algebraic_topology.dold_kan.compatibility

(last sync)

feat(algebraic_topology/dold_kan): The Dold-Kan equivalence for abelian categories (#17926)

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

Diff

@@ -36,7 +36,9 @@ inverse of `eB`:
 but whose inverse functor is `G`.
 
 When extra assumptions are given, we shall also provide simplification lemmas for the
-unit and counit isomorphisms of `equivalence`. (TODO)
+unit and counit isomorphisms of `equivalence`.
+
+(See `equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
 
 -/

feat(algebraic_topology/dold_kan): tools for compatibilities, lemmas (#17923)

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

Diff

@@ -77,7 +77,7 @@ lemma equivalence₁_inverse : (equivalence₁ hF).inverse = e'.inverse ⋙ eA.i
 def equivalence₁_counit_iso :
   (e'.inverse ⋙ eA.inverse) ⋙ F ≅ 𝟭 B' :=
 calc (e'.inverse ⋙ eA.inverse) ⋙ F
-  ≅ (e'.inverse ⋙ eA.inverse) ⋙ (eA.functor ⋙ e'.functor) : iso_whisker_left _ hF.symm
+    ≅ (e'.inverse ⋙ eA.inverse) ⋙ (eA.functor ⋙ e'.functor) : iso_whisker_left _ hF.symm
 ... ≅ e'.inverse ⋙ (eA.inverse ⋙ eA.functor) ⋙ e'.functor : iso.refl _
 ... ≅ e'.inverse ⋙ 𝟭 _ ⋙ e'.functor : iso_whisker_left _ (iso_whisker_right eA.counit_iso _)
 ... ≅ e'.inverse ⋙ e'.functor : iso.refl _
@@ -97,7 +97,7 @@ def equivalence₁_unit_iso :
 calc 𝟭 A ≅ eA.functor ⋙ eA.inverse : eA.unit_iso
 ... ≅ eA.functor ⋙ 𝟭 A' ⋙ eA.inverse : iso.refl _
 ... ≅ eA.functor ⋙ (e'.functor ⋙ e'.inverse) ⋙ eA.inverse :
-  iso_whisker_left _ (iso_whisker_right e'.unit_iso _)
+        iso_whisker_left _ (iso_whisker_right e'.unit_iso _)
 ... ≅ (eA.functor ⋙ e'.functor) ⋙ (e'.inverse ⋙ eA.inverse) : iso.refl _
 ... ≅ F ⋙ (e'.inverse ⋙ eA.inverse) : iso_whisker_right hF _
 
@@ -124,9 +124,9 @@ lemma equivalence₂_inverse : (equivalence₂ eB hF).inverse =
 def equivalence₂_counit_iso :
   (eB.functor ⋙ e'.inverse ⋙ eA.inverse) ⋙ (F ⋙ eB.inverse) ≅ 𝟭 B :=
 calc (eB.functor ⋙ e'.inverse ⋙ eA.inverse) ⋙ (F ⋙ eB.inverse)
-  ≅ eB.functor ⋙ (e'.inverse ⋙ eA.inverse ⋙ F) ⋙ eB.inverse : iso.refl _
+    ≅ eB.functor ⋙ (e'.inverse ⋙ eA.inverse ⋙ F) ⋙ eB.inverse : iso.refl _
 ... ≅ eB.functor ⋙ 𝟭 _ ⋙ eB.inverse :
-  iso_whisker_left _ (iso_whisker_right (equivalence₁_counit_iso hF) _)
+        iso_whisker_left _ (iso_whisker_right (equivalence₁_counit_iso hF) _)
 ... ≅ eB.functor ⋙ eB.inverse : iso.refl _
 ... ≅ 𝟭 B : eB.unit_iso.symm
 
@@ -146,7 +146,7 @@ def equivalence₂_unit_iso :
 calc 𝟭 A ≅ F ⋙ e'.inverse ⋙ eA.inverse : equivalence₁_unit_iso hF
 ... ≅ F ⋙ 𝟭 B' ⋙ (e'.inverse ⋙ eA.inverse) : iso.refl _
 ... ≅ F ⋙ (eB.inverse ⋙ eB.functor) ⋙ e'.inverse ⋙ eA.inverse :
-  iso_whisker_left _ (iso_whisker_right eB.counit_iso.symm _)
+        iso_whisker_left _ (iso_whisker_right eB.counit_iso.symm _)
 ... ≅ (F ⋙ eB.inverse) ⋙ (eB.functor ⋙ e'.inverse ⋙ eA.inverse) : iso.refl _
 
 lemma equivalence₂_unit_iso_eq :
@@ -169,7 +169,7 @@ begin
   letI : is_equivalence G := begin
     refine is_equivalence.of_iso _ (is_equivalence.of_equivalence (equivalence₂ eB hF).symm),
     calc eB.functor ⋙ e'.inverse ⋙ eA.inverse
-      ≅ (eB.functor ⋙ e'.inverse) ⋙ eA.inverse : iso.refl _
+        ≅ (eB.functor ⋙ e'.inverse) ⋙ eA.inverse : iso.refl _
     ... ≅ (G ⋙ eA.functor) ⋙ eA.inverse : iso_whisker_right hG _
     ... ≅ G ⋙ 𝟭 A : iso_whisker_left _ eA.unit_iso.symm
     ... ≅ G : functor.right_unitor G,
@@ -179,6 +179,119 @@ end
 
 lemma equivalence_functor : (equivalence hF hG).functor = F ⋙ eB.inverse := rfl
 
+omit hG hF
+
+/-- The isomorphism `eB.functor ⋙ e'.inverse ⋙ e'.functor ≅ eB.functor` deduced
+from the counit isomorphism of `e'`. -/
+@[simps hom_app]
+def τ₀ : eB.functor ⋙ e'.inverse ⋙ e'.functor ≅ eB.functor :=
+calc eB.functor ⋙ e'.inverse ⋙ e'.functor
+        ≅ eB.functor ⋙ 𝟭 _ : iso_whisker_left _ e'.counit_iso
+...     ≅ eB.functor : functor.right_unitor _
+
+include hF hG
+
+/-- The isomorphism `eB.functor ⋙ e'.inverse ⋙ e'.functor ≅ eB.functor` deduced
+from the isomorphisms `hF : eA.functor ⋙ e'.functor ≅ F`,
+`hG : eB.functor ⋙ e'.inverse ≅ G ⋙ eA.functor` and the datum of
+an isomorphism `η : G ⋙ F ≅ eB.functor`. -/
+@[simps hom_app]
+def τ₁ (η : G ⋙ F ≅ eB.functor) :
+  eB.functor ⋙ e'.inverse ⋙ e'.functor ≅ eB.functor :=
+calc eB.functor ⋙ e'.inverse ⋙ e'.functor
+    ≅ (eB.functor ⋙ e'.inverse) ⋙ e'.functor : iso.refl _
+... ≅ (G ⋙ eA.functor) ⋙ e'.functor : iso_whisker_right hG _
+... ≅ G ⋙ (eA.functor ⋙ e'.functor) : by refl
+... ≅ G ⋙ F : iso_whisker_left _ hF
+... ≅ eB.functor : η
+
+variables (η : G ⋙ F ≅ eB.functor) (hη : τ₀ = τ₁ hF hG η)
+
+omit hF hG
+include η
+
+/-- The counit isomorphism of `equivalence`. -/
+@[simps]
+def equivalence_counit_iso : G ⋙ (F ⋙ eB.inverse) ≅ 𝟭 B :=
+calc G ⋙ (F ⋙ eB.inverse) ≅ (G ⋙ F) ⋙ eB.inverse : iso.refl _
+... ≅ eB.functor ⋙ eB.inverse : iso_whisker_right η _
+... ≅ 𝟭 B : eB.unit_iso.symm
+
+variables {η hF hG}
+include hη
+
+lemma equivalence_counit_iso_eq :
+  (equivalence hF hG).counit_iso = equivalence_counit_iso η :=
+begin
+  ext1, apply nat_trans.ext, ext Y,
+  dsimp [equivalence, equivalence_counit_iso, is_equivalence.of_equivalence],
+  simp only [equivalence₂_counit_iso_eq eB hF],
+  erw [nat_trans.id_app, nat_trans.id_app],
+  dsimp [equivalence₂, equivalence₁],
+  simp only [assoc, comp_id, F.map_id, id_comp,
+    equivalence₂_counit_iso_hom_app, ← eB.inverse.map_comp_assoc,
+    ← τ₀_hom_app, hη, τ₁_hom_app],
+  erw hF.inv.naturality_assoc,
+  congr' 2,
+  dsimp,
+  simp only [assoc, ← e'.functor.map_comp_assoc, eA.functor.map_comp,
+    equivalence.fun_inv_map, iso.inv_hom_id_app_assoc, hG.inv_hom_id_app],
+  dsimp,
+  rw [comp_id, eA.functor_unit_iso_comp, e'.functor.map_id, id_comp, hF.inv_hom_id_app_assoc],
+end
+
+omit hη η eB
+include hF
+
+variable (hF)
+
+/-- The isomorphism `eA.functor ≅ F ⋙ e'.inverse` deduced from the
+unit isomorphism of `e'` and the isomorphism `hF : eA.functor ⋙ e'.functor ≅ F`. -/
+@[simps]
+def υ : eA.functor ≅ F ⋙ e'.inverse :=
+calc eA.functor ≅ eA.functor ⋙ 𝟭 A' : (functor.left_unitor _).symm
+... ≅ eA.functor ⋙ (e'.functor ⋙ e'.inverse) : iso_whisker_left _ e'.unit_iso
+... ≅ (eA.functor ⋙ e'.functor) ⋙ e'.inverse : iso.refl _
+... ≅ F ⋙ e'.inverse : iso_whisker_right hF _
+
+variables (ε : eA.functor ≅ F ⋙ e'.inverse) (hε : υ hF = ε)
+
+include ε hG
+omit hF
+
+variable (hG)
+
+/-- The unit isomorphism of `equivalence`. -/
+@[simps]
+def equivalence_unit_iso : 𝟭 A ≅ (F ⋙ eB.inverse) ⋙ G :=
+calc 𝟭 A ≅ eA.functor ⋙ eA.inverse : eA.unit_iso
+... ≅ (F ⋙ e'.inverse) ⋙ eA.inverse : iso_whisker_right ε _
+... ≅ F ⋙ 𝟭 B' ⋙ e'.inverse ⋙ eA.inverse : iso.refl _
+... ≅ F ⋙ (eB.inverse ⋙ eB.functor) ⋙ (e'.inverse ⋙ eA.inverse) :
+      iso_whisker_left _ (iso_whisker_right eB.counit_iso.symm _)
+... ≅ (F ⋙ eB.inverse) ⋙ (eB.functor ⋙ e'.inverse) ⋙ eA.inverse : iso.refl _
+... ≅ (F ⋙ eB.inverse) ⋙ (G ⋙ eA.functor) ⋙ eA.inverse :
+      iso_whisker_left _ (iso_whisker_right hG _)
+... ≅ (F ⋙ eB.inverse ⋙ G) ⋙ (eA.functor ⋙ eA.inverse) : iso.refl _
+... ≅ (F ⋙ eB.inverse ⋙ G) ⋙ 𝟭 A : iso_whisker_left _ eA.unit_iso.symm
+... ≅ (F ⋙ eB.inverse) ⋙ G : iso.refl _
+
+include hε
+variables {ε hF hG}
+
+lemma equivalence_unit_iso_eq :
+  (equivalence hF hG).unit_iso = equivalence_unit_iso hG ε :=
+begin
+  ext1, apply nat_trans.ext, ext X,
+  dsimp [equivalence, iso.refl, nat_iso.hcomp, is_equivalence.inverse,
+    is_equivalence.of_equivalence],
+  erw [nat_trans.id_app, id_comp, G.map_id, comp_id, comp_id],
+  simp only [equivalence₂_unit_iso_eq eB hF, equivalence₂_unit_iso_hom_app],
+  dsimp [equivalence₂, equivalence₁],
+  simp only [assoc, equivalence_unit_iso_hom_app, nat_iso.cancel_nat_iso_hom_left,
+    ← eA.inverse.map_comp_assoc, ← hε, υ_hom_app],
+end
+
 end compatibility
 
 end dold_kan

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

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) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 -/
-import Mathbin.CategoryTheory.Equivalence
+import CategoryTheory.Equivalence
 
 #align_import algebraic_topology.dold_kan.compatibility from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"

bump to nightly-2023-08-06-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

b0e28731

Diff

@@ -5,7 +5,7 @@ Authors: Joël Riou
 -/
 import Mathbin.CategoryTheory.Equivalence
 
-#align_import algebraic_topology.dold_kan.compatibility from "leanprover-community/mathlib"@"18ee599842a5d17f189fe572f0ed8cb1d064d772"
+#align_import algebraic_topology.dold_kan.compatibility from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 
 /-!
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
@@ -37,7 +37,9 @@ inverse of `eB`:
 but whose inverse functor is `G`.
 
 When extra assumptions are given, we shall also provide simplification lemmas for the
-unit and counit isomorphisms of `equivalence`. (TODO)
+unit and counit isomorphisms of `equivalence`.
+
+(See `equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
 
 -/

bump to nightly-2023-08-02-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

7aca3f15

Diff

@@ -216,6 +216,7 @@ theorem equivalence_functor : (equivalence hF hG).Functor = F ⋙ eB.inverse :=
 #align algebraic_topology.dold_kan.compatibility.equivalence_functor AlgebraicTopology.DoldKan.Compatibility.equivalence_functor
 -/
 
+#print AlgebraicTopology.DoldKan.Compatibility.τ₀ /-
 /-- The isomorphism `eB.functor ⋙ e'.inverse ⋙ e'.functor ≅ eB.functor` deduced
 from the counit isomorphism of `e'`. -/
 @[simps hom_app]
@@ -224,7 +225,9 @@ def τ₀ : eB.Functor ⋙ e'.inverse ⋙ e'.Functor ≅ eB.Functor :=
     eB.Functor ⋙ e'.inverse ⋙ e'.Functor ≅ eB.Functor ⋙ 𝟭 _ := isoWhiskerLeft _ e'.counitIso
     _ ≅ eB.Functor := Functor.rightUnitor _
 #align algebraic_topology.dold_kan.compatibility.τ₀ AlgebraicTopology.DoldKan.Compatibility.τ₀
+-/
 
+#print AlgebraicTopology.DoldKan.Compatibility.τ₁ /-
 /-- The isomorphism `eB.functor ⋙ e'.inverse ⋙ e'.functor ≅ eB.functor` deduced
 from the isomorphisms `hF : eA.functor ⋙ e'.functor ≅ F`,
 `hG : eB.functor ⋙ e'.inverse ≅ G ⋙ eA.functor` and the datum of
@@ -238,9 +241,11 @@ def τ₁ (η : G ⋙ F ≅ eB.Functor) : eB.Functor ⋙ e'.inverse ⋙ e'.Funct
     _ ≅ G ⋙ F := (isoWhiskerLeft _ hF)
     _ ≅ eB.Functor := η
 #align algebraic_topology.dold_kan.compatibility.τ₁ AlgebraicTopology.DoldKan.Compatibility.τ₁
+-/
 
 variable (η : G ⋙ F ≅ eB.Functor) (hη : τ₀ = τ₁ hF hG η)
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso /-
 /-- The counit isomorphism of `equivalence`. -/
 @[simps]
 def equivalenceCounitIso : G ⋙ F ⋙ eB.inverse ≅ 𝟭 B :=
@@ -249,9 +254,11 @@ def equivalenceCounitIso : G ⋙ F ⋙ eB.inverse ≅ 𝟭 B :=
     _ ≅ eB.Functor ⋙ eB.inverse := (isoWhiskerRight η _)
     _ ≅ 𝟭 B := eB.unitIso.symm
 #align algebraic_topology.dold_kan.compatibility.equivalence_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso
+-/
 
 variable {η hF hG}
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_eq /-
 theorem equivalenceCounitIso_eq : (equivalence hF hG).counitIso = equivalenceCounitIso η :=
   by
   ext1; apply nat_trans.ext; ext Y
@@ -269,9 +276,11 @@ theorem equivalenceCounitIso_eq : (equivalence hF hG).counitIso = equivalenceCou
   dsimp
   rw [comp_id, eA.functor_unit_iso_comp, e'.functor.map_id, id_comp, hF.inv_hom_id_app_assoc]
 #align algebraic_topology.dold_kan.compatibility.equivalence_counit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_eq
+-/
 
 variable (hF)
 
+#print AlgebraicTopology.DoldKan.Compatibility.υ /-
 /-- The isomorphism `eA.functor ≅ F ⋙ e'.inverse` deduced from the
 unit isomorphism of `e'` and the isomorphism `hF : eA.functor ⋙ e'.functor ≅ F`. -/
 @[simps]
@@ -282,11 +291,13 @@ def υ : eA.Functor ≅ F ⋙ e'.inverse :=
     _ ≅ (eA.Functor ⋙ e'.Functor) ⋙ e'.inverse := (Iso.refl _)
     _ ≅ F ⋙ e'.inverse := isoWhiskerRight hF _
 #align algebraic_topology.dold_kan.compatibility.υ AlgebraicTopology.DoldKan.Compatibility.υ
+-/
 
 variable (ε : eA.Functor ≅ F ⋙ e'.inverse) (hε : υ hF = ε)
 
 variable (hG)
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso /-
 /-- The unit isomorphism of `equivalence`. -/
 @[simps]
 def equivalenceUnitIso : 𝟭 A ≅ (F ⋙ eB.inverse) ⋙ G :=
@@ -303,9 +314,11 @@ def equivalenceUnitIso : 𝟭 A ≅ (F ⋙ eB.inverse) ⋙ G :=
     _ ≅ (F ⋙ eB.inverse ⋙ G) ⋙ 𝟭 A := (isoWhiskerLeft _ eA.unitIso.symm)
     _ ≅ (F ⋙ eB.inverse) ⋙ G := Iso.refl _
 #align algebraic_topology.dold_kan.compatibility.equivalence_unit_iso AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso
+-/
 
 variable {ε hF hG}
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_eq /-
 theorem equivalenceUnitIso_eq : (equivalence hF hG).unitIso = equivalenceUnitIso hG ε :=
   by
   ext1; apply nat_trans.ext; ext X
@@ -317,6 +330,7 @@ theorem equivalenceUnitIso_eq : (equivalence hF hG).unitIso = equivalenceUnitIso
   simp only [assoc, equivalence_unit_iso_hom_app, nat_iso.cancel_nat_iso_hom_left, ←
     eA.inverse.map_comp_assoc, ← hε, υ_hom_app]
 #align algebraic_topology.dold_kan.compatibility.equivalence_unit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_eq
+-/
 
 end Compatibility

bump to nightly-2023-07-26-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/18ee599842a5d17f189fe572f0ed8cb1d064d772

d702c376

Diff

@@ -5,7 +5,7 @@ Authors: Joël Riou
 -/
 import Mathbin.CategoryTheory.Equivalence
 
-#align_import algebraic_topology.dold_kan.compatibility from "leanprover-community/mathlib"@"d64d67d000b974f0d86a2be7918cf800be6271c8"
+#align_import algebraic_topology.dold_kan.compatibility from "leanprover-community/mathlib"@"18ee599842a5d17f189fe572f0ed8cb1d064d772"
 
 /-!
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
@@ -216,6 +216,108 @@ theorem equivalence_functor : (equivalence hF hG).Functor = F ⋙ eB.inverse :=
 #align algebraic_topology.dold_kan.compatibility.equivalence_functor AlgebraicTopology.DoldKan.Compatibility.equivalence_functor
 -/
 
+/-- The isomorphism `eB.functor ⋙ e'.inverse ⋙ e'.functor ≅ eB.functor` deduced
+from the counit isomorphism of `e'`. -/
+@[simps hom_app]
+def τ₀ : eB.Functor ⋙ e'.inverse ⋙ e'.Functor ≅ eB.Functor :=
+  calc
+    eB.Functor ⋙ e'.inverse ⋙ e'.Functor ≅ eB.Functor ⋙ 𝟭 _ := isoWhiskerLeft _ e'.counitIso
+    _ ≅ eB.Functor := Functor.rightUnitor _
+#align algebraic_topology.dold_kan.compatibility.τ₀ AlgebraicTopology.DoldKan.Compatibility.τ₀
+
+/-- The isomorphism `eB.functor ⋙ e'.inverse ⋙ e'.functor ≅ eB.functor` deduced
+from the isomorphisms `hF : eA.functor ⋙ e'.functor ≅ F`,
+`hG : eB.functor ⋙ e'.inverse ≅ G ⋙ eA.functor` and the datum of
+an isomorphism `η : G ⋙ F ≅ eB.functor`. -/
+@[simps hom_app]
+def τ₁ (η : G ⋙ F ≅ eB.Functor) : eB.Functor ⋙ e'.inverse ⋙ e'.Functor ≅ eB.Functor :=
+  calc
+    eB.Functor ⋙ e'.inverse ⋙ e'.Functor ≅ (eB.Functor ⋙ e'.inverse) ⋙ e'.Functor := Iso.refl _
+    _ ≅ (G ⋙ eA.Functor) ⋙ e'.Functor := (isoWhiskerRight hG _)
+    _ ≅ G ⋙ eA.Functor ⋙ e'.Functor := by rfl
+    _ ≅ G ⋙ F := (isoWhiskerLeft _ hF)
+    _ ≅ eB.Functor := η
+#align algebraic_topology.dold_kan.compatibility.τ₁ AlgebraicTopology.DoldKan.Compatibility.τ₁
+
+variable (η : G ⋙ F ≅ eB.Functor) (hη : τ₀ = τ₁ hF hG η)
+
+/-- The counit isomorphism of `equivalence`. -/
+@[simps]
+def equivalenceCounitIso : G ⋙ F ⋙ eB.inverse ≅ 𝟭 B :=
+  calc
+    G ⋙ F ⋙ eB.inverse ≅ (G ⋙ F) ⋙ eB.inverse := Iso.refl _
+    _ ≅ eB.Functor ⋙ eB.inverse := (isoWhiskerRight η _)
+    _ ≅ 𝟭 B := eB.unitIso.symm
+#align algebraic_topology.dold_kan.compatibility.equivalence_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso
+
+variable {η hF hG}
+
+theorem equivalenceCounitIso_eq : (equivalence hF hG).counitIso = equivalenceCounitIso η :=
+  by
+  ext1; apply nat_trans.ext; ext Y
+  dsimp [Equivalence, equivalence_counit_iso, is_equivalence.of_equivalence]
+  simp only [equivalence₂_counit_iso_eq eB hF]
+  erw [nat_trans.id_app, nat_trans.id_app]
+  dsimp [equivalence₂, equivalence₁]
+  simp only [assoc, comp_id, F.map_id, id_comp, equivalence₂_counit_iso_hom_app, ←
+    eB.inverse.map_comp_assoc, ← τ₀_hom_app, hη, τ₁_hom_app]
+  erw [hF.inv.naturality_assoc]
+  congr 2
+  dsimp
+  simp only [assoc, ← e'.functor.map_comp_assoc, eA.functor.map_comp, equivalence.fun_inv_map,
+    iso.inv_hom_id_app_assoc, hG.inv_hom_id_app]
+  dsimp
+  rw [comp_id, eA.functor_unit_iso_comp, e'.functor.map_id, id_comp, hF.inv_hom_id_app_assoc]
+#align algebraic_topology.dold_kan.compatibility.equivalence_counit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_eq
+
+variable (hF)
+
+/-- The isomorphism `eA.functor ≅ F ⋙ e'.inverse` deduced from the
+unit isomorphism of `e'` and the isomorphism `hF : eA.functor ⋙ e'.functor ≅ F`. -/
+@[simps]
+def υ : eA.Functor ≅ F ⋙ e'.inverse :=
+  calc
+    eA.Functor ≅ eA.Functor ⋙ 𝟭 A' := (Functor.leftUnitor _).symm
+    _ ≅ eA.Functor ⋙ e'.Functor ⋙ e'.inverse := (isoWhiskerLeft _ e'.unitIso)
+    _ ≅ (eA.Functor ⋙ e'.Functor) ⋙ e'.inverse := (Iso.refl _)
+    _ ≅ F ⋙ e'.inverse := isoWhiskerRight hF _
+#align algebraic_topology.dold_kan.compatibility.υ AlgebraicTopology.DoldKan.Compatibility.υ
+
+variable (ε : eA.Functor ≅ F ⋙ e'.inverse) (hε : υ hF = ε)
+
+variable (hG)
+
+/-- The unit isomorphism of `equivalence`. -/
+@[simps]
+def equivalenceUnitIso : 𝟭 A ≅ (F ⋙ eB.inverse) ⋙ G :=
+  calc
+    𝟭 A ≅ eA.Functor ⋙ eA.inverse := eA.unitIso
+    _ ≅ (F ⋙ e'.inverse) ⋙ eA.inverse := (isoWhiskerRight ε _)
+    _ ≅ F ⋙ 𝟭 B' ⋙ e'.inverse ⋙ eA.inverse := (Iso.refl _)
+    _ ≅ F ⋙ (eB.inverse ⋙ eB.Functor) ⋙ e'.inverse ⋙ eA.inverse :=
+      (isoWhiskerLeft _ (isoWhiskerRight eB.counitIso.symm _))
+    _ ≅ (F ⋙ eB.inverse) ⋙ (eB.Functor ⋙ e'.inverse) ⋙ eA.inverse := (Iso.refl _)
+    _ ≅ (F ⋙ eB.inverse) ⋙ (G ⋙ eA.Functor) ⋙ eA.inverse :=
+      (isoWhiskerLeft _ (isoWhiskerRight hG _))
+    _ ≅ (F ⋙ eB.inverse ⋙ G) ⋙ eA.Functor ⋙ eA.inverse := (Iso.refl _)
+    _ ≅ (F ⋙ eB.inverse ⋙ G) ⋙ 𝟭 A := (isoWhiskerLeft _ eA.unitIso.symm)
+    _ ≅ (F ⋙ eB.inverse) ⋙ G := Iso.refl _
+#align algebraic_topology.dold_kan.compatibility.equivalence_unit_iso AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso
+
+variable {ε hF hG}
+
+theorem equivalenceUnitIso_eq : (equivalence hF hG).unitIso = equivalenceUnitIso hG ε :=
+  by
+  ext1; apply nat_trans.ext; ext X
+  dsimp [Equivalence, iso.refl, nat_iso.hcomp, is_equivalence.inverse,
+    is_equivalence.of_equivalence]
+  erw [nat_trans.id_app, id_comp, G.map_id, comp_id, comp_id]
+  simp only [equivalence₂_unit_iso_eq eB hF, equivalence₂_unit_iso_hom_app]
+  dsimp [equivalence₂, equivalence₁]
+  simp only [assoc, equivalence_unit_iso_hom_app, nat_iso.cancel_nat_iso_hom_left, ←
+    eA.inverse.map_comp_assoc, ← hε, υ_hom_app]
+#align algebraic_topology.dold_kan.compatibility.equivalence_unit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_eq
+
 end Compatibility
 
 end DoldKan

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) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
-
-! This file was ported from Lean 3 source module algebraic_topology.dold_kan.compatibility
-! leanprover-community/mathlib commit d64d67d000b974f0d86a2be7918cf800be6271c8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Equivalence
 
+#align_import algebraic_topology.dold_kan.compatibility from "leanprover-community/mathlib"@"d64d67d000b974f0d86a2be7918cf800be6271c8"
+
 /-!
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
 > Any changes to this file require a corresponding PR to mathlib4.

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -57,16 +57,17 @@ variable {A A' B B' : Type _} [Category A] [Category A'] [Category B] [Category
   (eB : B ≌ B') (e' : A' ≌ B') {F : A ⥤ B'} (hF : eA.Functor ⋙ e'.Functor ≅ F) {G : B ⥤ A}
   (hG : eB.Functor ⋙ e'.inverse ≅ G ⋙ eA.Functor)
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalence₀ /-
 /-- A basic equivalence `A ≅ B'` obtained by composing `eA : A ≅ A'` and `e' : A' ≅ B'`. -/
 @[simps Functor inverse unit_iso_hom_app]
 def equivalence₀ : A ≌ B' :=
   eA.trans e'
 #align algebraic_topology.dold_kan.compatibility.equivalence₀ AlgebraicTopology.DoldKan.Compatibility.equivalence₀
-
-include hF
+-/
 
 variable {eA} {e'}
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalence₁ /-
 /-- An intermediate equivalence `A ≅ B'` whose functor is `F` and whose inverse is
 `e'.inverse ⋙ eA.inverse`. -/
 @[simps Functor]
@@ -75,11 +76,15 @@ def equivalence₁ : A ≌ B' :=
     is_equivalence.of_iso hF (is_equivalence.of_equivalence (equivalence₀ eA e'))
   F.as_equivalence
 #align algebraic_topology.dold_kan.compatibility.equivalence₁ AlgebraicTopology.DoldKan.Compatibility.equivalence₁
+-/
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalence₁_inverse /-
 theorem equivalence₁_inverse : (equivalence₁ hF).inverse = e'.inverse ⋙ eA.inverse :=
   rfl
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_inverse AlgebraicTopology.DoldKan.Compatibility.equivalence₁_inverse
+-/
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso /-
 /-- The counit isomorphism of the equivalence `equivalence₁` between `A` and `B'`. -/
 @[simps]
 def equivalence₁CounitIso : (e'.inverse ⋙ eA.inverse) ⋙ F ≅ 𝟭 B' :=
@@ -91,14 +96,18 @@ def equivalence₁CounitIso : (e'.inverse ⋙ eA.inverse) ⋙ F ≅ 𝟭 B' :=
     _ ≅ e'.inverse ⋙ e'.Functor := (Iso.refl _)
     _ ≅ 𝟭 B' := e'.counitIso
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso
+-/
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_eq /-
 theorem equivalence₁CounitIso_eq : (equivalence₁ hF).counitIso = equivalence₁CounitIso hF :=
   by
   ext Y
   dsimp [equivalence₀, equivalence₁, is_equivalence.inverse, is_equivalence.of_equivalence]
   simp only [equivalence₁_counit_iso_hom_app, CategoryTheory.Functor.map_id, comp_id]
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_counit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_eq
+-/
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso /-
 /-- The unit isomorphism of the equivalence `equivalence₁` between `A` and `B'`. -/
 @[simps]
 def equivalence₁UnitIso : 𝟭 A ≅ F ⋙ e'.inverse ⋙ eA.inverse :=
@@ -110,28 +119,34 @@ def equivalence₁UnitIso : 𝟭 A ≅ F ⋙ e'.inverse ⋙ eA.inverse :=
     _ ≅ (eA.Functor ⋙ e'.Functor) ⋙ e'.inverse ⋙ eA.inverse := (Iso.refl _)
     _ ≅ F ⋙ e'.inverse ⋙ eA.inverse := isoWhiskerRight hF _
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_unit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso
+-/
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_eq /-
 theorem equivalence₁UnitIso_eq : (equivalence₁ hF).unitIso = equivalence₁UnitIso hF :=
   by
   ext X
   dsimp [equivalence₀, equivalence₁, nat_iso.hcomp, is_equivalence.of_equivalence]
   simp only [id_comp, assoc, equivalence₁_unit_iso_hom_app]
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_unit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_eq
+-/
 
-include eB
-
+#print AlgebraicTopology.DoldKan.Compatibility.equivalence₂ /-
 /-- An intermediate equivalence `A ≅ B` obtained as the composition of `equivalence₁` and
 the inverse of `eB : B ≌ B'`. -/
 @[simps Functor]
 def equivalence₂ : A ≌ B :=
   (equivalence₁ hF).trans eB.symm
 #align algebraic_topology.dold_kan.compatibility.equivalence₂ AlgebraicTopology.DoldKan.Compatibility.equivalence₂
+-/
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalence₂_inverse /-
 theorem equivalence₂_inverse :
     (equivalence₂ eB hF).inverse = eB.Functor ⋙ e'.inverse ⋙ eA.inverse :=
   rfl
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_inverse AlgebraicTopology.DoldKan.Compatibility.equivalence₂_inverse
+-/
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso /-
 /-- The counit isomorphism of the equivalence `equivalence₂` between `A` and `B`. -/
 @[simps]
 def equivalence₂CounitIso : (eB.Functor ⋙ e'.inverse ⋙ eA.inverse) ⋙ F ⋙ eB.inverse ≅ 𝟭 B :=
@@ -144,7 +159,9 @@ def equivalence₂CounitIso : (eB.Functor ⋙ e'.inverse ⋙ eA.inverse) ⋙ F 
     _ ≅ eB.Functor ⋙ eB.inverse := (Iso.refl _)
     _ ≅ 𝟭 B := eB.unitIso.symm
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso
+-/
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_eq /-
 theorem equivalence₂CounitIso_eq : (equivalence₂ eB hF).counitIso = equivalence₂CounitIso eB hF :=
   by
   ext Y'
@@ -152,7 +169,9 @@ theorem equivalence₂CounitIso_eq : (equivalence₂ eB hF).counitIso = equivale
   simp only [equivalence₁_counit_iso_eq, equivalence₂_counit_iso_hom_app,
     equivalence₁_counit_iso_hom_app, functor.map_comp, assoc]
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_counit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_eq
+-/
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso /-
 /-- The unit isomorphism of the equivalence `equivalence₂` between `A` and `B`. -/
 @[simps]
 def equivalence₂UnitIso : 𝟭 A ≅ (F ⋙ eB.inverse) ⋙ eB.Functor ⋙ e'.inverse ⋙ eA.inverse :=
@@ -163,7 +182,9 @@ def equivalence₂UnitIso : 𝟭 A ≅ (F ⋙ eB.inverse) ⋙ eB.Functor ⋙ e'.
       (isoWhiskerLeft _ (isoWhiskerRight eB.counitIso.symm _))
     _ ≅ (F ⋙ eB.inverse) ⋙ eB.Functor ⋙ e'.inverse ⋙ eA.inverse := Iso.refl _
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_unit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso
+-/
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_eq /-
 theorem equivalence₂UnitIso_eq : (equivalence₂ eB hF).unitIso = equivalence₂UnitIso eB hF :=
   by
   ext X
@@ -171,11 +192,11 @@ theorem equivalence₂UnitIso_eq : (equivalence₂ eB hF).unitIso = equivalence
   simpa only [equivalence₂_unit_iso_hom_app, equivalence₁_unit_iso_eq,
     equivalence₁_unit_iso_hom_app, assoc, nat_iso.cancel_nat_iso_hom_left]
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_unit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_eq
+-/
 
 variable {eB}
 
-include hG
-
+#print AlgebraicTopology.DoldKan.Compatibility.equivalence /-
 /-- The equivalence `A ≅ B` whose functor is `F ⋙ eB.inverse` and
 whose inverse is `G : B ≅ A`. -/
 @[simps inverse]
@@ -190,10 +211,13 @@ def equivalence : A ≌ B :=
       _ ≅ G := functor.right_unitor G
   G.as_equivalence.symm
 #align algebraic_topology.dold_kan.compatibility.equivalence AlgebraicTopology.DoldKan.Compatibility.equivalence
+-/
 
+#print AlgebraicTopology.DoldKan.Compatibility.equivalence_functor /-
 theorem equivalence_functor : (equivalence hF hG).Functor = F ⋙ eB.inverse :=
   rfl
 #align algebraic_topology.dold_kan.compatibility.equivalence_functor AlgebraicTopology.DoldKan.Compatibility.equivalence_functor
+-/
 
 end Compatibility

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -90,7 +90,6 @@ def equivalence₁CounitIso : (e'.inverse ⋙ eA.inverse) ⋙ F ≅ 𝟭 B' :=
     _ ≅ e'.inverse ⋙ 𝟭 _ ⋙ e'.Functor := (isoWhiskerLeft _ (isoWhiskerRight eA.counitIso _))
     _ ≅ e'.inverse ⋙ e'.Functor := (Iso.refl _)
     _ ≅ 𝟭 B' := e'.counitIso
-    
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso
 
 theorem equivalence₁CounitIso_eq : (equivalence₁ hF).counitIso = equivalence₁CounitIso hF :=
@@ -110,7 +109,6 @@ def equivalence₁UnitIso : 𝟭 A ≅ F ⋙ e'.inverse ⋙ eA.inverse :=
       (isoWhiskerLeft _ (isoWhiskerRight e'.unitIso _))
     _ ≅ (eA.Functor ⋙ e'.Functor) ⋙ e'.inverse ⋙ eA.inverse := (Iso.refl _)
     _ ≅ F ⋙ e'.inverse ⋙ eA.inverse := isoWhiskerRight hF _
-    
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_unit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso
 
 theorem equivalence₁UnitIso_eq : (equivalence₁ hF).unitIso = equivalence₁UnitIso hF :=
@@ -145,7 +143,6 @@ def equivalence₂CounitIso : (eB.Functor ⋙ e'.inverse ⋙ eA.inverse) ⋙ F 
       (isoWhiskerLeft _ (isoWhiskerRight (equivalence₁CounitIso hF) _))
     _ ≅ eB.Functor ⋙ eB.inverse := (Iso.refl _)
     _ ≅ 𝟭 B := eB.unitIso.symm
-    
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso
 
 theorem equivalence₂CounitIso_eq : (equivalence₂ eB hF).counitIso = equivalence₂CounitIso eB hF :=
@@ -165,7 +162,6 @@ def equivalence₂UnitIso : 𝟭 A ≅ (F ⋙ eB.inverse) ⋙ eB.Functor ⋙ e'.
     _ ≅ F ⋙ (eB.inverse ⋙ eB.Functor) ⋙ e'.inverse ⋙ eA.inverse :=
       (isoWhiskerLeft _ (isoWhiskerRight eB.counitIso.symm _))
     _ ≅ (F ⋙ eB.inverse) ⋙ eB.Functor ⋙ e'.inverse ⋙ eA.inverse := Iso.refl _
-    
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_unit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso
 
 theorem equivalence₂UnitIso_eq : (equivalence₂ eB hF).unitIso = equivalence₂UnitIso eB hF :=
@@ -192,7 +188,6 @@ def equivalence : A ≌ B :=
       _ ≅ (G ⋙ eA.functor) ⋙ eA.inverse := (iso_whisker_right hG _)
       _ ≅ G ⋙ 𝟭 A := (iso_whisker_left _ eA.unit_iso.symm)
       _ ≅ G := functor.right_unitor G
-      
   G.as_equivalence.symm
 #align algebraic_topology.dold_kan.compatibility.equivalence AlgebraicTopology.DoldKan.Compatibility.equivalence

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -57,12 +57,6 @@ variable {A A' B B' : Type _} [Category A] [Category A'] [Category B] [Category
   (eB : B ≌ B') (e' : A' ≌ B') {F : A ⥤ B'} (hF : eA.Functor ⋙ e'.Functor ≅ F) {G : B ⥤ A}
   (hG : eB.Functor ⋙ e'.inverse ≅ G ⋙ eA.Functor)
 
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-lean 3 declaration is
-  forall {A : Type.{u1}} {A' : Type.{u2}} {B' : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u4, u1} A] [_inst_2 : CategoryTheory.Category.{u5, u2} A'] [_inst_4 : CategoryTheory.Category.{u6, u3} B'], (CategoryTheory.Equivalence.{u4, u5, u1, u2} A _inst_1 A' _inst_2) -> (CategoryTheory.Equivalence.{u5, u6, u2, u3} A' _inst_2 B' _inst_4) -> (CategoryTheory.Equivalence.{u4, u6, u1, u3} A _inst_1 B' _inst_4)
-but is expected to have type
-  forall {A : Type.{u1}} {A' : Type.{u2}} {B' : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u4, u1} A] [_inst_2 : CategoryTheory.Category.{u5, u2} A'] [_inst_4 : CategoryTheory.Category.{u6, u3} B'], (CategoryTheory.Equivalence.{u4, u5, u1, u2} A A' _inst_1 _inst_2) -> (CategoryTheory.Equivalence.{u5, u6, u2, u3} A' B' _inst_2 _inst_4) -> (CategoryTheory.Equivalence.{u4, u6, u1, u3} A B' _inst_1 _inst_4)
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₀ AlgebraicTopology.DoldKan.Compatibility.equivalence₀ₓ'. -/
 /-- A basic equivalence `A ≅ B'` obtained by composing `eA : A ≅ A'` and `e' : A' ≅ B'`. -/
 @[simps Functor inverse unit_iso_hom_app]
 def equivalence₀ : A ≌ B' :=
@@ -73,12 +67,6 @@ include hF
 
 variable {eA} {e'}
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₁ AlgebraicTopology.DoldKan.Compatibility.equivalence₁ₓ'. -/
 /-- An intermediate equivalence `A ≅ B'` whose functor is `F` and whose inverse is
 `e'.inverse ⋙ eA.inverse`. -/
 @[simps Functor]
@@ -88,22 +76,10 @@ def equivalence₁ : A ≌ B' :=
   F.as_equivalence
 #align algebraic_topology.dold_kan.compatibility.equivalence₁ AlgebraicTopology.DoldKan.Compatibility.equivalence₁
 
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 theorem equivalence₁_inverse : (equivalence₁ hF).inverse = e'.inverse ⋙ eA.inverse :=
   rfl
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_inverse AlgebraicTopology.DoldKan.Compatibility.equivalence₁_inverse
 
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 /-- The counit isomorphism of the equivalence `equivalence₁` between `A` and `B'`. -/
 @[simps]
 def equivalence₁CounitIso : (e'.inverse ⋙ eA.inverse) ⋙ F ≅ 𝟭 B' :=
@@ -117,12 +93,6 @@ def equivalence₁CounitIso : (e'.inverse ⋙ eA.inverse) ⋙ F ≅ 𝟭 B' :=
     
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso
 
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 theorem equivalence₁CounitIso_eq : (equivalence₁ hF).counitIso = equivalence₁CounitIso hF :=
   by
   ext Y
@@ -130,12 +100,6 @@ theorem equivalence₁CounitIso_eq : (equivalence₁ hF).counitIso = equivalence
   simp only [equivalence₁_counit_iso_hom_app, CategoryTheory.Functor.map_id, comp_id]
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_counit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_eq
 
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 /-- The unit isomorphism of the equivalence `equivalence₁` between `A` and `B'`. -/
 @[simps]
 def equivalence₁UnitIso : 𝟭 A ≅ F ⋙ e'.inverse ⋙ eA.inverse :=
@@ -149,12 +113,6 @@ def equivalence₁UnitIso : 𝟭 A ≅ F ⋙ e'.inverse ⋙ eA.inverse :=
     
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_unit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso
 
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 theorem equivalence₁UnitIso_eq : (equivalence₁ hF).unitIso = equivalence₁UnitIso hF :=
   by
   ext X
@@ -164,12 +122,6 @@ theorem equivalence₁UnitIso_eq : (equivalence₁ hF).unitIso = equivalence₁U
 
 include eB
 
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 /-- An intermediate equivalence `A ≅ B` obtained as the composition of `equivalence₁` and
 the inverse of `eB : B ≌ B'`. -/
 @[simps Functor]
@@ -177,23 +129,11 @@ def equivalence₂ : A ≌ B :=
   (equivalence₁ hF).trans eB.symm
 #align algebraic_topology.dold_kan.compatibility.equivalence₂ AlgebraicTopology.DoldKan.Compatibility.equivalence₂
 
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 theorem equivalence₂_inverse :
     (equivalence₂ eB hF).inverse = eB.Functor ⋙ e'.inverse ⋙ eA.inverse :=
   rfl
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_inverse AlgebraicTopology.DoldKan.Compatibility.equivalence₂_inverse
 
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 /-- The counit isomorphism of the equivalence `equivalence₂` between `A` and `B`. -/
 @[simps]
 def equivalence₂CounitIso : (eB.Functor ⋙ e'.inverse ⋙ eA.inverse) ⋙ F ⋙ eB.inverse ≅ 𝟭 B :=
@@ -208,9 +148,6 @@ def equivalence₂CounitIso : (eB.Functor ⋙ e'.inverse ⋙ eA.inverse) ⋙ F 
     
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso
 
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 theorem equivalence₂CounitIso_eq : (equivalence₂ eB hF).counitIso = equivalence₂CounitIso eB hF :=
   by
   ext Y'
@@ -219,12 +156,6 @@ theorem equivalence₂CounitIso_eq : (equivalence₂ eB hF).counitIso = equivale
     equivalence₁_counit_iso_hom_app, functor.map_comp, assoc]
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_counit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_eq
 
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 /-- The unit isomorphism of the equivalence `equivalence₂` between `A` and `B`. -/
 @[simps]
 def equivalence₂UnitIso : 𝟭 A ≅ (F ⋙ eB.inverse) ⋙ eB.Functor ⋙ e'.inverse ⋙ eA.inverse :=
@@ -237,9 +168,6 @@ def equivalence₂UnitIso : 𝟭 A ≅ (F ⋙ eB.inverse) ⋙ eB.Functor ⋙ e'.
     
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_unit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso
 
-/- warning: algebraic_topology.dold_kan.compatibility.equivalence₂_unit_iso_eq -> AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₂_unit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_eqₓ'. -/
 theorem equivalence₂UnitIso_eq : (equivalence₂ eB hF).unitIso = equivalence₂UnitIso eB hF :=
   by
   ext X
@@ -252,12 +180,6 @@ variable {eB}
 
 include hG
 
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 /-- The equivalence `A ≅ B` whose functor is `F ⋙ eB.inverse` and
 whose inverse is `G : B ≅ A`. -/
 @[simps inverse]
@@ -274,9 +196,6 @@ def equivalence : A ≌ B :=
   G.as_equivalence.symm
 #align algebraic_topology.dold_kan.compatibility.equivalence AlgebraicTopology.DoldKan.Compatibility.equivalence
 
-/- warning: algebraic_topology.dold_kan.compatibility.equivalence_functor -> AlgebraicTopology.DoldKan.Compatibility.equivalence_functor is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence_functor AlgebraicTopology.DoldKan.Compatibility.equivalence_functorₓ'. -/
 theorem equivalence_functor : (equivalence hF hG).Functor = F ⋙ eB.inverse :=
   rfl
 #align algebraic_topology.dold_kan.compatibility.equivalence_functor AlgebraicTopology.DoldKan.Compatibility.equivalence_functor

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -209,10 +209,7 @@ def equivalence₂CounitIso : (eB.Functor ⋙ e'.inverse ⋙ eA.inverse) ⋙ F 
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso
 
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 theorem equivalence₂CounitIso_eq : (equivalence₂ eB hF).counitIso = equivalence₂CounitIso eB hF :=
   by
@@ -241,10 +238,7 @@ def equivalence₂UnitIso : 𝟭 A ≅ (F ⋙ eB.inverse) ⋙ eB.Functor ⋙ e'.
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_unit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₂_unit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_eqₓ'. -/
 theorem equivalence₂UnitIso_eq : (equivalence₂ eB hF).unitIso = equivalence₂UnitIso eB hF :=
   by
@@ -281,10 +275,7 @@ def equivalence : A ≌ B :=
 #align algebraic_topology.dold_kan.compatibility.equivalence AlgebraicTopology.DoldKan.Compatibility.equivalence
 
 /- warning: algebraic_topology.dold_kan.compatibility.equivalence_functor -> AlgebraicTopology.DoldKan.Compatibility.equivalence_functor is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence_functor AlgebraicTopology.DoldKan.Compatibility.equivalence_functorₓ'. -/
 theorem equivalence_functor : (equivalence hF hG).Functor = F ⋙ eB.inverse :=
   rfl

bump to nightly-2023-04-06-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/06a655b5fcfbda03502f9158bbf6c0f1400886f9

89485060

Diff

@@ -4,13 +4,16 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 
 ! This file was ported from Lean 3 source module algebraic_topology.dold_kan.compatibility
-! leanprover-community/mathlib commit 160f568dcf772b2477791c844fc605f2f91f73d1
+! leanprover-community/mathlib commit d64d67d000b974f0d86a2be7918cf800be6271c8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Equivalence
 
-/-! Tools for compatibilities between Dold-Kan equivalences
+/-!
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+ Tools for compatibilities between Dold-Kan equivalences
 
 The purpose of this file is to introduce tools which will enable the
 construction of the Dold-Kan equivalence `simplicial_object C ≌ chain_complex C ℕ`

bump to nightly-2023-04-03-12

mathlib commit https://github.com/leanprover-community/mathlib/commit/d95bef0d215ea58c0fd7bbc4b151bf3fe952c095

c6c3ccde

Diff

@@ -54,6 +54,12 @@ variable {A A' B B' : Type _} [Category A] [Category A'] [Category B] [Category
   (eB : B ≌ B') (e' : A' ≌ B') {F : A ⥤ B'} (hF : eA.Functor ⋙ e'.Functor ≅ F) {G : B ⥤ A}
   (hG : eB.Functor ⋙ e'.inverse ≅ G ⋙ eA.Functor)
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₀ AlgebraicTopology.DoldKan.Compatibility.equivalence₀ₓ'. -/
 /-- A basic equivalence `A ≅ B'` obtained by composing `eA : A ≅ A'` and `e' : A' ≅ B'`. -/
 @[simps Functor inverse unit_iso_hom_app]
 def equivalence₀ : A ≌ B' :=
@@ -64,6 +70,12 @@ include hF
 
 variable {eA} {e'}
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₁ AlgebraicTopology.DoldKan.Compatibility.equivalence₁ₓ'. -/
 /-- An intermediate equivalence `A ≅ B'` whose functor is `F` and whose inverse is
 `e'.inverse ⋙ eA.inverse`. -/
 @[simps Functor]
@@ -73,10 +85,22 @@ def equivalence₁ : A ≌ B' :=
   F.as_equivalence
 #align algebraic_topology.dold_kan.compatibility.equivalence₁ AlgebraicTopology.DoldKan.Compatibility.equivalence₁
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₁_inverse AlgebraicTopology.DoldKan.Compatibility.equivalence₁_inverseₓ'. -/
 theorem equivalence₁_inverse : (equivalence₁ hF).inverse = e'.inverse ⋙ eA.inverse :=
   rfl
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_inverse AlgebraicTopology.DoldKan.Compatibility.equivalence₁_inverse
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₁_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIsoₓ'. -/
 /-- The counit isomorphism of the equivalence `equivalence₁` between `A` and `B'`. -/
 @[simps]
 def equivalence₁CounitIso : (e'.inverse ⋙ eA.inverse) ⋙ F ≅ 𝟭 B' :=
@@ -90,6 +114,12 @@ def equivalence₁CounitIso : (e'.inverse ⋙ eA.inverse) ⋙ F ≅ 𝟭 B' :=
     
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₁_counit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_eqₓ'. -/
 theorem equivalence₁CounitIso_eq : (equivalence₁ hF).counitIso = equivalence₁CounitIso hF :=
   by
   ext Y
@@ -97,6 +127,12 @@ theorem equivalence₁CounitIso_eq : (equivalence₁ hF).counitIso = equivalence
   simp only [equivalence₁_counit_iso_hom_app, CategoryTheory.Functor.map_id, comp_id]
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_counit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_eq
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₁_unit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIsoₓ'. -/
 /-- The unit isomorphism of the equivalence `equivalence₁` between `A` and `B'`. -/
 @[simps]
 def equivalence₁UnitIso : 𝟭 A ≅ F ⋙ e'.inverse ⋙ eA.inverse :=
@@ -110,6 +146,12 @@ def equivalence₁UnitIso : 𝟭 A ≅ F ⋙ e'.inverse ⋙ eA.inverse :=
     
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_unit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₁_unit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_eqₓ'. -/
 theorem equivalence₁UnitIso_eq : (equivalence₁ hF).unitIso = equivalence₁UnitIso hF :=
   by
   ext X
@@ -119,6 +161,12 @@ theorem equivalence₁UnitIso_eq : (equivalence₁ hF).unitIso = equivalence₁U
 
 include eB
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₂ AlgebraicTopology.DoldKan.Compatibility.equivalence₂ₓ'. -/
 /-- An intermediate equivalence `A ≅ B` obtained as the composition of `equivalence₁` and
 the inverse of `eB : B ≌ B'`. -/
 @[simps Functor]
@@ -126,11 +174,23 @@ def equivalence₂ : A ≌ B :=
   (equivalence₁ hF).trans eB.symm
 #align algebraic_topology.dold_kan.compatibility.equivalence₂ AlgebraicTopology.DoldKan.Compatibility.equivalence₂
 
+/- warning: algebraic_topology.dold_kan.compatibility.equivalence₂_inverse -> AlgebraicTopology.DoldKan.Compatibility.equivalence₂_inverse is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₂_inverse AlgebraicTopology.DoldKan.Compatibility.equivalence₂_inverseₓ'. -/
 theorem equivalence₂_inverse :
     (equivalence₂ eB hF).inverse = eB.Functor ⋙ e'.inverse ⋙ eA.inverse :=
   rfl
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_inverse AlgebraicTopology.DoldKan.Compatibility.equivalence₂_inverse
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₂_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIsoₓ'. -/
 /-- The counit isomorphism of the equivalence `equivalence₂` between `A` and `B`. -/
 @[simps]
 def equivalence₂CounitIso : (eB.Functor ⋙ e'.inverse ⋙ eA.inverse) ⋙ F ⋙ eB.inverse ≅ 𝟭 B :=
@@ -145,6 +205,12 @@ def equivalence₂CounitIso : (eB.Functor ⋙ e'.inverse ⋙ eA.inverse) ⋙ F 
     
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso
 
+/- warning: algebraic_topology.dold_kan.compatibility.equivalence₂_counit_iso_eq -> AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_eq is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₂_counit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_eqₓ'. -/
 theorem equivalence₂CounitIso_eq : (equivalence₂ eB hF).counitIso = equivalence₂CounitIso eB hF :=
   by
   ext Y'
@@ -153,6 +219,12 @@ theorem equivalence₂CounitIso_eq : (equivalence₂ eB hF).counitIso = equivale
     equivalence₁_counit_iso_hom_app, functor.map_comp, assoc]
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_counit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso_eq
 
+/- warning: algebraic_topology.dold_kan.compatibility.equivalence₂_unit_iso -> AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₂_unit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIsoₓ'. -/
 /-- The unit isomorphism of the equivalence `equivalence₂` between `A` and `B`. -/
 @[simps]
 def equivalence₂UnitIso : 𝟭 A ≅ (F ⋙ eB.inverse) ⋙ eB.Functor ⋙ e'.inverse ⋙ eA.inverse :=
@@ -165,6 +237,12 @@ def equivalence₂UnitIso : 𝟭 A ≅ (F ⋙ eB.inverse) ⋙ eB.Functor ⋙ e'.
     
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_unit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso
 
+/- warning: algebraic_topology.dold_kan.compatibility.equivalence₂_unit_iso_eq -> AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_eq is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence₂_unit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso_eqₓ'. -/
 theorem equivalence₂UnitIso_eq : (equivalence₂ eB hF).unitIso = equivalence₂UnitIso eB hF :=
   by
   ext X
@@ -177,6 +255,12 @@ variable {eB}
 
 include hG
 
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+  forall {A : Type.{u1}} {A' : Type.{u2}} {B : Type.{u3}} {B' : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u5, u1} A] [_inst_2 : CategoryTheory.Category.{u6, u2} A'] [_inst_3 : CategoryTheory.Category.{u7, u3} B] [_inst_4 : CategoryTheory.Category.{u8, u4} B'] {eA : CategoryTheory.Equivalence.{u5, u6, u1, u2} A _inst_1 A' _inst_2} {eB : CategoryTheory.Equivalence.{u7, u8, u3, u4} B _inst_3 B' _inst_4} {e' : CategoryTheory.Equivalence.{u6, u8, u2, u4} A' _inst_2 B' _inst_4} {F : CategoryTheory.Functor.{u5, u8, u1, u4} A _inst_1 B' _inst_4}, (CategoryTheory.Iso.{max u1 u8, max u5 u8 u1 u4} (CategoryTheory.Functor.{u5, u8, u1, u4} A _inst_1 B' _inst_4) (CategoryTheory.Functor.category.{u5, u8, u1, u4} A _inst_1 B' _inst_4) (CategoryTheory.Functor.comp.{u5, u6, u8, u1, u2, u4} A _inst_1 A' _inst_2 B' _inst_4 (CategoryTheory.Equivalence.functor.{u5, u6, u1, u2} A _inst_1 A' _inst_2 eA) (CategoryTheory.Equivalence.functor.{u6, u8, u2, u4} A' _inst_2 B' _inst_4 e')) F) -> (forall {G : CategoryTheory.Functor.{u7, u5, u3, u1} B _inst_3 A _inst_1}, (CategoryTheory.Iso.{max u3 u6, max u7 u6 u3 u2} (CategoryTheory.Functor.{u7, u6, u3, u2} B _inst_3 A' _inst_2) (CategoryTheory.Functor.category.{u7, u6, u3, u2} B _inst_3 A' _inst_2) (CategoryTheory.Functor.comp.{u7, u8, u6, u3, u4, u2} B _inst_3 B' _inst_4 A' _inst_2 (CategoryTheory.Equivalence.functor.{u7, u8, u3, u4} B _inst_3 B' _inst_4 eB) (CategoryTheory.Equivalence.inverse.{u6, u8, u2, u4} A' _inst_2 B' _inst_4 e')) (CategoryTheory.Functor.comp.{u7, u5, u6, u3, u1, u2} B _inst_3 A _inst_1 A' _inst_2 G (CategoryTheory.Equivalence.functor.{u5, u6, u1, u2} A _inst_1 A' _inst_2 eA))) -> (CategoryTheory.Equivalence.{u5, u7, u1, u3} A _inst_1 B _inst_3))
+but is expected to have type
+  forall {A : Type.{u1}} {A' : Type.{u2}} {B : Type.{u3}} {B' : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u5, u1} A] [_inst_2 : CategoryTheory.Category.{u6, u2} A'] [_inst_3 : CategoryTheory.Category.{u7, u3} B] [_inst_4 : CategoryTheory.Category.{u8, u4} B'] {eA : CategoryTheory.Equivalence.{u5, u6, u1, u2} A A' _inst_1 _inst_2} {eB : CategoryTheory.Equivalence.{u7, u8, u3, u4} B B' _inst_3 _inst_4} {e' : CategoryTheory.Equivalence.{u6, u8, u2, u4} A' B' _inst_2 _inst_4} {F : CategoryTheory.Functor.{u5, u8, u1, u4} A _inst_1 B' _inst_4}, (CategoryTheory.Iso.{max u1 u8, max (max (max u4 u1) u8) u5} (CategoryTheory.Functor.{u5, u8, u1, u4} A _inst_1 B' _inst_4) (CategoryTheory.Functor.category.{u5, u8, u1, u4} A _inst_1 B' _inst_4) (CategoryTheory.Functor.comp.{u5, u6, u8, u1, u2, u4} A _inst_1 A' _inst_2 B' _inst_4 (CategoryTheory.Equivalence.functor.{u5, u6, u1, u2} A A' _inst_1 _inst_2 eA) (CategoryTheory.Equivalence.functor.{u6, u8, u2, u4} A' B' _inst_2 _inst_4 e')) F) -> (forall {G : CategoryTheory.Functor.{u7, u5, u3, u1} B _inst_3 A _inst_1}, (CategoryTheory.Iso.{max u3 u6, max (max (max u2 u3) u6) u7} (CategoryTheory.Functor.{u7, u6, u3, u2} B _inst_3 A' _inst_2) (CategoryTheory.Functor.category.{u7, u6, u3, u2} B _inst_3 A' _inst_2) (CategoryTheory.Functor.comp.{u7, u8, u6, u3, u4, u2} B _inst_3 B' _inst_4 A' _inst_2 (CategoryTheory.Equivalence.functor.{u7, u8, u3, u4} B B' _inst_3 _inst_4 eB) (CategoryTheory.Equivalence.inverse.{u6, u8, u2, u4} A' B' _inst_2 _inst_4 e')) (CategoryTheory.Functor.comp.{u7, u5, u6, u3, u1, u2} B _inst_3 A _inst_1 A' _inst_2 G (CategoryTheory.Equivalence.functor.{u5, u6, u1, u2} A A' _inst_1 _inst_2 eA))) -> (CategoryTheory.Equivalence.{u5, u7, u1, u3} A B _inst_1 _inst_3))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence AlgebraicTopology.DoldKan.Compatibility.equivalenceₓ'. -/
 /-- The equivalence `A ≅ B` whose functor is `F ⋙ eB.inverse` and
 whose inverse is `G : B ≅ A`. -/
 @[simps inverse]
@@ -193,6 +277,12 @@ def equivalence : A ≌ B :=
   G.as_equivalence.symm
 #align algebraic_topology.dold_kan.compatibility.equivalence AlgebraicTopology.DoldKan.Compatibility.equivalence
 
+/- warning: algebraic_topology.dold_kan.compatibility.equivalence_functor -> AlgebraicTopology.DoldKan.Compatibility.equivalence_functor is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} {A' : Type.{u2}} {B : Type.{u3}} {B' : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u5, u1} A] [_inst_2 : CategoryTheory.Category.{u6, u2} A'] [_inst_3 : CategoryTheory.Category.{u7, u3} B] [_inst_4 : CategoryTheory.Category.{u8, u4} B'] {eA : CategoryTheory.Equivalence.{u5, u6, u1, u2} A _inst_1 A' _inst_2} {eB : CategoryTheory.Equivalence.{u7, u8, u3, u4} B _inst_3 B' _inst_4} {e' : CategoryTheory.Equivalence.{u6, u8, u2, u4} A' _inst_2 B' _inst_4} {F : CategoryTheory.Functor.{u5, u8, u1, u4} A _inst_1 B' _inst_4} (hF : CategoryTheory.Iso.{max u1 u8, max u5 u8 u1 u4} (CategoryTheory.Functor.{u5, u8, u1, u4} A _inst_1 B' _inst_4) (CategoryTheory.Functor.category.{u5, u8, u1, u4} A _inst_1 B' _inst_4) (CategoryTheory.Functor.comp.{u5, u6, u8, u1, u2, u4} A _inst_1 A' _inst_2 B' _inst_4 (CategoryTheory.Equivalence.functor.{u5, u6, u1, u2} A _inst_1 A' _inst_2 eA) (CategoryTheory.Equivalence.functor.{u6, u8, u2, u4} A' _inst_2 B' _inst_4 e')) F) {G : CategoryTheory.Functor.{u7, u5, u3, u1} B _inst_3 A _inst_1} (hG : CategoryTheory.Iso.{max u3 u6, max u7 u6 u3 u2} (CategoryTheory.Functor.{u7, u6, u3, u2} B _inst_3 A' _inst_2) (CategoryTheory.Functor.category.{u7, u6, u3, u2} B _inst_3 A' _inst_2) (CategoryTheory.Functor.comp.{u7, u8, u6, u3, u4, u2} B _inst_3 B' _inst_4 A' _inst_2 (CategoryTheory.Equivalence.functor.{u7, u8, u3, u4} B _inst_3 B' _inst_4 eB) (CategoryTheory.Equivalence.inverse.{u6, u8, u2, u4} A' _inst_2 B' _inst_4 e')) (CategoryTheory.Functor.comp.{u7, u5, u6, u3, u1, u2} B _inst_3 A _inst_1 A' _inst_2 G (CategoryTheory.Equivalence.functor.{u5, u6, u1, u2} A _inst_1 A' _inst_2 eA))), Eq.{succ (max u5 u7 u1 u3)} (CategoryTheory.Functor.{u5, u7, u1, u3} A _inst_1 B _inst_3) (CategoryTheory.Equivalence.functor.{u5, u7, u1, u3} A _inst_1 B _inst_3 (AlgebraicTopology.DoldKan.Compatibility.equivalence.{u1, u2, u3, u4, u5, u6, u7, u8} A A' B B' _inst_1 _inst_2 _inst_3 _inst_4 eA eB e' F hF G hG)) (CategoryTheory.Functor.comp.{u5, u8, u7, u1, u4, u3} A _inst_1 B' _inst_4 B _inst_3 F (CategoryTheory.Equivalence.inverse.{u7, u8, u3, u4} B _inst_3 B' _inst_4 eB))
+but is expected to have type
+  forall {A : Type.{u8}} {A' : Type.{u4}} {B : Type.{u7}} {B' : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u6, u8} A] [_inst_2 : CategoryTheory.Category.{u2, u4} A'] [_inst_3 : CategoryTheory.Category.{u5, u7} B] [_inst_4 : CategoryTheory.Category.{u1, u3} B'] {eA : CategoryTheory.Equivalence.{u6, u2, u8, u4} A A' _inst_1 _inst_2} {eB : CategoryTheory.Equivalence.{u5, u1, u7, u3} B B' _inst_3 _inst_4} {e' : CategoryTheory.Equivalence.{u2, u1, u4, u3} A' B' _inst_2 _inst_4} {F : CategoryTheory.Functor.{u6, u1, u8, u3} A _inst_1 B' _inst_4} (hF : CategoryTheory.Iso.{max u8 u1, max (max (max u3 u8) u1) u6} (CategoryTheory.Functor.{u6, u1, u8, u3} A _inst_1 B' _inst_4) (CategoryTheory.Functor.category.{u6, u1, u8, u3} A _inst_1 B' _inst_4) (CategoryTheory.Functor.comp.{u6, u2, u1, u8, u4, u3} A _inst_1 A' _inst_2 B' _inst_4 (CategoryTheory.Equivalence.functor.{u6, u2, u8, u4} A A' _inst_1 _inst_2 eA) (CategoryTheory.Equivalence.functor.{u2, u1, u4, u3} A' B' _inst_2 _inst_4 e')) F) {G : CategoryTheory.Functor.{u5, u6, u7, u8} B _inst_3 A _inst_1} (hG : CategoryTheory.Iso.{max u7 u2, max (max (max u4 u7) u2) u5} (CategoryTheory.Functor.{u5, u2, u7, u4} B _inst_3 A' _inst_2) (CategoryTheory.Functor.category.{u5, u2, u7, u4} B _inst_3 A' _inst_2) (CategoryTheory.Functor.comp.{u5, u1, u2, u7, u3, u4} B _inst_3 B' _inst_4 A' _inst_2 (CategoryTheory.Equivalence.functor.{u5, u1, u7, u3} B B' _inst_3 _inst_4 eB) (CategoryTheory.Equivalence.inverse.{u2, u1, u4, u3} A' B' _inst_2 _inst_4 e')) (CategoryTheory.Functor.comp.{u5, u6, u2, u7, u8, u4} B _inst_3 A _inst_1 A' _inst_2 G (CategoryTheory.Equivalence.functor.{u6, u2, u8, u4} A A' _inst_1 _inst_2 eA))), Eq.{max (max (max (succ u8) (succ u7)) (succ u6)) (succ u5)} (CategoryTheory.Functor.{u6, u5, u8, u7} A _inst_1 B _inst_3) (CategoryTheory.Equivalence.functor.{u6, u5, u8, u7} A B _inst_1 _inst_3 (AlgebraicTopology.DoldKan.Compatibility.equivalence.{u8, u4, u7, u3, u6, u2, u5, u1} A A' B B' _inst_1 _inst_2 _inst_3 _inst_4 eA eB e' F hF G hG)) (CategoryTheory.Functor.comp.{u6, u1, u5, u8, u3, u7} A _inst_1 B' _inst_4 B _inst_3 F (CategoryTheory.Equivalence.inverse.{u5, u1, u7, u3} B B' _inst_3 _inst_4 eB))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility.equivalence_functor AlgebraicTopology.DoldKan.Compatibility.equivalence_functorₓ'. -/
 theorem equivalence_functor : (equivalence hF hG).Functor = F ⋙ eB.inverse :=
   rfl
 #align algebraic_topology.dold_kan.compatibility.equivalence_functor AlgebraicTopology.DoldKan.Compatibility.equivalence_functor

bump to nightly-2023-03-30-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/b685f506164f8d17a6404048bc4d696739c5d976

af7dd13c

Changes in mathlib4

mathlib3

mathlib4

chore: superfluous parentheses part 2 (#12131)

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

d48d30ac

Diff

@@ -246,7 +246,7 @@ unit isomorphism of `e'` and the isomorphism `hF : eA.functor ⋙ e'.functor ≅
 def υ : eA.functor ≅ F ⋙ e'.inverse :=
   calc
     eA.functor ≅ eA.functor ⋙ 𝟭 A' := (Functor.leftUnitor _).symm
-    _ ≅ eA.functor ⋙ e'.functor ⋙ e'.inverse := (isoWhiskerLeft _ e'.unitIso)
+    _ ≅ eA.functor ⋙ e'.functor ⋙ e'.inverse := isoWhiskerLeft _ e'.unitIso
     _ ≅ (eA.functor ⋙ e'.functor) ⋙ e'.inverse := Iso.refl _
     _ ≅ F ⋙ e'.inverse := isoWhiskerRight hF _
 #align algebraic_topology.dold_kan.compatibility.υ AlgebraicTopology.DoldKan.Compatibility.υ

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

@@ -65,8 +65,8 @@ variable {eA} {e'}
 `e'.inverse ⋙ eA.inverse`. -/
 @[simps! functor]
 def equivalence₁ : A ≌ B' :=
-  letI : IsEquivalence F :=
-    IsEquivalence.ofIso hF (IsEquivalence.ofEquivalence (equivalence₀ eA e'))
+  letI : F.IsEquivalence :=
+    Functor.IsEquivalence.ofIso hF (Functor.IsEquivalence.ofEquivalence (equivalence₀ eA e'))
   F.asEquivalence
 #align algebraic_topology.dold_kan.compatibility.equivalence₁ AlgebraicTopology.DoldKan.Compatibility.equivalence₁
 
@@ -88,7 +88,8 @@ def equivalence₁CounitIso : (e'.inverse ⋙ eA.inverse) ⋙ F ≅ 𝟭 B' :=
 
 theorem equivalence₁CounitIso_eq : (equivalence₁ hF).counitIso = equivalence₁CounitIso hF := by
   ext Y
-  dsimp [equivalence₁, equivalence₀, IsEquivalence.inverse, IsEquivalence.ofEquivalence]
+  dsimp [equivalence₁, equivalence₀, Functor.IsEquivalence.inverse,
+    Functor.IsEquivalence.ofEquivalence]
   simp
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_counit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_eq
 
@@ -106,7 +107,7 @@ def equivalence₁UnitIso : 𝟭 A ≅ F ⋙ e'.inverse ⋙ eA.inverse :=
 
 theorem equivalence₁UnitIso_eq : (equivalence₁ hF).unitIso = equivalence₁UnitIso hF := by
   ext X
-  dsimp [equivalence₁, NatIso.hcomp, IsEquivalence.ofEquivalence]
+  dsimp [equivalence₁, NatIso.hcomp, Functor.IsEquivalence.ofEquivalence]
   simp
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_unit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_eq
 
@@ -168,8 +169,9 @@ variable {eB}
 whose inverse is `G : B ≅ A`. -/
 @[simps! inverse]
 def equivalence : A ≌ B :=
-  letI : IsEquivalence G := by
-    refine' IsEquivalence.ofIso _ (IsEquivalence.ofEquivalence (equivalence₂ eB hF).symm)
+  letI : G.IsEquivalence := by
+    refine' Functor.IsEquivalence.ofIso _
+      (Functor.IsEquivalence.ofEquivalence (equivalence₂ eB hF).symm)
     calc
       eB.functor ⋙ e'.inverse ⋙ eA.inverse ≅ (eB.functor ⋙ e'.inverse) ⋙ eA.inverse := Iso.refl _
       _ ≅ (G ⋙ eA.functor) ⋙ eA.inverse := isoWhiskerRight hG _
@@ -221,8 +223,8 @@ variable {η hF hG}
 
 theorem equivalenceCounitIso_eq : (equivalence hF hG).counitIso = equivalenceCounitIso η := by
   ext1; apply NatTrans.ext; ext Y
-  dsimp [equivalence, Functor.asEquivalence, IsEquivalence.ofEquivalence]
-  rw [equivalenceCounitIso_hom_app, IsEquivalence.ofIso_unitIso_inv_app]
+  dsimp [equivalence, Functor.asEquivalence, Functor.IsEquivalence.ofEquivalence]
+  rw [equivalenceCounitIso_hom_app, Functor.IsEquivalence.ofIso_unitIso_inv_app]
   dsimp
   simp only [comp_id, id_comp, F.map_comp, assoc,
     equivalence₂CounitIso_eq, equivalence₂CounitIso_hom_app,
@@ -272,8 +274,9 @@ variable {ε hF hG}
 
 theorem equivalenceUnitIso_eq : (equivalence hF hG).unitIso = equivalenceUnitIso hG ε := by
   ext1; apply NatTrans.ext; ext X
-  dsimp [equivalence, Functor.asEquivalence, IsEquivalence.ofEquivalence, IsEquivalence.inverse]
-  rw [IsEquivalence.ofIso_counitIso_inv_app]
+  dsimp [equivalence, Functor.asEquivalence, Functor.IsEquivalence.ofEquivalence,
+    Functor.IsEquivalence.inverse]
+  rw [Functor.IsEquivalence.ofIso_counitIso_inv_app]
   dsimp
   erw [id_comp, comp_id]
   simp only [equivalence₂UnitIso_eq eB hF, equivalence₂UnitIso_hom_app,

chore: move Mathlib to v4.7.0-rc1 (#11162)

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

fa48894a

Diff

@@ -88,9 +88,7 @@ def equivalence₁CounitIso : (e'.inverse ⋙ eA.inverse) ⋙ F ≅ 𝟭 B' :=
 
 theorem equivalence₁CounitIso_eq : (equivalence₁ hF).counitIso = equivalence₁CounitIso hF := by
   ext Y
-  dsimp [equivalence₁]
-  unfold Functor.asEquivalence
-  dsimp [equivalence₀, IsEquivalence.inverse, IsEquivalence.ofEquivalence]
+  dsimp [equivalence₁, equivalence₀, IsEquivalence.inverse, IsEquivalence.ofEquivalence]
   simp
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_counit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso_eq
 
@@ -108,9 +106,7 @@ def equivalence₁UnitIso : 𝟭 A ≅ F ⋙ e'.inverse ⋙ eA.inverse :=
 
 theorem equivalence₁UnitIso_eq : (equivalence₁ hF).unitIso = equivalence₁UnitIso hF := by
   ext X
-  dsimp [equivalence₁]
-  unfold Functor.asEquivalence
-  dsimp [NatIso.hcomp, IsEquivalence.ofEquivalence]
+  dsimp [equivalence₁, NatIso.hcomp, IsEquivalence.ofEquivalence]
   simp
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_unit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso_eq

chore: fix SHA for Dold-Kan equivalence files (#6834)

cf01bdac

Diff

@@ -5,7 +5,7 @@ Authors: Joël Riou
 -/
 import Mathlib.CategoryTheory.Equivalence
 
-#align_import algebraic_topology.dold_kan.compatibility from "leanprover-community/mathlib"@"18ee599842a5d17f189fe572f0ed8cb1d064d772"
+#align_import algebraic_topology.dold_kan.compatibility from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 
 /-! Tools for compatibilities between Dold-Kan equivalences

feat: forward port of Mathlib.AlgebraicTopology.DoldKan.Equivalence (#6444)

In this PR (which is a forward port of https://github.com/leanprover-community/mathlib/pull/17926), the Dold-Kan equivalence between simplicial objects and chain complexes in abelian categories is constructed.

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

c532d7b8

Diff

@@ -36,6 +36,8 @@ but whose inverse functor is `G`.
 When extra assumptions are given, we shall also provide simplification lemmas for the
 unit and counit isomorphisms of `equivalence`.
 
+(See `Equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
+
 -/

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

@@ -47,7 +47,7 @@ namespace DoldKan
 
 namespace Compatibility
 
-variable {A A' B B' : Type _} [Category A] [Category A'] [Category B] [Category B'] (eA : A ≌ A')
+variable {A A' B B' : Type*} [Category A] [Category A'] [Category B] [Category B'] (eA : A ≌ A')
   (eB : B ≌ B') (e' : A' ≌ B') {F : A ⥤ B'} (hF : eA.functor ⋙ e'.functor ≅ F) {G : B ⥤ A}
   (hG : eB.functor ⋙ e'.inverse ≅ G ⋙ eA.functor)

feat: forward port AlgebraicTopology.DoldKan.Compatibility (#6186)

This PR is a forward port of mathlib3 PR 3#17923

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

2471abe6

Diff

@@ -5,7 +5,7 @@ Authors: Joël Riou
 -/
 import Mathlib.CategoryTheory.Equivalence
 
-#align_import algebraic_topology.dold_kan.compatibility from "leanprover-community/mathlib"@"160f568dcf772b2477791c844fc605f2f91f73d1"
+#align_import algebraic_topology.dold_kan.compatibility from "leanprover-community/mathlib"@"18ee599842a5d17f189fe572f0ed8cb1d064d772"
 
 /-! Tools for compatibilities between Dold-Kan equivalences
 
@@ -34,7 +34,7 @@ inverse of `eB`:
 but whose inverse functor is `G`.
 
 When extra assumptions are given, we shall also provide simplification lemmas for the
-unit and counit isomorphisms of `equivalence`. (TODO)
+unit and counit isomorphisms of `equivalence`.
 
 -/
 
@@ -78,9 +78,9 @@ def equivalence₁CounitIso : (e'.inverse ⋙ eA.inverse) ⋙ F ≅ 𝟭 B' :=
   calc
     (e'.inverse ⋙ eA.inverse) ⋙ F ≅ (e'.inverse ⋙ eA.inverse) ⋙ eA.functor ⋙ e'.functor :=
       isoWhiskerLeft _ hF.symm
-    _ ≅ e'.inverse ⋙ (eA.inverse ⋙ eA.functor) ⋙ e'.functor := (Iso.refl _)
-    _ ≅ e'.inverse ⋙ 𝟭 _ ⋙ e'.functor := (isoWhiskerLeft _ (isoWhiskerRight eA.counitIso _))
-    _ ≅ e'.inverse ⋙ e'.functor := (Iso.refl _)
+    _ ≅ e'.inverse ⋙ (eA.inverse ⋙ eA.functor) ⋙ e'.functor := Iso.refl _
+    _ ≅ e'.inverse ⋙ 𝟭 _ ⋙ e'.functor := isoWhiskerLeft _ (isoWhiskerRight eA.counitIso _)
+    _ ≅ e'.inverse ⋙ e'.functor := Iso.refl _
     _ ≅ 𝟭 B' := e'.counitIso
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso
 
@@ -97,10 +97,10 @@ theorem equivalence₁CounitIso_eq : (equivalence₁ hF).counitIso = equivalence
 def equivalence₁UnitIso : 𝟭 A ≅ F ⋙ e'.inverse ⋙ eA.inverse :=
   calc
     𝟭 A ≅ eA.functor ⋙ eA.inverse := eA.unitIso
-    _ ≅ eA.functor ⋙ 𝟭 A' ⋙ eA.inverse := (Iso.refl _)
+    _ ≅ eA.functor ⋙ 𝟭 A' ⋙ eA.inverse := Iso.refl _
     _ ≅ eA.functor ⋙ (e'.functor ⋙ e'.inverse) ⋙ eA.inverse :=
-      (isoWhiskerLeft _ (isoWhiskerRight e'.unitIso _))
-    _ ≅ (eA.functor ⋙ e'.functor) ⋙ e'.inverse ⋙ eA.inverse := (Iso.refl _)
+      isoWhiskerLeft _ (isoWhiskerRight e'.unitIso _)
+    _ ≅ (eA.functor ⋙ e'.functor) ⋙ e'.inverse ⋙ eA.inverse := Iso.refl _
     _ ≅ F ⋙ e'.inverse ⋙ eA.inverse := isoWhiskerRight hF _
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_unit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₁UnitIso
 
@@ -132,8 +132,8 @@ def equivalence₂CounitIso : (eB.functor ⋙ e'.inverse ⋙ eA.inverse) ⋙ F 
         eB.functor ⋙ (e'.inverse ⋙ eA.inverse ⋙ F) ⋙ eB.inverse :=
       Iso.refl _
     _ ≅ eB.functor ⋙ 𝟭 _ ⋙ eB.inverse :=
-      (isoWhiskerLeft _ (isoWhiskerRight (equivalence₁CounitIso hF) _))
-    _ ≅ eB.functor ⋙ eB.inverse := (Iso.refl _)
+      isoWhiskerLeft _ (isoWhiskerRight (equivalence₁CounitIso hF) _)
+    _ ≅ eB.functor ⋙ eB.inverse := Iso.refl _
     _ ≅ 𝟭 B := eB.unitIso.symm
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso
 
@@ -150,9 +150,9 @@ theorem equivalence₂CounitIso_eq :
 def equivalence₂UnitIso : 𝟭 A ≅ (F ⋙ eB.inverse) ⋙ eB.functor ⋙ e'.inverse ⋙ eA.inverse :=
   calc
     𝟭 A ≅ F ⋙ e'.inverse ⋙ eA.inverse := equivalence₁UnitIso hF
-    _ ≅ F ⋙ 𝟭 B' ⋙ e'.inverse ⋙ eA.inverse := (Iso.refl _)
+    _ ≅ F ⋙ 𝟭 B' ⋙ e'.inverse ⋙ eA.inverse := Iso.refl _
     _ ≅ F ⋙ (eB.inverse ⋙ eB.functor) ⋙ e'.inverse ⋙ eA.inverse :=
-      (isoWhiskerLeft _ (isoWhiskerRight eB.counitIso.symm _))
+      isoWhiskerLeft _ (isoWhiskerRight eB.counitIso.symm _)
     _ ≅ (F ⋙ eB.inverse) ⋙ eB.functor ⋙ e'.inverse ⋙ eA.inverse := Iso.refl _
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_unit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₂UnitIso
 
@@ -174,8 +174,8 @@ def equivalence : A ≌ B :=
     refine' IsEquivalence.ofIso _ (IsEquivalence.ofEquivalence (equivalence₂ eB hF).symm)
     calc
       eB.functor ⋙ e'.inverse ⋙ eA.inverse ≅ (eB.functor ⋙ e'.inverse) ⋙ eA.inverse := Iso.refl _
-      _ ≅ (G ⋙ eA.functor) ⋙ eA.inverse := (isoWhiskerRight hG _)
-      _ ≅ G ⋙ 𝟭 A := (isoWhiskerLeft _ eA.unitIso.symm)
+      _ ≅ (G ⋙ eA.functor) ⋙ eA.inverse := isoWhiskerRight hG _
+      _ ≅ G ⋙ 𝟭 A := isoWhiskerLeft _ eA.unitIso.symm
       _ ≅ G := Functor.rightUnitor G
   G.asEquivalence.symm
 #align algebraic_topology.dold_kan.compatibility.equivalence AlgebraicTopology.DoldKan.Compatibility.equivalence
@@ -184,6 +184,104 @@ theorem equivalence_functor : (equivalence hF hG).functor = F ⋙ eB.inverse :=
   rfl
 #align algebraic_topology.dold_kan.compatibility.equivalence_functor AlgebraicTopology.DoldKan.Compatibility.equivalence_functor
 
+/-- The isomorphism `eB.functor ⋙ e'.inverse ⋙ e'.functor ≅ eB.functor` deduced
+from the counit isomorphism of `e'`. -/
+@[simps! hom_app]
+def τ₀ : eB.functor ⋙ e'.inverse ⋙ e'.functor ≅ eB.functor :=
+  calc
+    eB.functor ⋙ e'.inverse ⋙ e'.functor ≅ eB.functor ⋙ 𝟭 _ := isoWhiskerLeft _ e'.counitIso
+    _ ≅ eB.functor := Functor.rightUnitor _
+#align algebraic_topology.dold_kan.compatibility.τ₀ AlgebraicTopology.DoldKan.Compatibility.τ₀
+
+/-- The isomorphism `eB.functor ⋙ e'.inverse ⋙ e'.functor ≅ eB.functor` deduced
+from the isomorphisms `hF : eA.functor ⋙ e'.functor ≅ F`,
+`hG : eB.functor ⋙ e'.inverse ≅ G ⋙ eA.functor` and the datum of
+an isomorphism `η : G ⋙ F ≅ eB.functor`. -/
+@[simps! hom_app]
+def τ₁ (η : G ⋙ F ≅ eB.functor) : eB.functor ⋙ e'.inverse ⋙ e'.functor ≅ eB.functor :=
+  calc
+    eB.functor ⋙ e'.inverse ⋙ e'.functor ≅ (eB.functor ⋙ e'.inverse) ⋙ e'.functor :=
+        Iso.refl _
+    _ ≅ (G ⋙ eA.functor) ⋙ e'.functor := isoWhiskerRight hG _
+    _ ≅ G ⋙ eA.functor ⋙ e'.functor := by rfl
+    _ ≅ G ⋙ F := isoWhiskerLeft _ hF
+    _ ≅ eB.functor := η
+#align algebraic_topology.dold_kan.compatibility.τ₁ AlgebraicTopology.DoldKan.Compatibility.τ₁
+
+variable (η : G ⋙ F ≅ eB.functor) (hη : τ₀ = τ₁ hF hG η)
+
+/-- The counit isomorphism of `equivalence`. -/
+@[simps!]
+def equivalenceCounitIso : G ⋙ F ⋙ eB.inverse ≅ 𝟭 B :=
+  calc
+    G ⋙ F ⋙ eB.inverse ≅ (G ⋙ F) ⋙ eB.inverse := Iso.refl _
+    _ ≅ eB.functor ⋙ eB.inverse := isoWhiskerRight η _
+    _ ≅ 𝟭 B := eB.unitIso.symm
+#align algebraic_topology.dold_kan.compatibility.equivalence_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso
+
+variable {η hF hG}
+
+theorem equivalenceCounitIso_eq : (equivalence hF hG).counitIso = equivalenceCounitIso η := by
+  ext1; apply NatTrans.ext; ext Y
+  dsimp [equivalence, Functor.asEquivalence, IsEquivalence.ofEquivalence]
+  rw [equivalenceCounitIso_hom_app, IsEquivalence.ofIso_unitIso_inv_app]
+  dsimp
+  simp only [comp_id, id_comp, F.map_comp, assoc,
+    equivalence₂CounitIso_eq, equivalence₂CounitIso_hom_app,
+    ← eB.inverse.map_comp_assoc, ← τ₀_hom_app, hη, τ₁_hom_app]
+  erw [hF.inv.naturality_assoc, hF.inv.naturality_assoc]
+  dsimp
+  congr 2
+  simp only [assoc, ← e'.functor.map_comp_assoc, Equivalence.fun_inv_map,
+    Iso.inv_hom_id_app_assoc, hG.inv_hom_id_app]
+  dsimp
+  rw [comp_id, eA.functor_unitIso_comp, e'.functor.map_id, id_comp, hF.inv_hom_id_app_assoc]
+#align algebraic_topology.dold_kan.compatibility.equivalence_counit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalenceCounitIso_eq
+
+variable (hF)
+
+/-- The isomorphism `eA.functor ≅ F ⋙ e'.inverse` deduced from the
+unit isomorphism of `e'` and the isomorphism `hF : eA.functor ⋙ e'.functor ≅ F`. -/
+@[simps!]
+def υ : eA.functor ≅ F ⋙ e'.inverse :=
+  calc
+    eA.functor ≅ eA.functor ⋙ 𝟭 A' := (Functor.leftUnitor _).symm
+    _ ≅ eA.functor ⋙ e'.functor ⋙ e'.inverse := (isoWhiskerLeft _ e'.unitIso)
+    _ ≅ (eA.functor ⋙ e'.functor) ⋙ e'.inverse := Iso.refl _
+    _ ≅ F ⋙ e'.inverse := isoWhiskerRight hF _
+#align algebraic_topology.dold_kan.compatibility.υ AlgebraicTopology.DoldKan.Compatibility.υ
+
+variable (ε : eA.functor ≅ F ⋙ e'.inverse) (hε : υ hF = ε) (hG)
+
+/-- The unit isomorphism of `equivalence`. -/
+@[simps!]
+def equivalenceUnitIso : 𝟭 A ≅ (F ⋙ eB.inverse) ⋙ G :=
+  calc
+    𝟭 A ≅ eA.functor ⋙ eA.inverse := eA.unitIso
+    _ ≅ (F ⋙ e'.inverse) ⋙ eA.inverse := isoWhiskerRight ε _
+    _ ≅ F ⋙ 𝟭 B' ⋙ e'.inverse ⋙ eA.inverse := Iso.refl _
+    _ ≅ F ⋙ (eB.inverse ⋙ eB.functor) ⋙ e'.inverse ⋙ eA.inverse :=
+      isoWhiskerLeft _ (isoWhiskerRight eB.counitIso.symm _)
+    _ ≅ (F ⋙ eB.inverse) ⋙ (eB.functor ⋙ e'.inverse) ⋙ eA.inverse := Iso.refl _
+    _ ≅ (F ⋙ eB.inverse) ⋙ (G ⋙ eA.functor) ⋙ eA.inverse :=
+      isoWhiskerLeft _ (isoWhiskerRight hG _)
+    _ ≅ (F ⋙ eB.inverse ⋙ G) ⋙ eA.functor ⋙ eA.inverse := Iso.refl _
+    _ ≅ (F ⋙ eB.inverse ⋙ G) ⋙ 𝟭 A := isoWhiskerLeft _ eA.unitIso.symm
+    _ ≅ (F ⋙ eB.inverse) ⋙ G := Iso.refl _
+#align algebraic_topology.dold_kan.compatibility.equivalence_unit_iso AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso
+
+variable {ε hF hG}
+
+theorem equivalenceUnitIso_eq : (equivalence hF hG).unitIso = equivalenceUnitIso hG ε := by
+  ext1; apply NatTrans.ext; ext X
+  dsimp [equivalence, Functor.asEquivalence, IsEquivalence.ofEquivalence, IsEquivalence.inverse]
+  rw [IsEquivalence.ofIso_counitIso_inv_app]
+  dsimp
+  erw [id_comp, comp_id]
+  simp only [equivalence₂UnitIso_eq eB hF, equivalence₂UnitIso_hom_app,
+    assoc, equivalenceUnitIso_hom_app, ← eA.inverse.map_comp_assoc, ← hε, υ_hom_app]
+#align algebraic_topology.dold_kan.compatibility.equivalence_unit_iso_eq AlgebraicTopology.DoldKan.Compatibility.equivalenceUnitIso_eq
+
 end Compatibility
 
 end DoldKan

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 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
-
-! This file was ported from Lean 3 source module algebraic_topology.dold_kan.compatibility
-! leanprover-community/mathlib commit 160f568dcf772b2477791c844fc605f2f91f73d1
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Equivalence
 
+#align_import algebraic_topology.dold_kan.compatibility from "leanprover-community/mathlib"@"160f568dcf772b2477791c844fc605f2f91f73d1"
+
 /-! Tools for compatibilities between Dold-Kan equivalences
 
 The purpose of this file is to introduce tools which will enable the

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

@@ -140,8 +140,8 @@ def equivalence₂CounitIso : (eB.functor ⋙ e'.inverse ⋙ eA.inverse) ⋙ F 
     _ ≅ 𝟭 B := eB.unitIso.symm
 #align algebraic_topology.dold_kan.compatibility.equivalence₂_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₂CounitIso
 
-theorem equivalence₂CounitIso_eq : (equivalence₂ eB hF).counitIso = equivalence₂CounitIso eB hF :=
-  by
+theorem equivalence₂CounitIso_eq :
+    (equivalence₂ eB hF).counitIso = equivalence₂CounitIso eB hF := by
   ext Y'
   dsimp [equivalence₂, Iso.refl]
   simp only [equivalence₁CounitIso_eq, equivalence₂CounitIso_hom_app,

chore: fix #align lines (#3640)

This PR fixes two things:

Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

2b42dc7c

Diff

@@ -85,7 +85,6 @@ def equivalence₁CounitIso : (e'.inverse ⋙ eA.inverse) ⋙ F ≅ 𝟭 B' :=
     _ ≅ e'.inverse ⋙ 𝟭 _ ⋙ e'.functor := (isoWhiskerLeft _ (isoWhiskerRight eA.counitIso _))
     _ ≅ e'.inverse ⋙ e'.functor := (Iso.refl _)
     _ ≅ 𝟭 B' := e'.counitIso
-
 #align algebraic_topology.dold_kan.compatibility.equivalence₁_counit_iso AlgebraicTopology.DoldKan.Compatibility.equivalence₁CounitIso
 
 theorem equivalence₁CounitIso_eq : (equivalence₁ hF).counitIso = equivalence₁CounitIso hF := by