.a A₂.a) A₂.str := by
   rw [← adjunction.hom_equiv_naturality_right, ← adjunction.hom_equiv_naturality_left, f.h]
 #align category_theory.endofunctor.adjunction.algebra.hom_equiv_naturality_str CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_str
+-/
 
+#print CategoryTheory.Endofunctor.Adjunction.Coalgebra.homEquiv_naturality_str_symm /-
 theorem Coalgebra.homEquiv_naturality_str_symm (adj : F ⊣ G) (V₁ V₂ : Coalgebra G) (f : V₁ ⟶ V₂) :
     F.map f.f ≫ (adj.homEquiv V₂.V V₂.V).symm V₂.str = (adj.homEquiv V₁.V V₁.V).symm V₁.str ≫ f.f :=
   by
   rw [← adjunction.hom_equiv_naturality_left_symm, ← adjunction.hom_equiv_naturality_right_symm,
     f.h]
 #align category_theory.endofunctor.adjunction.coalgebra.hom_equiv_naturality_str_symm CategoryTheory.Endofunctor.Adjunction.Coalgebra.homEquiv_naturality_str_symm
+-/
 
 #print CategoryTheory.Endofunctor.Adjunction.Algebra.toCoalgebraOf /-
 /-- Given an adjunction `F ⊣ G`, the functor that associates to an algebra over `F` a
@@ -600,6 +622,7 @@ def AlgCoalgEquiv.counitIso (adj : F ⊣ G) :
 #align category_theory.endofunctor.adjunction.alg_coalg_equiv.counit_iso CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso
 -/
 
+#print CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv /-
 /-- If `F` is left adjoint to `G`, then the category of algebras over `F` is equivalent to the
 category of coalgebras over `G`. -/
 def algebraCoalgebraEquiv (adj : F ⊣ G) : Algebra F ≌ Coalgebra G
@@ -610,6 +633,7 @@ def algebraCoalgebraEquiv (adj : F ⊣ G) : Algebra F ≌ Coalgebra G
   counitIso := AlgCoalgEquiv.counitIso adj
   functor_unitIso_comp' A := by ext; exact category.comp_id _
 #align category_theory.endofunctor.adjunction.algebra_coalgebra_equiv CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv
+-/
 
 end Adjunction

2ed2c631

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -273,7 +273,7 @@ theorem left_inv : strInv h ≫ A.str = 𝟙 _ :=
 theorem right_inv : A.str ≫ strInv h = 𝟙 _ :=
   by
   rw [str_inv, ← (h.to ⟨F.obj A.1, F.map A.str⟩).h, ← F.map_id, ← F.map_comp]
-  congr ; exact left_inv h
+  congr; exact left_inv h
 #align category_theory.endofunctor.algebra.initial.right_inv CategoryTheory.Endofunctor.Algebra.Initial.right_inv
 
 /-- The structure map of the inital algebra is an isomorphism,

2ed2c631

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -137,12 +137,6 @@ theorem comp_f : (f ≫ g).1 = f.1 ≫ g.1 :=
 /-- Algebras of an endofunctor `F` form a category -/
 instance (F : C ⥤ C) : Category (Algebra F) where
 
-/- warning: category_theory.endofunctor.algebra.iso_mk -> CategoryTheory.Endofunctor.Algebra.isoMk is a dubious translation:
-lean 3 declaration is
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 /-- To construct an isomorphism of algebras, it suffices to give an isomorphism of the As which
 commutes with the structure morphisms.
 -/
@@ -244,12 +238,6 @@ def functorOfNatTransEq {F G : C ⥤ C} {α β : F ⟶ G} (h : α = β) :
 #align category_theory.endofunctor.algebra.functor_of_nat_trans_eq CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq
 -/
 
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 /-- Naturally isomorphic endofunctors give equivalent categories of algebras.
 Furthermore, they are equivalent as categories over `C`, that is,
 we have `equiv_of_nat_iso h ⋙ forget = forget`.
@@ -268,53 +256,26 @@ namespace Initial
 
 variable {A} (h : Limits.IsInitial A)
 
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 /-- The inverse of the structure map of an initial algebra -/
 @[simp]
 def strInv : A.1 ⟶ F.obj A.1 :=
   (h.to ⟨F.obj A.1, F.map A.str⟩).1
 #align category_theory.endofunctor.algebra.initial.str_inv CategoryTheory.Endofunctor.Algebra.Initial.strInv
 
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 theorem left_inv' : (⟨strInv h ≫ A.str⟩ : A ⟶ A) = 𝟙 A :=
   Limits.IsInitial.hom_ext h _ (𝟙 A)
 #align category_theory.endofunctor.algebra.initial.left_inv' CategoryTheory.Endofunctor.Algebra.Initial.left_inv'
 
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 theorem left_inv : strInv h ≫ A.str = 𝟙 _ :=
   congr_arg Hom.f (left_inv' h)
 #align category_theory.endofunctor.algebra.initial.left_inv CategoryTheory.Endofunctor.Algebra.Initial.left_inv
 
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 theorem right_inv : A.str ≫ strInv h = 𝟙 _ :=
   by
   rw [str_inv, ← (h.to ⟨F.obj A.1, F.map A.str⟩).h, ← F.map_id, ← F.map_comp]
   congr ; exact left_inv h
 #align category_theory.endofunctor.algebra.initial.right_inv CategoryTheory.Endofunctor.Algebra.Initial.right_inv
 
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 /-- The structure map of the inital algebra is an isomorphism,
 hence endofunctors preserve their initial algebras
 -/
@@ -423,12 +384,6 @@ theorem comp_f : (f ≫ g).1 = f.1 ≫ g.1 :=
 /-- Coalgebras of an endofunctor `F` form a category -/
 instance (F : C ⥤ C) : Category (Coalgebra F) where
 
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 /-- To construct an isomorphism of coalgebras, it suffices to give an isomorphism of the Vs which
 commutes with the structure morphisms.
 -/
@@ -535,12 +490,6 @@ def functorOfNatTransEq {F G : C ⥤ C} {α β : F ⟶ G} (h : α = β) :
 #align category_theory.endofunctor.coalgebra.functor_of_nat_trans_eq CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq
 -/
 
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 /-- Naturally isomorphic endofunctors give equivalent categories of coalgebras.
 Furthermore, they are equivalent as categories over `C`, that is,
 we have `equiv_of_nat_iso h ⋙ forget = forget`.
@@ -561,17 +510,11 @@ namespace Adjunction
 
 variable {F : C ⥤ C} {G : C ⥤ C}
 
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 theorem Algebra.homEquiv_naturality_str (adj : F ⊣ G) (A₁ A₂ : Algebra F) (f : A₁ ⟶ A₂) :
     (adj.homEquiv A₁.a A₁.a) A₁.str ≫ G.map f.f = f.f ≫ (adj.homEquiv A₂.a A₂.a) A₂.str := by
   rw [← adjunction.hom_equiv_naturality_right, ← adjunction.hom_equiv_naturality_left, f.h]
 #align category_theory.endofunctor.adjunction.algebra.hom_equiv_naturality_str CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_str
 
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 theorem Coalgebra.homEquiv_naturality_str_symm (adj : F ⊣ G) (V₁ V₂ : Coalgebra G) (f : V₁ ⟶ V₂) :
     F.map f.f ≫ (adj.homEquiv V₂.V V₂.V).symm V₂.str = (adj.homEquiv V₁.V V₁.V).symm V₁.str ≫ f.f :=
   by
@@ -657,12 +600,6 @@ def AlgCoalgEquiv.counitIso (adj : F ⊣ G) :
 #align category_theory.endofunctor.adjunction.alg_coalg_equiv.counit_iso CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso
 -/
 
-/- warning: category_theory.endofunctor.adjunction.algebra_coalgebra_equiv -> CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv is a dubious translation:
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-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {F : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 C _inst_1} {G : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 C _inst_1}, (CategoryTheory.Adjunction.{u1, u1, u2, u2} C _inst_1 C _inst_1 F G) -> (CategoryTheory.Equivalence.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.Endofunctor.Algebra.{u1, u2} C _inst_1 F) (CategoryTheory.Endofunctor.Algebra.CategoryTheory.category.{u1, u2} C _inst_1 F) (CategoryTheory.Endofunctor.Coalgebra.{u1, u2} C _inst_1 G) (CategoryTheory.Endofunctor.Coalgebra.CategoryTheory.category.{u1, u2} C _inst_1 G))
-but is expected to have type
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {F : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 C _inst_1} {G : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 C _inst_1}, (CategoryTheory.Adjunction.{u1, u1, u2, u2} C _inst_1 C _inst_1 F G) -> (CategoryTheory.Equivalence.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.Endofunctor.Algebra.{u1, u2} C _inst_1 F) (CategoryTheory.Endofunctor.Coalgebra.{u1, u2} C _inst_1 G) (CategoryTheory.Endofunctor.Algebra.instCategoryAlgebra.{u1, u2} C _inst_1 F) (CategoryTheory.Endofunctor.Coalgebra.instCategoryCoalgebra.{u1, u2} C _inst_1 G))
-Case conversion may be inaccurate. Consider using '#align category_theory.endofunctor.adjunction.algebra_coalgebra_equiv CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquivₓ'. -/
 /-- If `F` is left adjoint to `G`, then the category of algebras over `F` is equivalent to the
 category of coalgebras over `G`. -/
 def algebraCoalgebraEquiv (adj : F ⊣ G) : Algebra F ≌ Coalgebra G

2ed2c631

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -152,9 +152,7 @@ def isoMk (h : A₀.1 ≅ A₁.1) (w : F.map h.Hom ≫ A₁.str = A₀.str ≫ h
   Hom := { f := h.Hom }
   inv :=
     { f := h.inv
-      h' := by
-        rw [h.eq_comp_inv, category.assoc, ← w, ← functor.map_comp_assoc]
-        simp }
+      h' := by rw [h.eq_comp_inv, category.assoc, ← w, ← functor.map_comp_assoc]; simp }
 #align category_theory.endofunctor.algebra.iso_mk CategoryTheory.Endofunctor.Algebra.isoMk
 
 #print CategoryTheory.Endofunctor.Algebra.forget /-
@@ -170,10 +168,7 @@ def forget (F : C ⥤ C) : Algebra F ⥤ C where
 /-- An algebra morphism with an underlying isomorphism hom in `C` is an algebra isomorphism. -/
 theorem iso_of_iso (f : A₀ ⟶ A₁) [IsIso f.1] : IsIso f :=
   ⟨⟨{   f := inv f.1
-        h' := by
-          rw [is_iso.eq_comp_inv f.1, category.assoc, ← f.h]
-          simp },
-      by tidy⟩⟩
+        h' := by rw [is_iso.eq_comp_inv f.1, category.assoc, ← f.h]; simp }, by tidy⟩⟩
 #align category_theory.endofunctor.algebra.iso_of_iso CategoryTheory.Endofunctor.Algebra.iso_of_iso
 -/
 
@@ -219,15 +214,7 @@ def functorOfNatTrans {F G : C ⥤ C} (α : G ⟶ F) : Algebra F ⥤ Algebra G
 /-- The identity transformation induces the identity endofunctor on the category of algebras. -/
 @[simps (config := { rhsMd := semireducible })]
 def functorOfNatTransId : functorOfNatTrans (𝟙 F) ≅ 𝟭 _ :=
-  NatIso.ofComponents
-    (fun X =>
-      isoMk (Iso.refl _)
-        (by
-          dsimp
-          simp))
-    fun X Y f => by
-    ext
-    dsimp
+  NatIso.ofComponents (fun X => isoMk (Iso.refl _) (by dsimp; simp)) fun X Y f => by ext; dsimp;
     simp
 #align category_theory.endofunctor.algebra.functor_of_nat_trans_id CategoryTheory.Endofunctor.Algebra.functorOfNatTransId
 -/
@@ -237,15 +224,7 @@ def functorOfNatTransId : functorOfNatTrans (𝟙 F) ≅ 𝟭 _ :=
 @[simps (config := { rhsMd := semireducible })]
 def functorOfNatTransComp {F₀ F₁ F₂ : C ⥤ C} (α : F₀ ⟶ F₁) (β : F₁ ⟶ F₂) :
     functorOfNatTrans (α ≫ β) ≅ functorOfNatTrans β ⋙ functorOfNatTrans α :=
-  NatIso.ofComponents
-    (fun X =>
-      isoMk (Iso.refl _)
-        (by
-          dsimp
-          simp))
-    fun X Y f => by
-    ext
-    dsimp
+  NatIso.ofComponents (fun X => isoMk (Iso.refl _) (by dsimp; simp)) fun X Y f => by ext; dsimp;
     simp
 #align category_theory.endofunctor.algebra.functor_of_nat_trans_comp CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp
 -/
@@ -260,15 +239,7 @@ lemmas about.
 @[simps (config := { rhsMd := semireducible })]
 def functorOfNatTransEq {F G : C ⥤ C} {α β : F ⟶ G} (h : α = β) :
     functorOfNatTrans α ≅ functorOfNatTrans β :=
-  NatIso.ofComponents
-    (fun X =>
-      isoMk (Iso.refl _)
-        (by
-          dsimp
-          simp [h]))
-    fun X Y f => by
-    ext
-    dsimp
+  NatIso.ofComponents (fun X => isoMk (Iso.refl _) (by dsimp; simp [h])) fun X Y f => by ext; dsimp;
     simp
 #align category_theory.endofunctor.algebra.functor_of_nat_trans_eq CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq
 -/
@@ -335,8 +306,7 @@ Case conversion may be inaccurate. Consider using '#align category_theory.endofu
 theorem right_inv : A.str ≫ strInv h = 𝟙 _ :=
   by
   rw [str_inv, ← (h.to ⟨F.obj A.1, F.map A.str⟩).h, ← F.map_id, ← F.map_comp]
-  congr
-  exact left_inv h
+  congr ; exact left_inv h
 #align category_theory.endofunctor.algebra.initial.right_inv CategoryTheory.Endofunctor.Algebra.Initial.right_inv
 
 /- warning: category_theory.endofunctor.algebra.initial.str_is_iso -> CategoryTheory.Endofunctor.Algebra.Initial.str_isIso is a dubious translation:
@@ -487,10 +457,8 @@ def forget (F : C ⥤ C) : Coalgebra F ⥤ C
 /-- A coalgebra morphism with an underlying isomorphism hom in `C` is a coalgebra isomorphism. -/
 theorem iso_of_iso (f : V₀ ⟶ V₁) [IsIso f.1] : IsIso f :=
   ⟨⟨{   f := inv f.1
-        h' := by
-          rw [is_iso.eq_inv_comp f.1, ← category.assoc, ← f.h, category.assoc]
-          simp },
-      by tidy⟩⟩
+        h' := by rw [is_iso.eq_inv_comp f.1, ← category.assoc, ← f.h, category.assoc]; simp }, by
+      tidy⟩⟩
 #align category_theory.endofunctor.coalgebra.iso_of_iso CategoryTheory.Endofunctor.Coalgebra.iso_of_iso
 -/
 
@@ -538,15 +506,7 @@ def functorOfNatTrans {F G : C ⥤ C} (α : F ⟶ G) : Coalgebra F ⥤ Coalgebra
 /-- The identity transformation induces the identity endofunctor on the category of coalgebras. -/
 @[simps (config := { rhsMd := semireducible })]
 def functorOfNatTransId : functorOfNatTrans (𝟙 F) ≅ 𝟭 _ :=
-  NatIso.ofComponents
-    (fun X =>
-      isoMk (Iso.refl _)
-        (by
-          dsimp
-          simp))
-    fun X Y f => by
-    ext
-    dsimp
+  NatIso.ofComponents (fun X => isoMk (Iso.refl _) (by dsimp; simp)) fun X Y f => by ext; dsimp;
     simp
 #align category_theory.endofunctor.coalgebra.functor_of_nat_trans_id CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId
 -/
@@ -556,15 +516,7 @@ def functorOfNatTransId : functorOfNatTrans (𝟙 F) ≅ 𝟭 _ :=
 @[simps (config := { rhsMd := semireducible })]
 def functorOfNatTransComp {F₀ F₁ F₂ : C ⥤ C} (α : F₀ ⟶ F₁) (β : F₁ ⟶ F₂) :
     functorOfNatTrans (α ≫ β) ≅ functorOfNatTrans α ⋙ functorOfNatTrans β :=
-  NatIso.ofComponents
-    (fun X =>
-      isoMk (Iso.refl _)
-        (by
-          dsimp
-          simp))
-    fun X Y f => by
-    ext
-    dsimp
+  NatIso.ofComponents (fun X => isoMk (Iso.refl _) (by dsimp; simp)) fun X Y f => by ext; dsimp;
     simp
 #align category_theory.endofunctor.coalgebra.functor_of_nat_trans_comp CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp
 -/
@@ -578,15 +530,7 @@ lemmas about.
 @[simps (config := { rhsMd := semireducible })]
 def functorOfNatTransEq {F G : C ⥤ C} {α β : F ⟶ G} (h : α = β) :
     functorOfNatTrans α ≅ functorOfNatTrans β :=
-  NatIso.ofComponents
-    (fun X =>
-      isoMk (Iso.refl _)
-        (by
-          dsimp
-          simp [h]))
-    fun X Y f => by
-    ext
-    dsimp
+  NatIso.ofComponents (fun X => isoMk (Iso.refl _) (by dsimp; simp [h])) fun X Y f => by ext; dsimp;
     simp
 #align category_theory.endofunctor.coalgebra.functor_of_nat_trans_eq CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq
 -/
@@ -675,28 +619,16 @@ def AlgCoalgEquiv.unitIso (adj : F ⊣ G) :
           h' := by
             erw [F.map_id, category.id_comp, category.comp_id]
             apply (adj.hom_equiv _ _).left_inv A.str }
-      naturality' := fun A₁ A₂ f => by
-        ext1
-        dsimp
-        erw [category.id_comp, category.comp_id]
-        rfl }
+      naturality' := fun A₁ A₂ f => by ext1; dsimp; erw [category.id_comp, category.comp_id]; rfl }
   inv :=
     { app := fun A =>
         { f := 𝟙 A.1
           h' := by
             erw [F.map_id, category.id_comp, category.comp_id]
             apply ((adj.hom_equiv _ _).left_inv A.str).symm }
-      naturality' := fun A₁ A₂ f => by
-        ext1
-        dsimp
-        erw [category.comp_id, category.id_comp]
-        rfl }
-  hom_inv_id' := by
-    ext
-    exact category.comp_id _
-  inv_hom_id' := by
-    ext
-    exact category.comp_id _
+      naturality' := fun A₁ A₂ f => by ext1; dsimp; erw [category.comp_id, category.id_comp]; rfl }
+  hom_inv_id' := by ext; exact category.comp_id _
+  inv_hom_id' := by ext; exact category.comp_id _
 #align category_theory.endofunctor.adjunction.alg_coalg_equiv.unit_iso CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso
 -/
 
@@ -710,32 +642,18 @@ def AlgCoalgEquiv.counitIso (adj : F ⊣ G) :
     { app := fun V =>
         { f := 𝟙 V.1
           h' := by
-            dsimp
-            erw [G.map_id, category.id_comp, category.comp_id]
+            dsimp; erw [G.map_id, category.id_comp, category.comp_id]
             apply (adj.hom_equiv _ _).right_inv V.str }
-      naturality' := fun V₁ V₂ f => by
-        ext1
-        dsimp
-        erw [category.comp_id, category.id_comp]
-        rfl }
+      naturality' := fun V₁ V₂ f => by ext1; dsimp; erw [category.comp_id, category.id_comp]; rfl }
   inv :=
     { app := fun V =>
         { f := 𝟙 V.1
           h' := by
-            dsimp
-            rw [G.map_id, category.comp_id, category.id_comp]
+            dsimp; rw [G.map_id, category.comp_id, category.id_comp]
             apply ((adj.hom_equiv _ _).right_inv V.str).symm }
-      naturality' := fun V₁ V₂ f => by
-        ext1
-        dsimp
-        erw [category.comp_id, category.id_comp]
-        rfl }
-  hom_inv_id' := by
-    ext
-    exact category.comp_id _
-  inv_hom_id' := by
-    ext
-    exact category.comp_id _
+      naturality' := fun V₁ V₂ f => by ext1; dsimp; erw [category.comp_id, category.id_comp]; rfl }
+  hom_inv_id' := by ext; exact category.comp_id _
+  inv_hom_id' := by ext; exact category.comp_id _
 #align category_theory.endofunctor.adjunction.alg_coalg_equiv.counit_iso CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso
 -/
 
@@ -753,9 +671,7 @@ def algebraCoalgebraEquiv (adj : F ⊣ G) : Algebra F ≌ Coalgebra G
   inverse := Coalgebra.toAlgebraOf adj
   unitIso := AlgCoalgEquiv.unitIso adj
   counitIso := AlgCoalgEquiv.counitIso adj
-  functor_unitIso_comp' A := by
-    ext
-    exact category.comp_id _
+  functor_unitIso_comp' A := by ext; exact category.comp_id _
 #align category_theory.endofunctor.adjunction.algebra_coalgebra_equiv CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv
 
 end Adjunction

2ed2c631

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -310,10 +310,7 @@ def strInv : A.1 ⟶ F.obj A.1 :=
 #align category_theory.endofunctor.algebra.initial.str_inv CategoryTheory.Endofunctor.Algebra.Initial.strInv
 
 /- warning: category_theory.endofunctor.algebra.initial.left_inv' -> CategoryTheory.Endofunctor.Algebra.Initial.left_inv' is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.endofunctor.algebra.initial.left_inv' CategoryTheory.Endofunctor.Algebra.Initial.left_inv'ₓ'. -/
 theorem left_inv' : (⟨strInv h ≫ A.str⟩ : A ⟶ A) = 𝟙 A :=
   Limits.IsInitial.hom_ext h _ (𝟙 A)
@@ -621,10 +618,7 @@ namespace Adjunction
 variable {F : C ⥤ C} {G : C ⥤ C}
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.endofunctor.adjunction.algebra.hom_equiv_naturality_str CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_strₓ'. -/
 theorem Algebra.homEquiv_naturality_str (adj : F ⊣ G) (A₁ A₂ : Algebra F) (f : A₁ ⟶ A₂) :
     (adj.homEquiv A₁.a A₁.a) A₁.str ≫ G.map f.f = f.f ≫ (adj.homEquiv A₂.a A₂.a) A₂.str := by
@@ -632,10 +626,7 @@ theorem Algebra.homEquiv_naturality_str (adj : F ⊣ G) (A₁ A₂ : Algebra F)
 #align category_theory.endofunctor.adjunction.algebra.hom_equiv_naturality_str CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_str
 
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(CategoryTheory.Endofunctor.Coalgebra.V.{u1, u2} C _inst_1 G V₁))) (CategoryTheory.Adjunction.homEquiv.{u1, u1, u2, u2} C _inst_1 C _inst_1 F G adj (CategoryTheory.Endofunctor.Coalgebra.V.{u1, u2} C _inst_1 G V₁) (CategoryTheory.Endofunctor.Coalgebra.V.{u1, u2} C _inst_1 G V₁))) (CategoryTheory.Endofunctor.Coalgebra.str.{u1, u2} C _inst_1 G V₁)) (CategoryTheory.Endofunctor.Coalgebra.Hom.f.{u1, u2} C _inst_1 G V₁ V₂ f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.endofunctor.adjunction.coalgebra.hom_equiv_naturality_str_symm CategoryTheory.Endofunctor.Adjunction.Coalgebra.homEquiv_naturality_str_symmₓ'. -/
 theorem Coalgebra.homEquiv_naturality_str_symm (adj : F ⊣ G) (V₁ V₂ : Coalgebra G) (f : V₁ ⟶ V₂) :
     F.map f.f ≫ (adj.homEquiv V₂.V V₂.V).symm V₂.str = (adj.homEquiv V₁.V V₁.V).symm V₁.str ≫ f.f :=

2ed2c631

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -77,7 +77,7 @@ structure Hom (A₀ A₁ : Algebra F) where
 
 restate_axiom hom.h'
 
-attribute [simp, reassoc.1] hom.h
+attribute [simp, reassoc] hom.h
 
 namespace Hom
 
@@ -396,7 +396,7 @@ structure Hom (V₀ V₁ : Coalgebra F) where
 
 restate_axiom hom.h'
 
-attribute [simp, reassoc.1] hom.h
+attribute [simp, reassoc] hom.h
 
 namespace Hom

2ed2c631

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -624,7 +624,7 @@ variable {F : C ⥤ C} {G : C ⥤ C}
 lean 3 declaration is
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 but is expected to have type
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 Case conversion may be inaccurate. Consider using '#align category_theory.endofunctor.adjunction.algebra.hom_equiv_naturality_str CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_strₓ'. -/
 theorem Algebra.homEquiv_naturality_str (adj : F ⊣ G) (A₁ A₂ : Algebra F) (f : A₁ ⟶ A₂) :
     (adj.homEquiv A₁.a A₁.a) A₁.str ≫ G.map f.f = f.f ≫ (adj.homEquiv A₂.a A₂.a) A₂.str := by
@@ -635,7 +635,7 @@ theorem Algebra.homEquiv_naturality_str (adj : F ⊣ G) (A₁ A₂ : Algebra F)
 lean 3 declaration is
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(CategoryTheory.Endofunctor.Coalgebra.V.{u1, u2} C _inst_1 G V₁))) (CategoryTheory.Adjunction.homEquiv.{u1, u1, u2, u2} C _inst_1 C _inst_1 F G adj (CategoryTheory.Endofunctor.Coalgebra.V.{u1, u2} C _inst_1 G V₁) (CategoryTheory.Endofunctor.Coalgebra.V.{u1, u2} C _inst_1 G V₁))) (CategoryTheory.Endofunctor.Coalgebra.str.{u1, u2} C _inst_1 G V₁)) (CategoryTheory.Endofunctor.Coalgebra.Hom.f.{u1, u2} C _inst_1 G V₁ V₂ f))
 Case conversion may be inaccurate. Consider using '#align category_theory.endofunctor.adjunction.coalgebra.hom_equiv_naturality_str_symm CategoryTheory.Endofunctor.Adjunction.Coalgebra.homEquiv_naturality_str_symmₓ'. -/
 theorem Coalgebra.homEquiv_naturality_str_symm (adj : F ⊣ G) (V₁ V₂ : Coalgebra G) (f : V₁ ⟶ V₂) :
     F.map f.f ≫ (adj.homEquiv V₂.V V₂.V).symm V₂.str = (adj.homEquiv V₁.V V₁.V).symm V₁.str ≫ f.f :=

2ed2c631

bump to nightly-2023-05-18-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

b46e9d53

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Bhavik Mehta, Johan Commelin, Reid Barton, Rob Lewis, Joseph Hua
 
 ! This file was ported from Lean 3 source module category_theory.endofunctor.algebra
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe
 ! 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.Limits.Shapes.Terminal
 
 # Algebras of endofunctors
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file defines (co)algebras of an endofunctor, and provides the category instance for them.
 It also defines the forgetful functor from the category of (co)algebras. It is shown that the
 structure map of the initial algebra of an endofunctor is an isomorphism. Furthermore, it is shown

70fd9563

bump to nightly-2023-05-16-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

9cb92e8c

Diff

@@ -37,11 +37,13 @@ namespace Endofunctor
 
 variable {C : Type u} [Category.{v} C]
 
+#print CategoryTheory.Endofunctor.Algebra /-
 /-- An algebra of an endofunctor; `str` stands for "structure morphism" -/
 structure Algebra (F : C ⥤ C) where
   a : C
   str : F.obj A ⟶ A
 #align category_theory.endofunctor.algebra CategoryTheory.Endofunctor.Algebra
+-/
 
 instance [Inhabited C] : Inhabited (Algebra (𝟭 C)) :=
   ⟨⟨default, 𝟙 _⟩⟩
@@ -50,6 +52,7 @@ namespace Algebra
 
 variable {F : C ⥤ C} (A : Algebra F) {A₀ A₁ A₂ : Algebra F}
 
+#print CategoryTheory.Endofunctor.Algebra.Hom /-
 /-
 ```
         str
@@ -67,6 +70,7 @@ structure Hom (A₀ A₁ : Algebra F) where
   f : A₀.1 ⟶ A₁.1
   h' : F.map f ≫ A₁.str = A₀.str ≫ f := by obviously
 #align category_theory.endofunctor.algebra.hom CategoryTheory.Endofunctor.Algebra.Hom
+-/
 
 restate_axiom hom.h'
 
@@ -74,16 +78,20 @@ attribute [simp, reassoc.1] hom.h
 
 namespace Hom
 
+#print CategoryTheory.Endofunctor.Algebra.Hom.id /-
 /-- The identity morphism of an algebra of endofunctor `F` -/
 def id : Hom A A where f := 𝟙 _
 #align category_theory.endofunctor.algebra.hom.id CategoryTheory.Endofunctor.Algebra.Hom.id
+-/
 
 instance : Inhabited (Hom A A) :=
   ⟨{ f := 𝟙 _ }⟩
 
+#print CategoryTheory.Endofunctor.Algebra.Hom.comp /-
 /-- The composition of morphisms between algebras of endofunctor `F` -/
 def comp (f : Hom A₀ A₁) (g : Hom A₁ A₂) : Hom A₀ A₂ where f := f.1 ≫ g.1
 #align category_theory.endofunctor.algebra.hom.comp CategoryTheory.Endofunctor.Algebra.Hom.comp
+-/
 
 end Hom
 
@@ -93,31 +101,45 @@ instance (F : C ⥤ C) : CategoryStruct (Algebra F)
   id := Hom.id
   comp := @Hom.comp _ _ _
 
+#print CategoryTheory.Endofunctor.Algebra.id_eq_id /-
 @[simp]
 theorem id_eq_id : Algebra.Hom.id A = 𝟙 A :=
   rfl
 #align category_theory.endofunctor.algebra.id_eq_id CategoryTheory.Endofunctor.Algebra.id_eq_id
+-/
 
+#print CategoryTheory.Endofunctor.Algebra.id_f /-
 @[simp]
 theorem id_f : (𝟙 _ : A ⟶ A).1 = 𝟙 A.1 :=
   rfl
 #align category_theory.endofunctor.algebra.id_f CategoryTheory.Endofunctor.Algebra.id_f
+-/
 
 variable {A₀ A₁ A₂} (f : A₀ ⟶ A₁) (g : A₁ ⟶ A₂)
 
+#print CategoryTheory.Endofunctor.Algebra.comp_eq_comp /-
 @[simp]
 theorem comp_eq_comp : Algebra.Hom.comp f g = f ≫ g :=
   rfl
 #align category_theory.endofunctor.algebra.comp_eq_comp CategoryTheory.Endofunctor.Algebra.comp_eq_comp
+-/
 
+#print CategoryTheory.Endofunctor.Algebra.comp_f /-
 @[simp]
 theorem comp_f : (f ≫ g).1 = f.1 ≫ g.1 :=
   rfl
 #align category_theory.endofunctor.algebra.comp_f CategoryTheory.Endofunctor.Algebra.comp_f
+-/
 
 /-- Algebras of an endofunctor `F` form a category -/
 instance (F : C ⥤ C) : Category (Algebra F) where
 
+/- warning: category_theory.endofunctor.algebra.iso_mk -> CategoryTheory.Endofunctor.Algebra.isoMk is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align category_theory.endofunctor.algebra.iso_mk CategoryTheory.Endofunctor.Algebra.isoMkₓ'. -/
 /-- To construct an isomorphism of algebras, it suffices to give an isomorphism of the As which
 commutes with the structure morphisms.
 -/
@@ -132,13 +154,16 @@ def isoMk (h : A₀.1 ≅ A₁.1) (w : F.map h.Hom ≫ A₁.str = A₀.str ≫ h
         simp }
 #align category_theory.endofunctor.algebra.iso_mk CategoryTheory.Endofunctor.Algebra.isoMk
 
+#print CategoryTheory.Endofunctor.Algebra.forget /-
 /-- The forgetful functor from the category of algebras, forgetting the algebraic structure. -/
 @[simps]
 def forget (F : C ⥤ C) : Algebra F ⥤ C where
   obj A := A.1
   map A B f := f.1
 #align category_theory.endofunctor.algebra.forget CategoryTheory.Endofunctor.Algebra.forget
+-/
 
+#print CategoryTheory.Endofunctor.Algebra.iso_of_iso /-
 /-- An algebra morphism with an underlying isomorphism hom in `C` is an algebra isomorphism. -/
 theorem iso_of_iso (f : A₀ ⟶ A₁) [IsIso f.1] : IsIso f :=
   ⟨⟨{   f := inv f.1
@@ -147,23 +172,33 @@ theorem iso_of_iso (f : A₀ ⟶ A₁) [IsIso f.1] : IsIso f :=
           simp },
       by tidy⟩⟩
 #align category_theory.endofunctor.algebra.iso_of_iso CategoryTheory.Endofunctor.Algebra.iso_of_iso
+-/
 
+#print CategoryTheory.Endofunctor.Algebra.forget_reflects_iso /-
 instance forget_reflects_iso : ReflectsIsomorphisms (forget F) where reflects A B := iso_of_iso
 #align category_theory.endofunctor.algebra.forget_reflects_iso CategoryTheory.Endofunctor.Algebra.forget_reflects_iso
+-/
 
+#print CategoryTheory.Endofunctor.Algebra.forget_faithful /-
 instance forget_faithful : Faithful (forget F) where
 #align category_theory.endofunctor.algebra.forget_faithful CategoryTheory.Endofunctor.Algebra.forget_faithful
+-/
 
+#print CategoryTheory.Endofunctor.Algebra.epi_of_epi /-
 /-- An algebra morphism with an underlying epimorphism hom in `C` is an algebra epimorphism. -/
 theorem epi_of_epi {X Y : Algebra F} (f : X ⟶ Y) [h : Epi f.1] : Epi f :=
   (forget F).epi_of_epi_map h
 #align category_theory.endofunctor.algebra.epi_of_epi CategoryTheory.Endofunctor.Algebra.epi_of_epi
+-/
 
+#print CategoryTheory.Endofunctor.Algebra.mono_of_mono /-
 /-- An algebra morphism with an underlying monomorphism hom in `C` is an algebra monomorphism. -/
 theorem mono_of_mono {X Y : Algebra F} (f : X ⟶ Y) [h : Mono f.1] : Mono f :=
   (forget F).mono_of_mono_map h
 #align category_theory.endofunctor.algebra.mono_of_mono CategoryTheory.Endofunctor.Algebra.mono_of_mono
+-/
 
+#print CategoryTheory.Endofunctor.Algebra.functorOfNatTrans /-
 /-- From a natural transformation `α : G → F` we get a functor from
 algebras of `F` to algebras of `G`.
 -/
@@ -175,7 +210,9 @@ def functorOfNatTrans {F G : C ⥤ C} (α : G ⟶ F) : Algebra F ⥤ Algebra G
       str := α.app A.1 ≫ A.str }
   map A₀ A₁ f := { f := f.1 }
 #align category_theory.endofunctor.algebra.functor_of_nat_trans CategoryTheory.Endofunctor.Algebra.functorOfNatTrans
+-/
 
+#print CategoryTheory.Endofunctor.Algebra.functorOfNatTransId /-
 /-- The identity transformation induces the identity endofunctor on the category of algebras. -/
 @[simps (config := { rhsMd := semireducible })]
 def functorOfNatTransId : functorOfNatTrans (𝟙 F) ≅ 𝟭 _ :=
@@ -190,7 +227,9 @@ def functorOfNatTransId : functorOfNatTrans (𝟙 F) ≅ 𝟭 _ :=
     dsimp
     simp
 #align category_theory.endofunctor.algebra.functor_of_nat_trans_id CategoryTheory.Endofunctor.Algebra.functorOfNatTransId
+-/
 
+#print CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp /-
 /-- A composition of natural transformations gives the composition of corresponding functors. -/
 @[simps (config := { rhsMd := semireducible })]
 def functorOfNatTransComp {F₀ F₁ F₂ : C ⥤ C} (α : F₀ ⟶ F₁) (β : F₁ ⟶ F₂) :
@@ -206,7 +245,9 @@ def functorOfNatTransComp {F₀ F₁ F₂ : C ⥤ C} (α : F₀ ⟶ F₁) (β :
     dsimp
     simp
 #align category_theory.endofunctor.algebra.functor_of_nat_trans_comp CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp
+-/
 
+#print CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq /-
 /--
 If `α` and `β` are two equal natural transformations, then the functors of algebras induced by them
 are isomorphic.
@@ -227,7 +268,14 @@ def functorOfNatTransEq {F G : C ⥤ C} {α β : F ⟶ G} (h : α = β) :
     dsimp
     simp
 #align category_theory.endofunctor.algebra.functor_of_nat_trans_eq CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq
+-/
 
+/- warning: category_theory.endofunctor.algebra.equiv_of_nat_iso -> CategoryTheory.Endofunctor.Algebra.equivOfNatIso is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align category_theory.endofunctor.algebra.equiv_of_nat_iso CategoryTheory.Endofunctor.Algebra.equivOfNatIsoₓ'. -/
 /-- Naturally isomorphic endofunctors give equivalent categories of algebras.
 Furthermore, they are equivalent as categories over `C`, that is,
 we have `equiv_of_nat_iso h ⋙ forget = forget`.
@@ -246,20 +294,44 @@ namespace Initial
 
 variable {A} (h : Limits.IsInitial A)
 
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 /-- The inverse of the structure map of an initial algebra -/
 @[simp]
 def strInv : A.1 ⟶ F.obj A.1 :=
   (h.to ⟨F.obj A.1, F.map A.str⟩).1
 #align category_theory.endofunctor.algebra.initial.str_inv CategoryTheory.Endofunctor.Algebra.Initial.strInv
 
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 theorem left_inv' : (⟨strInv h ≫ A.str⟩ : A ⟶ A) = 𝟙 A :=
   Limits.IsInitial.hom_ext h _ (𝟙 A)
 #align category_theory.endofunctor.algebra.initial.left_inv' CategoryTheory.Endofunctor.Algebra.Initial.left_inv'
 
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 theorem left_inv : strInv h ≫ A.str = 𝟙 _ :=
   congr_arg Hom.f (left_inv' h)
 #align category_theory.endofunctor.algebra.initial.left_inv CategoryTheory.Endofunctor.Algebra.Initial.left_inv
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.endofunctor.algebra.initial.right_inv CategoryTheory.Endofunctor.Algebra.Initial.right_invₓ'. -/
 theorem right_inv : A.str ≫ strInv h = 𝟙 _ :=
   by
   rw [str_inv, ← (h.to ⟨F.obj A.1, F.map A.str⟩).h, ← F.map_id, ← F.map_comp]
@@ -267,6 +339,12 @@ theorem right_inv : A.str ≫ strInv h = 𝟙 _ :=
   exact left_inv h
 #align category_theory.endofunctor.algebra.initial.right_inv CategoryTheory.Endofunctor.Algebra.Initial.right_inv
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.endofunctor.algebra.initial.str_is_iso CategoryTheory.Endofunctor.Algebra.Initial.str_isIsoₓ'. -/
 /-- The structure map of the inital algebra is an isomorphism,
 hence endofunctors preserve their initial algebras
 -/
@@ -278,11 +356,13 @@ end Initial
 
 end Algebra
 
+#print CategoryTheory.Endofunctor.Coalgebra /-
 /-- A coalgebra of an endofunctor; `str` stands for "structure morphism" -/
 structure Coalgebra (F : C ⥤ C) where
   V : C
   str : V ⟶ F.obj V
 #align category_theory.endofunctor.coalgebra CategoryTheory.Endofunctor.Coalgebra
+-/
 
 instance [Inhabited C] : Inhabited (Coalgebra (𝟭 C)) :=
   ⟨⟨default, 𝟙 _⟩⟩
@@ -291,6 +371,7 @@ namespace Coalgebra
 
 variable {F : C ⥤ C} (V : Coalgebra F) {V₀ V₁ V₂ : Coalgebra F}
 
+#print CategoryTheory.Endofunctor.Coalgebra.Hom /-
 /-
 ```
         str
@@ -308,6 +389,7 @@ structure Hom (V₀ V₁ : Coalgebra F) where
   f : V₀.1 ⟶ V₁.1
   h' : V₀.str ≫ F.map f = f ≫ V₁.str := by obviously
 #align category_theory.endofunctor.coalgebra.hom CategoryTheory.Endofunctor.Coalgebra.Hom
+-/
 
 restate_axiom hom.h'
 
@@ -315,16 +397,20 @@ attribute [simp, reassoc.1] hom.h
 
 namespace Hom
 
+#print CategoryTheory.Endofunctor.Coalgebra.Hom.id /-
 /-- The identity morphism of an algebra of endofunctor `F` -/
 def id : Hom V V where f := 𝟙 _
 #align category_theory.endofunctor.coalgebra.hom.id CategoryTheory.Endofunctor.Coalgebra.Hom.id
+-/
 
 instance : Inhabited (Hom V V) :=
   ⟨{ f := 𝟙 _ }⟩
 
+#print CategoryTheory.Endofunctor.Coalgebra.Hom.comp /-
 /-- The composition of morphisms between algebras of endofunctor `F` -/
 def comp (f : Hom V₀ V₁) (g : Hom V₁ V₂) : Hom V₀ V₂ where f := f.1 ≫ g.1
 #align category_theory.endofunctor.coalgebra.hom.comp CategoryTheory.Endofunctor.Coalgebra.Hom.comp
+-/
 
 end Hom
 
@@ -334,31 +420,45 @@ instance (F : C ⥤ C) : CategoryStruct (Coalgebra F)
   id := Hom.id
   comp := @Hom.comp _ _ _
 
+#print CategoryTheory.Endofunctor.Coalgebra.id_eq_id /-
 @[simp]
 theorem id_eq_id : Coalgebra.Hom.id V = 𝟙 V :=
   rfl
 #align category_theory.endofunctor.coalgebra.id_eq_id CategoryTheory.Endofunctor.Coalgebra.id_eq_id
+-/
 
+#print CategoryTheory.Endofunctor.Coalgebra.id_f /-
 @[simp]
 theorem id_f : (𝟙 _ : V ⟶ V).1 = 𝟙 V.1 :=
   rfl
 #align category_theory.endofunctor.coalgebra.id_f CategoryTheory.Endofunctor.Coalgebra.id_f
+-/
 
 variable {V₀ V₁ V₂} (f : V₀ ⟶ V₁) (g : V₁ ⟶ V₂)
 
+#print CategoryTheory.Endofunctor.Coalgebra.comp_eq_comp /-
 @[simp]
 theorem comp_eq_comp : Coalgebra.Hom.comp f g = f ≫ g :=
   rfl
 #align category_theory.endofunctor.coalgebra.comp_eq_comp CategoryTheory.Endofunctor.Coalgebra.comp_eq_comp
+-/
 
+#print CategoryTheory.Endofunctor.Coalgebra.comp_f /-
 @[simp]
 theorem comp_f : (f ≫ g).1 = f.1 ≫ g.1 :=
   rfl
 #align category_theory.endofunctor.coalgebra.comp_f CategoryTheory.Endofunctor.Coalgebra.comp_f
+-/
 
 /-- Coalgebras of an endofunctor `F` form a category -/
 instance (F : C ⥤ C) : Category (Coalgebra F) where
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.endofunctor.coalgebra.iso_mk CategoryTheory.Endofunctor.Coalgebra.isoMkₓ'. -/
 /-- To construct an isomorphism of coalgebras, it suffices to give an isomorphism of the Vs which
 commutes with the structure morphisms.
 -/
@@ -373,6 +473,7 @@ def isoMk (h : V₀.1 ≅ V₁.1) (w : V₀.str ≫ F.map h.Hom = h.Hom ≫ V₁
         simp only [iso.hom_inv_id, Functor.map_id, category.comp_id] }
 #align category_theory.endofunctor.coalgebra.iso_mk CategoryTheory.Endofunctor.Coalgebra.isoMk
 
+#print CategoryTheory.Endofunctor.Coalgebra.forget /-
 /-- The forgetful functor from the category of coalgebras, forgetting the coalgebraic structure. -/
 @[simps]
 def forget (F : C ⥤ C) : Coalgebra F ⥤ C
@@ -380,7 +481,9 @@ def forget (F : C ⥤ C) : Coalgebra F ⥤ C
   obj A := A.1
   map A B f := f.1
 #align category_theory.endofunctor.coalgebra.forget CategoryTheory.Endofunctor.Coalgebra.forget
+-/
 
+#print CategoryTheory.Endofunctor.Coalgebra.iso_of_iso /-
 /-- A coalgebra morphism with an underlying isomorphism hom in `C` is a coalgebra isomorphism. -/
 theorem iso_of_iso (f : V₀ ⟶ V₁) [IsIso f.1] : IsIso f :=
   ⟨⟨{   f := inv f.1
@@ -389,23 +492,33 @@ theorem iso_of_iso (f : V₀ ⟶ V₁) [IsIso f.1] : IsIso f :=
           simp },
       by tidy⟩⟩
 #align category_theory.endofunctor.coalgebra.iso_of_iso CategoryTheory.Endofunctor.Coalgebra.iso_of_iso
+-/
 
+#print CategoryTheory.Endofunctor.Coalgebra.forget_reflects_iso /-
 instance forget_reflects_iso : ReflectsIsomorphisms (forget F) where reflects A B := iso_of_iso
 #align category_theory.endofunctor.coalgebra.forget_reflects_iso CategoryTheory.Endofunctor.Coalgebra.forget_reflects_iso
+-/
 
+#print CategoryTheory.Endofunctor.Coalgebra.forget_faithful /-
 instance forget_faithful : Faithful (forget F) where
 #align category_theory.endofunctor.coalgebra.forget_faithful CategoryTheory.Endofunctor.Coalgebra.forget_faithful
+-/
 
+#print CategoryTheory.Endofunctor.Coalgebra.epi_of_epi /-
 /-- An algebra morphism with an underlying epimorphism hom in `C` is an algebra epimorphism. -/
 theorem epi_of_epi {X Y : Coalgebra F} (f : X ⟶ Y) [h : Epi f.1] : Epi f :=
   (forget F).epi_of_epi_map h
 #align category_theory.endofunctor.coalgebra.epi_of_epi CategoryTheory.Endofunctor.Coalgebra.epi_of_epi
+-/
 
+#print CategoryTheory.Endofunctor.Coalgebra.mono_of_mono /-
 /-- An algebra morphism with an underlying monomorphism hom in `C` is an algebra monomorphism. -/
 theorem mono_of_mono {X Y : Coalgebra F} (f : X ⟶ Y) [h : Mono f.1] : Mono f :=
   (forget F).mono_of_mono_map h
 #align category_theory.endofunctor.coalgebra.mono_of_mono CategoryTheory.Endofunctor.Coalgebra.mono_of_mono
+-/
 
+#print CategoryTheory.Endofunctor.Coalgebra.functorOfNatTrans /-
 /-- From a natural transformation `α : F → G` we get a functor from
 coalgebras of `F` to coalgebras of `G`.
 -/
@@ -419,7 +532,9 @@ def functorOfNatTrans {F G : C ⥤ C} (α : F ⟶ G) : Coalgebra F ⥤ Coalgebra
     { f := f.1
       h' := by rw [category.assoc, ← α.naturality, ← category.assoc, f.h, category.assoc] }
 #align category_theory.endofunctor.coalgebra.functor_of_nat_trans CategoryTheory.Endofunctor.Coalgebra.functorOfNatTrans
+-/
 
+#print CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId /-
 /-- The identity transformation induces the identity endofunctor on the category of coalgebras. -/
 @[simps (config := { rhsMd := semireducible })]
 def functorOfNatTransId : functorOfNatTrans (𝟙 F) ≅ 𝟭 _ :=
@@ -434,7 +549,9 @@ def functorOfNatTransId : functorOfNatTrans (𝟙 F) ≅ 𝟭 _ :=
     dsimp
     simp
 #align category_theory.endofunctor.coalgebra.functor_of_nat_trans_id CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId
+-/
 
+#print CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp /-
 /-- A composition of natural transformations gives the composition of corresponding functors. -/
 @[simps (config := { rhsMd := semireducible })]
 def functorOfNatTransComp {F₀ F₁ F₂ : C ⥤ C} (α : F₀ ⟶ F₁) (β : F₁ ⟶ F₂) :
@@ -450,7 +567,9 @@ def functorOfNatTransComp {F₀ F₁ F₂ : C ⥤ C} (α : F₀ ⟶ F₁) (β :
     dsimp
     simp
 #align category_theory.endofunctor.coalgebra.functor_of_nat_trans_comp CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp
+-/
 
+#print CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq /-
 /-- If `α` and `β` are two equal natural transformations, then the functors of coalgebras induced by
 them are isomorphic.
 We define it like this as opposed to using `eq_to_iso` so that the components are nicer to prove
@@ -470,7 +589,14 @@ def functorOfNatTransEq {F G : C ⥤ C} {α β : F ⟶ G} (h : α = β) :
     dsimp
     simp
 #align category_theory.endofunctor.coalgebra.functor_of_nat_trans_eq CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq
+-/
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.endofunctor.coalgebra.equiv_of_nat_iso CategoryTheory.Endofunctor.Coalgebra.equivOfNatIsoₓ'. -/
 /-- Naturally isomorphic endofunctors give equivalent categories of coalgebras.
 Furthermore, they are equivalent as categories over `C`, that is,
 we have `equiv_of_nat_iso h ⋙ forget = forget`.
@@ -491,11 +617,23 @@ namespace Adjunction
 
 variable {F : C ⥤ C} {G : C ⥤ C}
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.endofunctor.adjunction.algebra.hom_equiv_naturality_str CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_strₓ'. -/
 theorem Algebra.homEquiv_naturality_str (adj : F ⊣ G) (A₁ A₂ : Algebra F) (f : A₁ ⟶ A₂) :
     (adj.homEquiv A₁.a A₁.a) A₁.str ≫ G.map f.f = f.f ≫ (adj.homEquiv A₂.a A₂.a) A₂.str := by
   rw [← adjunction.hom_equiv_naturality_right, ← adjunction.hom_equiv_naturality_left, f.h]
 #align category_theory.endofunctor.adjunction.algebra.hom_equiv_naturality_str CategoryTheory.Endofunctor.Adjunction.Algebra.homEquiv_naturality_str
 
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+Case conversion may be inaccurate. Consider using '#align category_theory.endofunctor.adjunction.coalgebra.hom_equiv_naturality_str_symm CategoryTheory.Endofunctor.Adjunction.Coalgebra.homEquiv_naturality_str_symmₓ'. -/
 theorem Coalgebra.homEquiv_naturality_str_symm (adj : F ⊣ G) (V₁ V₂ : Coalgebra G) (f : V₁ ⟶ V₂) :
     F.map f.f ≫ (adj.homEquiv V₂.V V₂.V).symm V₂.str = (adj.homEquiv V₁.V V₁.V).symm V₁.str ≫ f.f :=
   by
@@ -503,6 +641,7 @@ theorem Coalgebra.homEquiv_naturality_str_symm (adj : F ⊣ G) (V₁ V₂ : Coal
     f.h]
 #align category_theory.endofunctor.adjunction.coalgebra.hom_equiv_naturality_str_symm CategoryTheory.Endofunctor.Adjunction.Coalgebra.homEquiv_naturality_str_symm
 
+#print CategoryTheory.Endofunctor.Adjunction.Algebra.toCoalgebraOf /-
 /-- Given an adjunction `F ⊣ G`, the functor that associates to an algebra over `F` a
 coalgebra over `G` defined via adjunction applied to the structure map. -/
 def Algebra.toCoalgebraOf (adj : F ⊣ G) : Algebra F ⥤ Coalgebra G
@@ -514,7 +653,9 @@ def Algebra.toCoalgebraOf (adj : F ⊣ G) : Algebra F ⥤ Coalgebra G
     { f := f.1
       h' := Algebra.homEquiv_naturality_str adj A₁ A₂ f }
 #align category_theory.endofunctor.adjunction.algebra.to_coalgebra_of CategoryTheory.Endofunctor.Adjunction.Algebra.toCoalgebraOf
+-/
 
+#print CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf /-
 /-- Given an adjunction `F ⊣ G`, the functor that associates to a coalgebra over `G` an algebra over
 `F` defined via adjunction applied to the structure map. -/
 def Coalgebra.toAlgebraOf (adj : F ⊣ G) : Coalgebra G ⥤ Algebra F
@@ -526,7 +667,9 @@ def Coalgebra.toAlgebraOf (adj : F ⊣ G) : Coalgebra G ⥤ Algebra F
     { f := f.1
       h' := Coalgebra.homEquiv_naturality_str_symm adj V₁ V₂ f }
 #align category_theory.endofunctor.adjunction.coalgebra.to_algebra_of CategoryTheory.Endofunctor.Adjunction.Coalgebra.toAlgebraOf
+-/
 
+#print CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso /-
 /-- Given an adjunction, assigning to an algebra over the left adjoint a coalgebra over its right
 adjoint and going back is isomorphic to the identity functor. -/
 def AlgCoalgEquiv.unitIso (adj : F ⊣ G) :
@@ -561,7 +704,9 @@ def AlgCoalgEquiv.unitIso (adj : F ⊣ G) :
     ext
     exact category.comp_id _
 #align category_theory.endofunctor.adjunction.alg_coalg_equiv.unit_iso CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso
+-/
 
+#print CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso /-
 /-- Given an adjunction, assigning to a coalgebra over the right adjoint an algebra over the left
 adjoint and going back is isomorphic to the identity functor. -/
 def AlgCoalgEquiv.counitIso (adj : F ⊣ G) :
@@ -598,7 +743,14 @@ def AlgCoalgEquiv.counitIso (adj : F ⊣ G) :
     ext
     exact category.comp_id _
 #align category_theory.endofunctor.adjunction.alg_coalg_equiv.counit_iso CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso
+-/
 
+/- warning: category_theory.endofunctor.adjunction.algebra_coalgebra_equiv -> CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {F : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 C _inst_1} {G : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 C _inst_1}, (CategoryTheory.Adjunction.{u1, u1, u2, u2} C _inst_1 C _inst_1 F G) -> (CategoryTheory.Equivalence.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.Endofunctor.Algebra.{u1, u2} C _inst_1 F) (CategoryTheory.Endofunctor.Algebra.CategoryTheory.category.{u1, u2} C _inst_1 F) (CategoryTheory.Endofunctor.Coalgebra.{u1, u2} C _inst_1 G) (CategoryTheory.Endofunctor.Coalgebra.CategoryTheory.category.{u1, u2} C _inst_1 G))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {F : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 C _inst_1} {G : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 C _inst_1}, (CategoryTheory.Adjunction.{u1, u1, u2, u2} C _inst_1 C _inst_1 F G) -> (CategoryTheory.Equivalence.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.Endofunctor.Algebra.{u1, u2} C _inst_1 F) (CategoryTheory.Endofunctor.Coalgebra.{u1, u2} C _inst_1 G) (CategoryTheory.Endofunctor.Algebra.instCategoryAlgebra.{u1, u2} C _inst_1 F) (CategoryTheory.Endofunctor.Coalgebra.instCategoryCoalgebra.{u1, u2} C _inst_1 G))
+Case conversion may be inaccurate. Consider using '#align category_theory.endofunctor.adjunction.algebra_coalgebra_equiv CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquivₓ'. -/
 /-- If `F` is left adjoint to `G`, then the category of algebras over `F` is equivalent to the
 category of coalgebras over `G`. -/
 def algebraCoalgebraEquiv (adj : F ⊣ G) : Algebra F ≌ Coalgebra G

70fd9563

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

70fd9563

chore(CategoryTheory): move Full, Faithful, EssSurj, IsEquivalence and ReflectsIsomorphisms to the Functor namespace (#11985)

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

65b7affc

Diff

@@ -152,10 +152,10 @@ theorem iso_of_iso (f : A₀ ⟶ A₁) [IsIso f.1] : IsIso f :=
         simp }, by aesop_cat, by aesop_cat⟩⟩
 #align category_theory.endofunctor.algebra.iso_of_iso CategoryTheory.Endofunctor.Algebra.iso_of_iso
 
-instance forget_reflects_iso : ReflectsIsomorphisms (forget F) where reflects := iso_of_iso
+instance forget_reflects_iso : (forget F).ReflectsIsomorphisms where reflects := iso_of_iso
 #align category_theory.endofunctor.algebra.forget_reflects_iso CategoryTheory.Endofunctor.Algebra.forget_reflects_iso
 
-instance forget_faithful : Faithful (forget F) := { }
+instance forget_faithful : (forget F).Faithful := { }
 #align category_theory.endofunctor.algebra.forget_faithful CategoryTheory.Endofunctor.Algebra.forget_faithful
 
 /-- An algebra morphism with an underlying epimorphism hom in `C` is an algebra epimorphism. -/
@@ -375,10 +375,10 @@ theorem iso_of_iso (f : V₀ ⟶ V₁) [IsIso f.1] : IsIso f :=
         simp }, by aesop_cat, by aesop_cat⟩⟩
 #align category_theory.endofunctor.coalgebra.iso_of_iso CategoryTheory.Endofunctor.Coalgebra.iso_of_iso
 
-instance forget_reflects_iso : ReflectsIsomorphisms (forget F) where reflects := iso_of_iso
+instance forget_reflects_iso : (forget F).ReflectsIsomorphisms where reflects := iso_of_iso
 #align category_theory.endofunctor.coalgebra.forget_reflects_iso CategoryTheory.Endofunctor.Coalgebra.forget_reflects_iso
 
-instance forget_faithful : Faithful (forget F) := { }
+instance forget_faithful : (forget F).Faithful := { }
 #align category_theory.endofunctor.coalgebra.forget_faithful CategoryTheory.Endofunctor.Coalgebra.forget_faithful
 
 /-- An algebra morphism with an underlying epimorphism hom in `C` is an algebra epimorphism. -/

70fd9563

chore: space after ← (#8178)

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

5fb9beab

Diff

@@ -230,7 +230,8 @@ def strInv : A.1 ⟶ F.obj A.1 :=
 
 #align category_theory.endofunctor.algebra.initial.str_inv CategoryTheory.Endofunctor.Algebra.Initial.strInv
 
-theorem left_inv' : ⟨strInv h ≫ A.str, by rw [←Category.assoc, F.map_comp, strInv, ←Hom.h]⟩ = 𝟙 A :=
+theorem left_inv' :
+    ⟨strInv h ≫ A.str, by rw [← Category.assoc, F.map_comp, strInv, ← Hom.h]⟩ = 𝟙 A :=
   Limits.IsInitial.hom_ext h _ (𝟙 A)
 #align category_theory.endofunctor.algebra.initial.left_inv' CategoryTheory.Endofunctor.Algebra.Initial.left_inv'
 
@@ -355,7 +356,7 @@ def isoMk (h : V₀.1 ≅ V₁.1) (w : V₀.str ≫ F.map h.hom = h.hom ≫ V₁
   inv :=
     { f := h.inv
       h := by
-        rw [h.eq_inv_comp, ←Category.assoc, ← w, Category.assoc, ← F.map_comp]
+        rw [h.eq_inv_comp, ← Category.assoc, ← w, Category.assoc, ← F.map_comp]
         simp only [Iso.hom_inv_id, Functor.map_id, Category.comp_id] }
 #align category_theory.endofunctor.coalgebra.iso_mk CategoryTheory.Endofunctor.Coalgebra.isoMk

70fd9563

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) 2022 Joseph Hua. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Bhavik Mehta, Johan Commelin, Reid Barton, Rob Lewis, Joseph Hua
-
-! This file was ported from Lean 3 source module category_theory.endofunctor.algebra
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Limits.Shapes.Terminal
 
+#align_import category_theory.endofunctor.algebra from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 
 # Algebras of endofunctors

70fd9563

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

@@ -333,7 +333,7 @@ theorem id_f : (𝟙 _ : V ⟶ V).1 = 𝟙 V.1 :=
   rfl
 #align category_theory.endofunctor.coalgebra.id_f CategoryTheory.Endofunctor.Coalgebra.id_f
 
-variable  (f : V₀ ⟶ V₁) (g : V₁ ⟶ V₂)
+variable (f : V₀ ⟶ V₁) (g : V₁ ⟶ V₂)
 
 @[simp]
 theorem comp_eq_comp : Coalgebra.Hom.comp f g = f ≫ g :=

70fd9563

chore: fix align linebreaks (#5683)

The result of running

find . -type f -name "*.lean" -exec sed -i -E 'N;s/^#align ([^[:space:]]+)\n *([^[:space:]]+)$/#align \1 \2/' {} \;

Hopefully for the last time...

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

2a702960

Diff

@@ -116,8 +116,7 @@ variable (f : A₀ ⟶ A₁) (g : A₁ ⟶ A₂)
 @[simp]
 theorem comp_eq_comp : Algebra.Hom.comp f g = f ≫ g :=
   rfl
-#align category_theory.endofunctor.algebra.comp_eq_comp
-       CategoryTheory.Endofunctor.Algebra.comp_eq_comp
+#align category_theory.endofunctor.algebra.comp_eq_comp CategoryTheory.Endofunctor.Algebra.comp_eq_comp
 
 @[simp]
 theorem comp_f : (f ≫ g).1 = f.1 ≫ g.1 :=

70fd9563

chore: formatting issues (#4947)

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

5068808d

Diff

@@ -75,7 +75,7 @@ structure Hom (A₀ A₁ : Algebra F) where
 -- restate_axiom Hom.h'
 
 -- Porting note: Originally `[simp, reassoc.1]`
-attribute [reassoc (attr:=simp)] Hom.h
+attribute [reassoc (attr := simp)] Hom.h
 
 namespace Hom
 
@@ -99,7 +99,7 @@ instance (F : C ⥤ C) : CategoryStruct (Algebra F) where
 
 @[ext]
 lemma ext {A B : Algebra F} {f g : A ⟶ B} (w : f.f = g.f := by aesop_cat) : f = g :=
-Hom.ext _ _ w
+  Hom.ext _ _ w
 
 @[simp]
 theorem id_eq_id : Algebra.Hom.id A = 𝟙 A :=
@@ -322,7 +322,7 @@ instance (F : C ⥤ C) : CategoryStruct (Coalgebra F) where
 
 @[ext]
 lemma ext {A B : Coalgebra F} {f g : A ⟶ B} (w : f.f = g.f := by aesop_cat) : f = g :=
-Hom.ext _ _ w
+  Hom.ext _ _ w
 
 @[simp]
 theorem id_eq_id : Coalgebra.Hom.id V = 𝟙 V :=

70fd9563

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

@@ -68,7 +68,7 @@ structure Hom (A₀ A₁ : Algebra F) where
   /-- underlying morphism between the carriers -/
   f : A₀.1 ⟶ A₁.1
   /-- compatibility condition -/
-  h : F.map f ≫ A₁.str = A₀.str ≫ f := by aesop_cat -- Porting note: was `obviously`
+  h : F.map f ≫ A₁.str = A₀.str ≫ f := by aesop_cat
 #align category_theory.endofunctor.algebra.hom CategoryTheory.Endofunctor.Algebra.Hom
 
 -- Porting note: No need to restate axiom
@@ -97,6 +97,10 @@ instance (F : C ⥤ C) : CategoryStruct (Algebra F) where
   id := Hom.id
   comp := @Hom.comp _ _ _
 
+@[ext]
+lemma ext {A B : Algebra F} {f g : A ⟶ B} (w : f.f = g.f := by aesop_cat) : f = g :=
+Hom.ext _ _ w
+
 @[simp]
 theorem id_eq_id : Algebra.Hom.id A = 𝟙 A :=
   rfl
@@ -121,27 +125,20 @@ theorem comp_f : (f ≫ g).1 = f.1 ≫ g.1 :=
 #align category_theory.endofunctor.algebra.comp_f CategoryTheory.Endofunctor.Algebra.comp_f
 
 /-- Algebras of an endofunctor `F` form a category -/
-instance (F : C ⥤ C) : Category (Algebra F) :=
--- Porting note: how to use empty constructor `{}` in Lean 4?
-{ (inferInstance : CategoryStruct (Algebra F)) with
-  id_comp := fun _ => Hom.ext _ _ <| by aesop_cat
-  comp_id := fun _ => Hom.ext _ _ <| by aesop_cat
-  assoc := fun _ _ _ => Hom.ext _ _ <| by aesop_cat }
-
+instance (F : C ⥤ C) : Category (Algebra F) := { }
 
 /-- To construct an isomorphism of algebras, it suffices to give an isomorphism of the As which
 commutes with the structure morphisms.
 -/
 @[simps!]
-def isoMk (h : A₀.1 ≅ A₁.1) (w : F.map h.hom ≫ A₁.str = A₀.str ≫ h.hom) : A₀ ≅ A₁ where
+def isoMk (h : A₀.1 ≅ A₁.1) (w : F.map h.hom ≫ A₁.str = A₀.str ≫ h.hom := by aesop_cat) :
+    A₀ ≅ A₁ where
   hom := { f := h.hom }
   inv :=
     { f := h.inv
       h := by
         rw [h.eq_comp_inv, Category.assoc, ← w, ← Functor.map_comp_assoc]
         simp }
-  hom_inv_id := Hom.ext _ _ (by aesop_cat)
-  inv_hom_id := Hom.ext _ _ (by aesop_cat)
 #align category_theory.endofunctor.algebra.iso_mk CategoryTheory.Endofunctor.Algebra.isoMk
 
 /-- The forgetful functor from the category of algebras, forgetting the algebraic structure. -/
@@ -156,16 +153,13 @@ theorem iso_of_iso (f : A₀ ⟶ A₁) [IsIso f.1] : IsIso f :=
   ⟨⟨{ f := inv f.1
       h := by
         rw [IsIso.eq_comp_inv f.1, Category.assoc, ← f.h]
-        simp }, Hom.ext _ _ <| by aesop, Hom.ext _ _ <| by aesop⟩⟩
--- Porting note: `tidy` can't finish
+        simp }, by aesop_cat, by aesop_cat⟩⟩
 #align category_theory.endofunctor.algebra.iso_of_iso CategoryTheory.Endofunctor.Algebra.iso_of_iso
 
 instance forget_reflects_iso : ReflectsIsomorphisms (forget F) where reflects := iso_of_iso
 #align category_theory.endofunctor.algebra.forget_reflects_iso CategoryTheory.Endofunctor.Algebra.forget_reflects_iso
 
-instance forget_faithful : Faithful (forget F) where
--- Porting note: how to use empty constructor `{}` in Lean 4?
-  map_injective h := Hom.ext _ _ h
+instance forget_faithful : Faithful (forget F) := { }
 #align category_theory.endofunctor.algebra.forget_faithful CategoryTheory.Endofunctor.Algebra.forget_faithful
 
 /-- An algebra morphism with an underlying epimorphism hom in `C` is an algebra epimorphism. -/
@@ -193,16 +187,7 @@ def functorOfNatTrans {F G : C ⥤ C} (α : G ⟶ F) : Algebra F ⥤ Algebra G w
 -- Porting note: removed @[simps (config := { rhsMd := semireducible })] and replaced with
 @[simps!]
 def functorOfNatTransId : functorOfNatTrans (𝟙 F) ≅ 𝟭 _ :=
-  NatIso.ofComponents
-    (fun X =>
-      isoMk (Iso.refl _)
-        (by
-          dsimp
-          simp))
-    fun f => by
-      refine Hom.ext _ _ ?_
-      dsimp
-      simp
+  NatIso.ofComponents fun X => isoMk (Iso.refl _)
 #align category_theory.endofunctor.algebra.functor_of_nat_trans_id CategoryTheory.Endofunctor.Algebra.functorOfNatTransId
 
 /-- A composition of natural transformations gives the composition of corresponding functors. -/
@@ -210,16 +195,7 @@ def functorOfNatTransId : functorOfNatTrans (𝟙 F) ≅ 𝟭 _ :=
 @[simps!]
 def functorOfNatTransComp {F₀ F₁ F₂ : C ⥤ C} (α : F₀ ⟶ F₁) (β : F₁ ⟶ F₂) :
     functorOfNatTrans (α ≫ β) ≅ functorOfNatTrans β ⋙ functorOfNatTrans α :=
-  NatIso.ofComponents
-    (fun X =>
-      isoMk (Iso.refl _)
-        (by
-          dsimp
-          simp))
-    fun f => by
-      refine Hom.ext _ _ ?_
-      dsimp
-      simp
+  NatIso.ofComponents fun X => isoMk (Iso.refl _)
 #align category_theory.endofunctor.algebra.functor_of_nat_trans_comp CategoryTheory.Endofunctor.Algebra.functorOfNatTransComp
 
 /--
@@ -232,16 +208,7 @@ lemmas about.
 @[simps!]
 def functorOfNatTransEq {F G : C ⥤ C} {α β : F ⟶ G} (h : α = β) :
     functorOfNatTrans α ≅ functorOfNatTrans β :=
-  NatIso.ofComponents
-    (fun X =>
-      isoMk (Iso.refl _)
-        (by
-          dsimp
-          simp [h]))
-    fun f => by
-      refine Hom.ext _ _ ?_
-      dsimp
-      simp
+  NatIso.ofComponents fun X => isoMk (Iso.refl _)
 #align category_theory.endofunctor.algebra.functor_of_nat_trans_eq CategoryTheory.Endofunctor.Algebra.functorOfNatTransEq
 
 /-- Naturally isomorphic endofunctors give equivalent categories of algebras.
@@ -255,8 +222,6 @@ def equivOfNatIso {F G : C ⥤ C} (α : F ≅ G) : Algebra F ≌ Algebra G where
   unitIso := functorOfNatTransId.symm ≪≫ functorOfNatTransEq (by simp) ≪≫ functorOfNatTransComp _ _
   counitIso :=
     (functorOfNatTransComp _ _).symm ≪≫ functorOfNatTransEq (by simp) ≪≫ functorOfNatTransId
-  -- Porting note : `aesop_cat` can't solve this on its own
-  functor_unitIso_comp := fun X => Hom.ext _ _ <| by aesop_cat
 #align category_theory.endofunctor.algebra.equiv_of_nat_iso CategoryTheory.Endofunctor.Algebra.equivOfNatIso
 
 namespace Initial
@@ -326,14 +291,14 @@ structure Hom (V₀ V₁ : Coalgebra F) where
   /-- underlying morphism between two carriers -/
   f : V₀.1 ⟶ V₁.1
   /-- compatibility condition -/
-  h : V₀.str ≫ F.map f = f ≫ V₁.str := by aesop
+  h : V₀.str ≫ F.map f = f ≫ V₁.str := by aesop_cat
 #align category_theory.endofunctor.coalgebra.hom CategoryTheory.Endofunctor.Coalgebra.Hom
 
 -- Porting note: no need for restate_axiom any more
 -- restate_axiom hom.h'
 
 -- Porting note: Originally `[simp, reassoc.1]`
-attribute [reassoc (attr:=simp)] Hom.h
+attribute [reassoc (attr := simp)] Hom.h
 
 namespace Hom
 
@@ -355,6 +320,10 @@ instance (F : C ⥤ C) : CategoryStruct (Coalgebra F) where
   id := Hom.id
   comp := @Hom.comp _ _ _
 
+@[ext]
+lemma ext {A B : Coalgebra F} {f g : A ⟶ B} (w : f.f = g.f := by aesop_cat) : f = g :=
+Hom.ext _ _ w
+
 @[simp]
 theorem id_eq_id : Coalgebra.Hom.id V = 𝟙 V :=
   rfl
@@ -378,27 +347,20 @@ theorem comp_f : (f ≫ g).1 = f.1 ≫ g.1 :=
 #align category_theory.endofunctor.coalgebra.comp_f CategoryTheory.Endofunctor.Coalgebra.comp_f
 
 /-- Coalgebras of an endofunctor `F` form a category -/
-instance (F : C ⥤ C) : Category (Coalgebra F) :=
--- Porting note: how to use empty constructor `{}` in Lean 4?
-{ (inferInstance : CategoryStruct (Coalgebra F)) with
-  id_comp := fun _ => Hom.ext _ _ <| by aesop_cat
-  comp_id := fun _ => Hom.ext _ _ <| by aesop_cat
-  assoc := fun _ _ _ => Hom.ext _ _ <| by aesop_cat }
-
+instance (F : C ⥤ C) : Category (Coalgebra F) := { }
 
 /-- To construct an isomorphism of coalgebras, it suffices to give an isomorphism of the Vs which
 commutes with the structure morphisms.
 -/
 @[simps]
-def isoMk (h : V₀.1 ≅ V₁.1) (w : V₀.str ≫ F.map h.hom = h.hom ≫ V₁.str) : V₀ ≅ V₁ where
+def isoMk (h : V₀.1 ≅ V₁.1) (w : V₀.str ≫ F.map h.hom = h.hom ≫ V₁.str := by aesop_cat) :
+    V₀ ≅ V₁ where
   hom := { f := h.hom }
   inv :=
     { f := h.inv
       h := by
         rw [h.eq_inv_comp, ←Category.assoc, ← w, Category.assoc, ← F.map_comp]
         simp only [Iso.hom_inv_id, Functor.map_id, Category.comp_id] }
-  hom_inv_id := Hom.ext _ _ <| by aesop
-  inv_hom_id := Hom.ext _ _ <| by aesop
 #align category_theory.endofunctor.coalgebra.iso_mk CategoryTheory.Endofunctor.Coalgebra.isoMk
 
 /-- The forgetful functor from the category of coalgebras, forgetting the coalgebraic structure. -/
@@ -413,16 +375,13 @@ theorem iso_of_iso (f : V₀ ⟶ V₁) [IsIso f.1] : IsIso f :=
   ⟨⟨{ f := inv f.1
       h := by
         rw [IsIso.eq_inv_comp f.1, ← Category.assoc, ← f.h, Category.assoc]
-        simp }, Hom.ext _ _ <| by aesop, Hom.ext _ _ <| by aesop⟩⟩
--- Porting note : `tidy` can not finish the goal
+        simp }, by aesop_cat, by aesop_cat⟩⟩
 #align category_theory.endofunctor.coalgebra.iso_of_iso CategoryTheory.Endofunctor.Coalgebra.iso_of_iso
 
 instance forget_reflects_iso : ReflectsIsomorphisms (forget F) where reflects := iso_of_iso
 #align category_theory.endofunctor.coalgebra.forget_reflects_iso CategoryTheory.Endofunctor.Coalgebra.forget_reflects_iso
 
--- Porting note: how to use `{}` in Lean 4?
-instance forget_faithful : Faithful (forget F) where
-  map_injective := Hom.ext _ _
+instance forget_faithful : Faithful (forget F) := { }
 #align category_theory.endofunctor.coalgebra.forget_faithful CategoryTheory.Endofunctor.Coalgebra.forget_faithful
 
 /-- An algebra morphism with an underlying epimorphism hom in `C` is an algebra epimorphism. -/
@@ -452,9 +411,7 @@ def functorOfNatTrans {F G : C ⥤ C} (α : F ⟶ G) : Coalgebra F ⥤ Coalgebra
 -- Porting note: removed @[simps (config := { rhsMd := semireducible })] and replaced with
 @[simps!]
 def functorOfNatTransId : functorOfNatTrans (𝟙 F) ≅ 𝟭 _ :=
-  NatIso.ofComponents
-    (fun X => isoMk (Iso.refl _) <| by simp)
-    fun f => Hom.ext _ _ <| by simp
+  NatIso.ofComponents fun X => isoMk (Iso.refl _)
 
 #align category_theory.endofunctor.coalgebra.functor_of_nat_trans_id CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransId
 
@@ -463,9 +420,7 @@ def functorOfNatTransId : functorOfNatTrans (𝟙 F) ≅ 𝟭 _ :=
 @[simps!]
 def functorOfNatTransComp {F₀ F₁ F₂ : C ⥤ C} (α : F₀ ⟶ F₁) (β : F₁ ⟶ F₂) :
     functorOfNatTrans (α ≫ β) ≅ functorOfNatTrans α ⋙ functorOfNatTrans β :=
-  NatIso.ofComponents
-    (fun X => isoMk (Iso.refl _) <| by simp)
-    fun f => Hom.ext _ _ <| by simp
+  NatIso.ofComponents fun X => isoMk (Iso.refl _)
 #align category_theory.endofunctor.coalgebra.functor_of_nat_trans_comp CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransComp
 
 /-- If `α` and `β` are two equal natural transformations, then the functors of coalgebras induced by
@@ -477,9 +432,7 @@ lemmas about.
 @[simps!]
 def functorOfNatTransEq {F G : C ⥤ C} {α β : F ⟶ G} (h : α = β) :
     functorOfNatTrans α ≅ functorOfNatTrans β :=
-  NatIso.ofComponents
-    (fun X => isoMk (Iso.refl _) <| by aesop)
-    fun f => Hom.ext _ _ <| by simp
+  NatIso.ofComponents fun X => isoMk (Iso.refl _)
 #align category_theory.endofunctor.coalgebra.functor_of_nat_trans_eq CategoryTheory.Endofunctor.Coalgebra.functorOfNatTransEq
 
 /-- Naturally isomorphic endofunctors give equivalent categories of coalgebras.
@@ -493,7 +446,6 @@ def equivOfNatIso {F G : C ⥤ C} (α : F ≅ G) : Coalgebra F ≌ Coalgebra G w
   unitIso := functorOfNatTransId.symm ≪≫ functorOfNatTransEq (by simp) ≪≫ functorOfNatTransComp _ _
   counitIso :=
     (functorOfNatTransComp _ _).symm ≪≫ functorOfNatTransEq (by simp) ≪≫ functorOfNatTransId
-  functor_unitIso_comp := fun _ => Hom.ext _ _ <| by aesop
 #align category_theory.endofunctor.coalgebra.equiv_of_nat_iso CategoryTheory.Endofunctor.Coalgebra.equivOfNatIso
 
 end Coalgebra
@@ -545,13 +497,7 @@ def AlgCoalgEquiv.unitIso (adj : F ⊣ G) :
         { f := 𝟙 A.1
           h := by
             erw [F.map_id, Category.id_comp, Category.comp_id]
-            apply (adj.homEquiv _ _).left_inv A.str }
-      naturality := fun A₁ A₂ f => by
-        -- Porting note: `ext` does not work
-        refine Algebra.Hom.ext _ _ ?_
-        dsimp
-        erw [Category.id_comp, Category.comp_id]
-        rfl }
+            apply (adj.homEquiv _ _).left_inv A.str } }
   inv :=
     { app := fun A =>
         { f := 𝟙 A.1
@@ -559,19 +505,10 @@ def AlgCoalgEquiv.unitIso (adj : F ⊣ G) :
             erw [F.map_id, Category.id_comp, Category.comp_id]
             apply ((adj.homEquiv _ _).left_inv A.str).symm }
       naturality := fun A₁ A₂ f => by
-        -- Porting note: `ext` does not work
-        refine Algebra.Hom.ext _ _ ?_
+        ext
         dsimp
         erw [Category.comp_id, Category.id_comp]
         rfl }
-  hom_inv_id := by
-    -- Porting note : `ext` does not see `Algebra.Hom.ext`
-    refine NatTrans.ext _ _ (funext <| fun x => Algebra.Hom.ext _ _ <| ?_)
-    exact Category.comp_id _
-  inv_hom_id := by
-    -- Porting note : `ext` does not see `Algebra.Hom.ext`
-    refine NatTrans.ext _ _ (funext <| fun x => Algebra.Hom.ext _ _ <| ?_)
-    exact Category.comp_id _
 #align category_theory.endofunctor.adjunction.alg_coalg_equiv.unit_iso CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.unitIso
 
 /-- Given an adjunction, assigning to a coalgebra over the right adjoint an algebra over the left
@@ -586,8 +523,7 @@ def AlgCoalgEquiv.counitIso (adj : F ⊣ G) :
             erw [G.map_id, Category.id_comp, Category.comp_id]
             apply (adj.homEquiv _ _).right_inv V.str }
       naturality := fun V₁ V₂ f => by
-        -- Porting note: `ext` does not work
-        refine Coalgebra.Hom.ext _ _ ?_
+        ext
         dsimp
         erw [Category.comp_id, Category.id_comp]
         rfl }
@@ -597,21 +533,7 @@ def AlgCoalgEquiv.counitIso (adj : F ⊣ G) :
           h := by
             dsimp
             rw [G.map_id, Category.comp_id, Category.id_comp]
-            apply ((adj.homEquiv _ _).right_inv V.str).symm }
-      naturality := fun V₁ V₂ f => by
-        -- Porting note : `ext` does not work
-        refine Coalgebra.Hom.ext _ _ ?_
-        dsimp
-        erw [Category.comp_id, Category.id_comp]
-        rfl }
-  hom_inv_id := by
-    -- Porting note : `ext` does not see `Coalgebra.Hom.ext`
-    refine NatTrans.ext _ _ (funext <| fun x => Coalgebra.Hom.ext _ _ <| ?_)
-    exact Category.comp_id _
-  inv_hom_id := by
-    -- Porting note : `ext` does not see `Coalgebra.Hom.ext`
-    refine NatTrans.ext _ _ (funext <| fun x => Coalgebra.Hom.ext _ _ <| ?_)
-    exact Category.comp_id _
+            apply ((adj.homEquiv _ _).right_inv V.str).symm } }
 #align category_theory.endofunctor.adjunction.alg_coalg_equiv.counit_iso CategoryTheory.Endofunctor.Adjunction.AlgCoalgEquiv.counitIso
 
 /-- If `F` is left adjoint to `G`, then the category of algebras over `F` is equivalent to the
@@ -622,8 +544,8 @@ def algebraCoalgebraEquiv (adj : F ⊣ G) : Algebra F ≌ Coalgebra G where
   unitIso := AlgCoalgEquiv.unitIso adj
   counitIso := AlgCoalgEquiv.counitIso adj
   functor_unitIso_comp A := by
-    -- Porting note : `ext` does not work
-    refine Coalgebra.Hom.ext _ _ ?_
+    ext
+    -- Porting note: why doesn't `simp` work here?
     exact Category.comp_id _
 #align category_theory.endofunctor.adjunction.algebra_coalgebra_equiv CategoryTheory.Endofunctor.Adjunction.algebraCoalgebraEquiv

70fd9563

chore: fix typos (#4518)

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

92beef58

Diff

@@ -283,7 +283,7 @@ theorem right_inv : A.str ≫ strInv h = 𝟙 _ := by
   exact left_inv h
 #align category_theory.endofunctor.algebra.initial.right_inv CategoryTheory.Endofunctor.Algebra.Initial.right_inv
 
-/-- The structure map of the inital algebra is an isomorphism,
+/-- The structure map of the initial algebra is an isomorphism,
 hence endofunctors preserve their initial algebras
 -/
 theorem str_isIso (h : Limits.IsInitial A) : IsIso A.str :=

70fd9563

feat: port CategoryTheory.Preadditive.EndoFunctor (#4042)

1ab36e45

Diff

@@ -156,7 +156,7 @@ theorem iso_of_iso (f : A₀ ⟶ A₁) [IsIso f.1] : IsIso f :=
   ⟨⟨{ f := inv f.1
       h := by
         rw [IsIso.eq_comp_inv f.1, Category.assoc, ← f.h]
-        simp }, Hom.ext _ _ <| by aesop, Hom.ext _ _ <| by aesop⟩⟩ 
+        simp }, Hom.ext _ _ <| by aesop, Hom.ext _ _ <| by aesop⟩⟩
 -- Porting note: `tidy` can't finish
 #align category_theory.endofunctor.algebra.iso_of_iso CategoryTheory.Endofunctor.Algebra.iso_of_iso
 
@@ -262,7 +262,6 @@ def equivOfNatIso {F G : C ⥤ C} (α : F ≅ G) : Algebra F ≌ Algebra G where
 namespace Initial
 
 variable {A} (h : @Limits.IsInitial (Algebra F) _ A)
-#check Algebra.mk
 /-- The inverse of the structure map of an initial algebra -/
 @[simp]
 def strInv : A.1 ⟶ F.obj A.1 :=

70fd9563

feat: port CategoryTheory.Endofunctor.Algebra (#3541)

Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com>

bb4ae7cd

`category_theory.endofunctor.algebra` ⟷ `Mathlib.CategoryTheory.Endofunctor.Algebra`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 83

category_theory.endofunctor.algebra ⟷ Mathlib.CategoryTheory.Endofunctor.Algebra

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 83

`category_theory.endofunctor.algebra` ⟷ `Mathlib.CategoryTheory.Endofunctor.Algebra`