algebraic_topology.dold_kan.equivalence ⟷ Mathlib.AlgebraicTopology.DoldKan.Equivalence

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

@@ -3,8 +3,8 @@ 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.AlgebraicTopology.DoldKan.EquivalencePseudoabelian
-import Mathbin.AlgebraicTopology.DoldKan.Normalized
+import AlgebraicTopology.DoldKan.EquivalencePseudoabelian
+import AlgebraicTopology.DoldKan.Normalized
 
 #align_import algebraic_topology.dold_kan.equivalence from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 

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

@@ -140,30 +140,37 @@ namespace DoldKan
 
 open AlgebraicTopology.DoldKan
 
+#print CategoryTheory.Abelian.DoldKan.N /-
 /-- The functor `N` for the equivalence is `normalized_Moore_complex A` -/
-def n : SimplicialObject A ⥤ ChainComplex A ℕ :=
+def N : SimplicialObject A ⥤ ChainComplex A ℕ :=
   AlgebraicTopology.normalizedMooreComplex A
-#align category_theory.abelian.dold_kan.N CategoryTheory.Abelian.DoldKan.n
+#align category_theory.abelian.dold_kan.N CategoryTheory.Abelian.DoldKan.N
+-/
 
+#print CategoryTheory.Abelian.DoldKan.Γ /-
 /-- The functor `Γ` for the equivalence is the same as in the pseudoabelian case. -/
 def Γ : ChainComplex A ℕ ⥤ SimplicialObject A :=
   Idempotents.DoldKan.Γ
 #align category_theory.abelian.dold_kan.Γ CategoryTheory.Abelian.DoldKan.Γ
+-/
 
+#print CategoryTheory.Abelian.DoldKan.comparisonN /-
 /-- The comparison isomorphism between `normalized_Moore_complex A` and
 the functor `idempotents.dold_kan.N` from the pseudoabelian case -/
 @[simps]
-def comparisonN : (n : SimplicialObject A ⥤ _) ≅ Idempotents.DoldKan.N :=
+def comparisonN : (N : SimplicialObject A ⥤ _) ≅ Idempotents.DoldKan.N :=
   calc
-    n ≅ n ⋙ 𝟭 _ := Functor.leftUnitor n
-    _ ≅ n ⋙ (toKaroubi_equivalence _).Functor ⋙ (toKaroubi_equivalence _).inverse :=
-      (isoWhiskerLeft _ (toKaroubi_equivalence _).unitIso)
-    _ ≅ (n ⋙ (toKaroubi_equivalence _).Functor) ⋙ (toKaroubi_equivalence _).inverse := (Iso.refl _)
-    _ ≅ N₁ ⋙ (toKaroubi_equivalence _).inverse :=
+    N ≅ N ⋙ 𝟭 _ := Functor.leftUnitor N
+    _ ≅ N ⋙ (toKaroubiEquivalence _).Functor ⋙ (toKaroubiEquivalence _).inverse :=
+      (isoWhiskerLeft _ (toKaroubiEquivalence _).unitIso)
+    _ ≅ (N ⋙ (toKaroubiEquivalence _).Functor) ⋙ (toKaroubiEquivalence _).inverse := (Iso.refl _)
+    _ ≅ N₁ ⋙ (toKaroubiEquivalence _).inverse :=
       (isoWhiskerRight (N₁_iso_normalizedMooreComplex_comp_toKaroubi A).symm _)
     _ ≅ Idempotents.DoldKan.N := by rfl
 #align category_theory.abelian.dold_kan.comparison_N CategoryTheory.Abelian.DoldKan.comparisonN
+-/
 
+#print CategoryTheory.Abelian.DoldKan.equivalence /-
 /-- The Dold-Kan equivalence for abelian categories -/
 @[simps Functor]
 def equivalence : SimplicialObject A ≌ ChainComplex A ℕ :=
@@ -173,10 +180,13 @@ def equivalence : SimplicialObject A ≌ ChainComplex A ℕ :=
   letI : is_equivalence (N : simplicial_object A ⥤ _) := is_equivalence.of_iso comparison_N.symm hF
   exact N.as_equivalence
 #align category_theory.abelian.dold_kan.equivalence CategoryTheory.Abelian.DoldKan.equivalence
+-/
 
+#print CategoryTheory.Abelian.DoldKan.equivalence_inverse /-
 theorem equivalence_inverse : (equivalence : SimplicialObject A ≌ _).inverse = Γ :=
   rfl
 #align category_theory.abelian.dold_kan.equivalence_inverse CategoryTheory.Abelian.DoldKan.equivalence_inverse
+-/
 
 end DoldKan
 

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

@@ -153,7 +153,7 @@ def Γ : ChainComplex A ℕ ⥤ SimplicialObject A :=
 /-- The comparison isomorphism between `normalized_Moore_complex A` and
 the functor `idempotents.dold_kan.N` from the pseudoabelian case -/
 @[simps]
-def comparisonN : (n : SimplicialObject A ⥤ _) ≅ Idempotents.DoldKan.n :=
+def comparisonN : (n : SimplicialObject A ⥤ _) ≅ Idempotents.DoldKan.N :=
   calc
     n ≅ n ⋙ 𝟭 _ := Functor.leftUnitor n
     _ ≅ n ⋙ (toKaroubi_equivalence _).Functor ⋙ (toKaroubi_equivalence _).inverse :=
@@ -161,7 +161,7 @@ def comparisonN : (n : SimplicialObject A ⥤ _) ≅ Idempotents.DoldKan.n :=
     _ ≅ (n ⋙ (toKaroubi_equivalence _).Functor) ⋙ (toKaroubi_equivalence _).inverse := (Iso.refl _)
     _ ≅ N₁ ⋙ (toKaroubi_equivalence _).inverse :=
       (isoWhiskerRight (N₁_iso_normalizedMooreComplex_comp_toKaroubi A).symm _)
-    _ ≅ Idempotents.DoldKan.n := by rfl
+    _ ≅ Idempotents.DoldKan.N := by rfl
 #align category_theory.abelian.dold_kan.comparison_N CategoryTheory.Abelian.DoldKan.comparisonN
 
 /-- The Dold-Kan equivalence for abelian categories -/

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

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

@@ -167,8 +167,9 @@ set_option linter.uppercaseLean3 false in
 @[simps! functor]
 def equivalence : SimplicialObject A ≌ ChainComplex A ℕ := by
   let F : SimplicialObject A ⥤ _ := Idempotents.DoldKan.N
-  let hF : IsEquivalence F := IsEquivalence.ofEquivalence Idempotents.DoldKan.equivalence
-  letI : IsEquivalence (N : SimplicialObject A ⥤ _) := IsEquivalence.ofIso comparisonN.symm hF
+  let hF : F.IsEquivalence := Functor.IsEquivalence.ofEquivalence Idempotents.DoldKan.equivalence
+  letI : (N : SimplicialObject A ⥤ _).IsEquivalence :=
+    Functor.IsEquivalence.ofIso comparisonN.symm hF
   exact N.asEquivalence
 #align category_theory.abelian.dold_kan.equivalence CategoryTheory.Abelian.DoldKan.equivalence
 

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>