algebraic_topology.dold_kan.normalized ⟷ Mathlib.AlgebraicTopology.DoldKan.Normalized

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

@@ -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.AlgebraicTopology.DoldKan.FunctorN
+import AlgebraicTopology.DoldKan.FunctorN
 
 #align_import algebraic_topology.dold_kan.normalized from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 

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

@@ -5,7 +5,7 @@ Authors: Joël Riou
 -/
 import Mathbin.AlgebraicTopology.DoldKan.FunctorN
 
-#align_import algebraic_topology.dold_kan.normalized from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+#align_import algebraic_topology.dold_kan.normalized from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 
 /-!
 
@@ -28,6 +28,8 @@ the Dold-Kan equivalence
 `category_theory.abelian.dold_kan.equivalence : simplicial_object A ≌ chain_complex A ℕ`
 with a functor (definitionally) equal to `normalized_Moore_complex A`.
 
+(See `equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
+
 -/
 
 

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

@@ -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.normalized
-! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicTopology.DoldKan.FunctorN
 
+#align_import algebraic_topology.dold_kan.normalized from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+
 /-!
 
 # Comparison with the normalized Moore complex functor

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

@@ -49,6 +49,7 @@ universe v
 
 variable {A : Type _} [Category A] [Abelian A] {X : SimplicialObject A}
 
+#print AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMap /-
 theorem HigherFacesVanish.inclusionOfMooreComplexMap (n : ℕ) :
     HigherFacesVanish (n + 1) ((inclusionOfMooreComplexMap X).f (n + 1)) := fun j hj =>
   by
@@ -58,7 +59,9 @@ theorem HigherFacesVanish.inclusionOfMooreComplexMap (n : ℕ) :
       (finset_inf_arrow_factors Finset.univ _ j (by simp only [Finset.mem_univ])),
     assoc, kernel_subobject_arrow_comp, comp_zero]
 #align algebraic_topology.dold_kan.higher_faces_vanish.inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMap
+-/
 
+#print AlgebraicTopology.DoldKan.factors_normalizedMooreComplex_PInfty /-
 theorem factors_normalizedMooreComplex_PInfty (n : ℕ) :
     Subobject.Factors (NormalizedMooreComplex.objX X n) (PInfty.f n) :=
   by
@@ -69,6 +72,7 @@ theorem factors_normalizedMooreComplex_PInfty (n : ℕ) :
     apply kernel_subobject_factors
     exact (higher_faces_vanish.of_P (n + 1) n) i le_add_self
 #align algebraic_topology.dold_kan.factors_normalized_Moore_complex_P_infty AlgebraicTopology.DoldKan.factors_normalizedMooreComplex_PInfty
+-/
 
 #print AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex /-
 /-- P_infty factors through the normalized Moore complex -/
@@ -85,10 +89,12 @@ def PInftyToNormalizedMooreComplex (X : SimplicialObject A) : K[X] ⟶ N[X] :=
 #align algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex
 -/
 
+#print AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap /-
 @[simp, reassoc]
 theorem PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap (X : SimplicialObject A) :
     PInftyToNormalizedMooreComplex X ≫ inclusionOfMooreComplexMap X = PInfty := by tidy
 #align algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex_comp_inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap
+-/
 
 #print AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_naturality /-
 @[simp, reassoc]
@@ -106,6 +112,7 @@ theorem PInfty_comp_PInftyToNormalizedMooreComplex (X : SimplicialObject A) :
 #align algebraic_topology.dold_kan.P_infty_comp_P_infty_to_normalized_Moore_complex AlgebraicTopology.DoldKan.PInfty_comp_PInftyToNormalizedMooreComplex
 -/
 
+#print AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty /-
 @[simp, reassoc]
 theorem inclusionOfMooreComplexMap_comp_PInfty (X : SimplicialObject A) :
     inclusionOfMooreComplexMap X ≫ PInfty = inclusionOfMooreComplexMap X :=
@@ -115,10 +122,12 @@ theorem inclusionOfMooreComplexMap_comp_PInfty (X : SimplicialObject A) :
   · dsimp; simp only [comp_id]
   · exact (higher_faces_vanish.inclusion_of_Moore_complex_map n).comp_P_eq_self
 #align algebraic_topology.dold_kan.inclusion_of_Moore_complex_map_comp_P_infty AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty
+-/
 
 instance : Mono (inclusionOfMooreComplexMap X) :=
   ⟨fun Y f₁ f₂ hf => by ext n; exact HomologicalComplex.congr_hom hf n⟩
 
+#print AlgebraicTopology.DoldKan.splitMonoInclusionOfMooreComplexMap /-
 /-- `inclusion_of_Moore_complex_map X` is a split mono. -/
 def splitMonoInclusionOfMooreComplexMap (X : SimplicialObject A) :
     SplitMono (inclusionOfMooreComplexMap X)
@@ -129,9 +138,11 @@ def splitMonoInclusionOfMooreComplexMap (X : SimplicialObject A) :
       P_infty_to_normalized_Moore_complex_comp_inclusion_of_Moore_complex_map,
       inclusion_of_Moore_complex_map_comp_P_infty]
 #align algebraic_topology.dold_kan.split_mono_inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.splitMonoInclusionOfMooreComplexMap
+-/
 
 variable (A)
 
+#print AlgebraicTopology.DoldKan.N₁_iso_normalizedMooreComplex_comp_toKaroubi /-
 /-- When the category `A` is abelian,
 the functor `N₁ : simplicial_object A ⥤ karoubi (chain_complex A ℕ)` defined
 using `P_infty` identifies to the composition of the normalized Moore complex functor
@@ -168,6 +179,7 @@ def N₁_iso_normalizedMooreComplex_comp_toKaroubi : N₁ ≅ normalizedMooreCom
     dsimp only [functor.comp_obj, to_karoubi]
     rw [id_comp]
 #align algebraic_topology.dold_kan.N₁_iso_normalized_Moore_complex_comp_to_karoubi AlgebraicTopology.DoldKan.N₁_iso_normalizedMooreComplex_comp_toKaroubi
+-/
 
 end DoldKan
 

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

@@ -34,8 +34,8 @@ with a functor (definitionally) equal to `normalized_Moore_complex A`.
 -/
 
 
-open
-  CategoryTheory CategoryTheory.Category CategoryTheory.Limits CategoryTheory.Subobject CategoryTheory.Idempotents
+open CategoryTheory CategoryTheory.Category CategoryTheory.Limits CategoryTheory.Subobject
+  CategoryTheory.Idempotents
 
 open scoped DoldKan
 

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

@@ -37,7 +37,7 @@ with a functor (definitionally) equal to `normalized_Moore_complex A`.
 open
   CategoryTheory CategoryTheory.Category CategoryTheory.Limits CategoryTheory.Subobject CategoryTheory.Idempotents
 
-open DoldKan
+open scoped DoldKan
 
 noncomputable section
 

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

@@ -49,9 +49,6 @@ universe v
 
 variable {A : Type _} [Category A] [Abelian A] {X : SimplicialObject A}
 
-/- warning: algebraic_topology.dold_kan.higher_faces_vanish.inclusion_of_Moore_complex_map -> AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMapₓ'. -/
 theorem HigherFacesVanish.inclusionOfMooreComplexMap (n : ℕ) :
     HigherFacesVanish (n + 1) ((inclusionOfMooreComplexMap X).f (n + 1)) := fun j hj =>
   by
@@ -62,12 +59,6 @@ theorem HigherFacesVanish.inclusionOfMooreComplexMap (n : ℕ) :
     assoc, kernel_subobject_arrow_comp, comp_zero]
 #align algebraic_topology.dold_kan.higher_faces_vanish.inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMap
 
-/- warning: algebraic_topology.dold_kan.factors_normalized_Moore_complex_P_infty -> AlgebraicTopology.DoldKan.factors_normalizedMooreComplex_PInfty 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 algebraic_topology.dold_kan.factors_normalized_Moore_complex_P_infty AlgebraicTopology.DoldKan.factors_normalizedMooreComplex_PInftyₓ'. -/
 theorem factors_normalizedMooreComplex_PInfty (n : ℕ) :
     Subobject.Factors (NormalizedMooreComplex.objX X n) (PInfty.f n) :=
   by
@@ -94,9 +85,6 @@ def PInftyToNormalizedMooreComplex (X : SimplicialObject A) : K[X] ⟶ N[X] :=
 #align algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex
 -/
 
-/- warning: algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex_comp_inclusion_of_Moore_complex_map -> AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex_comp_inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMapₓ'. -/
 @[simp, reassoc]
 theorem PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap (X : SimplicialObject A) :
     PInftyToNormalizedMooreComplex X ≫ inclusionOfMooreComplexMap X = PInfty := by tidy
@@ -118,9 +106,6 @@ theorem PInfty_comp_PInftyToNormalizedMooreComplex (X : SimplicialObject A) :
 #align algebraic_topology.dold_kan.P_infty_comp_P_infty_to_normalized_Moore_complex AlgebraicTopology.DoldKan.PInfty_comp_PInftyToNormalizedMooreComplex
 -/
 
-/- warning: algebraic_topology.dold_kan.inclusion_of_Moore_complex_map_comp_P_infty -> AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.inclusion_of_Moore_complex_map_comp_P_infty AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInftyₓ'. -/
 @[simp, reassoc]
 theorem inclusionOfMooreComplexMap_comp_PInfty (X : SimplicialObject A) :
     inclusionOfMooreComplexMap X ≫ PInfty = inclusionOfMooreComplexMap X :=
@@ -134,9 +119,6 @@ theorem inclusionOfMooreComplexMap_comp_PInfty (X : SimplicialObject A) :
 instance : Mono (inclusionOfMooreComplexMap X) :=
   ⟨fun Y f₁ f₂ hf => by ext n; exact HomologicalComplex.congr_hom hf n⟩
 
-/- warning: algebraic_topology.dold_kan.split_mono_inclusion_of_Moore_complex_map -> AlgebraicTopology.DoldKan.splitMonoInclusionOfMooreComplexMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.split_mono_inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.splitMonoInclusionOfMooreComplexMapₓ'. -/
 /-- `inclusion_of_Moore_complex_map X` is a split mono. -/
 def splitMonoInclusionOfMooreComplexMap (X : SimplicialObject A) :
     SplitMono (inclusionOfMooreComplexMap X)
@@ -150,9 +132,6 @@ def splitMonoInclusionOfMooreComplexMap (X : SimplicialObject A) :
 
 variable (A)
 
-/- warning: algebraic_topology.dold_kan.N₁_iso_normalized_Moore_complex_comp_to_karoubi -> AlgebraicTopology.DoldKan.N₁_iso_normalizedMooreComplex_comp_toKaroubi is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.N₁_iso_normalized_Moore_complex_comp_to_karoubi AlgebraicTopology.DoldKan.N₁_iso_normalizedMooreComplex_comp_toKaroubiₓ'. -/
 /-- When the category `A` is abelian,
 the functor `N₁ : simplicial_object A ⥤ karoubi (chain_complex A ℕ)` defined
 using `P_infty` identifies to the composition of the normalized Moore complex functor

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

@@ -127,15 +127,12 @@ theorem inclusionOfMooreComplexMap_comp_PInfty (X : SimplicialObject A) :
   by
   ext n
   cases n
-  · dsimp
-    simp only [comp_id]
+  · dsimp; simp only [comp_id]
   · exact (higher_faces_vanish.inclusion_of_Moore_complex_map n).comp_P_eq_self
 #align algebraic_topology.dold_kan.inclusion_of_Moore_complex_map_comp_P_infty AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty
 
 instance : Mono (inclusionOfMooreComplexMap X) :=
-  ⟨fun Y f₁ f₂ hf => by
-    ext n
-    exact HomologicalComplex.congr_hom hf n⟩
+  ⟨fun Y f₁ f₂ hf => by ext n; exact HomologicalComplex.congr_hom hf n⟩
 
 /- warning: algebraic_topology.dold_kan.split_mono_inclusion_of_Moore_complex_map -> AlgebraicTopology.DoldKan.splitMonoInclusionOfMooreComplexMap is a dubious translation:
 <too large>
@@ -174,8 +171,7 @@ def N₁_iso_normalizedMooreComplex_comp_toKaroubi : N₁ ≅ normalizedMooreCom
     { app := fun X =>
         { f := inclusionOfMooreComplexMap X
           comm := by erw [inclusion_of_Moore_complex_map_comp_P_infty, id_comp] }
-      naturality' := fun X Y f => by
-        ext
+      naturality' := fun X Y f => by ext;
         simp only [functor.comp_map, normalized_Moore_complex_map, karoubi.comp_f, to_karoubi_map_f,
           HomologicalComplex.comp_f, normalized_Moore_complex.map_f,
           inclusion_of_Moore_complex_map_f, factor_thru_arrow, N₁_map_f,

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

@@ -50,10 +50,7 @@ universe v
 variable {A : Type _} [Category A] [Abelian A] {X : SimplicialObject A}
 
 /- warning: algebraic_topology.dold_kan.higher_faces_vanish.inclusion_of_Moore_complex_map -> AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMap is a dubious translation:
-lean 3 declaration is
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(AlgebraicTopology.inclusionOfMooreComplexMap.{u2, u1} A _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMapₓ'. -/
 theorem HigherFacesVanish.inclusionOfMooreComplexMap (n : ℕ) :
     HigherFacesVanish (n + 1) ((inclusionOfMooreComplexMap X).f (n + 1)) := fun j hj =>
@@ -98,10 +95,7 @@ def PInftyToNormalizedMooreComplex (X : SimplicialObject A) : K[X] ⟶ N[X] :=
 -/
 
 /- warning: algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex_comp_inclusion_of_Moore_complex_map -> AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap is a dubious translation:
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(AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex.{u1, u2} A _inst_1 _inst_2 X) (AlgebraicTopology.inclusionOfMooreComplexMap.{u1, u2} A _inst_1 _inst_2 X)) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2) X)
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex_comp_inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMapₓ'. -/
 @[simp, reassoc]
 theorem PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap (X : SimplicialObject A) :
@@ -125,10 +119,7 @@ theorem PInfty_comp_PInftyToNormalizedMooreComplex (X : SimplicialObject A) :
 -/
 
 /- warning: algebraic_topology.dold_kan.inclusion_of_Moore_complex_map_comp_P_infty -> AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.inclusion_of_Moore_complex_map_comp_P_infty AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInftyₓ'. -/
 @[simp, reassoc]
 theorem inclusionOfMooreComplexMap_comp_PInfty (X : SimplicialObject A) :
@@ -147,10 +138,7 @@ instance : Mono (inclusionOfMooreComplexMap X) :=
     exact HomologicalComplex.congr_hom hf n⟩
 
 /- warning: algebraic_topology.dold_kan.split_mono_inclusion_of_Moore_complex_map -> AlgebraicTopology.DoldKan.splitMonoInclusionOfMooreComplexMap is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.split_mono_inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.splitMonoInclusionOfMooreComplexMapₓ'. -/
 /-- `inclusion_of_Moore_complex_map X` is a split mono. -/
 def splitMonoInclusionOfMooreComplexMap (X : SimplicialObject A) :
@@ -166,10 +154,7 @@ def splitMonoInclusionOfMooreComplexMap (X : SimplicialObject A) :
 variable (A)
 
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_inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (AlgebraicTopology.normalizedMooreComplex.{u1, u2} A _inst_1 _inst_2) (CategoryTheory.Idempotents.toKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.N₁_iso_normalized_Moore_complex_comp_to_karoubi AlgebraicTopology.DoldKan.N₁_iso_normalizedMooreComplex_comp_toKaroubiₓ'. -/
 /-- When the category `A` is abelian,
 the functor `N₁ : simplicial_object A ⥤ karoubi (chain_complex A ℕ)` defined

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

@@ -103,13 +103,13 @@ lean 3 declaration is
 but is expected to have type
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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (AlgebraicTopology.alternatingFaceMapComplex.{u1, u2} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2))) X) (AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex.{u1, u2} A _inst_1 _inst_2 X) (AlgebraicTopology.inclusionOfMooreComplexMap.{u1, u2} A _inst_1 _inst_2 X)) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2) X)
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex_comp_inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMapₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap (X : SimplicialObject A) :
     PInftyToNormalizedMooreComplex X ≫ inclusionOfMooreComplexMap X = PInfty := by tidy
 #align algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex_comp_inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap
 
 #print AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_naturality /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem PInftyToNormalizedMooreComplex_naturality {X Y : SimplicialObject A} (f : X ⟶ Y) :
     AlternatingFaceMapComplex.map f ≫ PInftyToNormalizedMooreComplex Y =
       PInftyToNormalizedMooreComplex X ≫ NormalizedMooreComplex.map f :=
@@ -118,7 +118,7 @@ theorem PInftyToNormalizedMooreComplex_naturality {X Y : SimplicialObject A} (f
 -/
 
 #print AlgebraicTopology.DoldKan.PInfty_comp_PInftyToNormalizedMooreComplex /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem PInfty_comp_PInftyToNormalizedMooreComplex (X : SimplicialObject A) :
     PInfty ≫ PInftyToNormalizedMooreComplex X = PInftyToNormalizedMooreComplex X := by tidy
 #align algebraic_topology.dold_kan.P_infty_comp_P_infty_to_normalized_Moore_complex AlgebraicTopology.DoldKan.PInfty_comp_PInftyToNormalizedMooreComplex
@@ -130,7 +130,7 @@ lean 3 declaration is
 but is expected to have type
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(OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (AlgebraicTopology.alternatingFaceMapComplex.{u1, u2} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2))) X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2) X) (AlgebraicTopology.inclusionOfMooreComplexMap.{u1, u2} A _inst_1 _inst_2 X) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2) X)) (AlgebraicTopology.inclusionOfMooreComplexMap.{u1, u2} A _inst_1 _inst_2 X)
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.inclusion_of_Moore_complex_map_comp_P_infty AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInftyₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem inclusionOfMooreComplexMap_comp_PInfty (X : SimplicialObject A) :
     inclusionOfMooreComplexMap X ≫ PInfty = inclusionOfMooreComplexMap X :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780

@@ -4,7 +4,7 @@ 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.normalized
-! leanprover-community/mathlib commit d1d69e99ed34c95266668af4e288fc1c598b9a7f
+! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.AlgebraicTopology.DoldKan.FunctorN
 
 # Comparison with the normalized Moore complex functor
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 TODO (@joelriou) continue adding the various files referenced below
 
 In this file, we show that when the category `A` is abelian,

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -46,6 +46,12 @@ universe v
 
 variable {A : Type _} [Category A] [Abelian A] {X : SimplicialObject A}
 
+/- warning: algebraic_topology.dold_kan.higher_faces_vanish.inclusion_of_Moore_complex_map -> AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMap is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(AlgebraicTopology.inclusionOfMooreComplexMap.{u2, u1} A _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMapₓ'. -/
 theorem HigherFacesVanish.inclusionOfMooreComplexMap (n : ℕ) :
     HigherFacesVanish (n + 1) ((inclusionOfMooreComplexMap X).f (n + 1)) := fun j hj =>
   by
@@ -56,7 +62,13 @@ theorem HigherFacesVanish.inclusionOfMooreComplexMap (n : ℕ) :
     assoc, kernel_subobject_arrow_comp, comp_zero]
 #align algebraic_topology.dold_kan.higher_faces_vanish.inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMap
 
-theorem factors_normalized_Moore_complex_pInfty (n : ℕ) :
+/- warning: algebraic_topology.dold_kan.factors_normalized_Moore_complex_P_infty -> AlgebraicTopology.DoldKan.factors_normalizedMooreComplex_PInfty 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 algebraic_topology.dold_kan.factors_normalized_Moore_complex_P_infty AlgebraicTopology.DoldKan.factors_normalizedMooreComplex_PInftyₓ'. -/
+theorem factors_normalizedMooreComplex_PInfty (n : ℕ) :
     Subobject.Factors (NormalizedMooreComplex.objX X n) (PInfty.f n) :=
   by
   cases n
@@ -65,40 +77,58 @@ theorem factors_normalized_Moore_complex_pInfty (n : ℕ) :
     intro i hi
     apply kernel_subobject_factors
     exact (higher_faces_vanish.of_P (n + 1) n) i le_add_self
-#align algebraic_topology.dold_kan.factors_normalized_Moore_complex_P_infty AlgebraicTopology.DoldKan.factors_normalized_Moore_complex_pInfty
+#align algebraic_topology.dold_kan.factors_normalized_Moore_complex_P_infty AlgebraicTopology.DoldKan.factors_normalizedMooreComplex_PInfty
 
+#print AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex /-
 /-- P_infty factors through the normalized Moore complex -/
 @[simps]
-def pInftyToNormalizedMooreComplex (X : SimplicialObject A) : K[X] ⟶ N[X] :=
-  ChainComplex.ofHom _ _ _ _ _ _
-    (fun n => factorThru _ _ (factors_normalized_Moore_complex_pInfty n)) fun n =>
+def PInftyToNormalizedMooreComplex (X : SimplicialObject A) : K[X] ⟶ N[X] :=
+  ChainComplex.ofHom _ _ _ _ _ _ (fun n => factorThru _ _ (factors_normalizedMooreComplex_PInfty n))
+    fun n =>
     by
     rw [← cancel_mono (normalized_Moore_complex.obj_X X n).arrow, assoc, assoc, factor_thru_arrow, ←
       inclusion_of_Moore_complex_map_f, ← normalized_Moore_complex_obj_d, ←
       (inclusion_of_Moore_complex_map X).comm' (n + 1) n rfl, inclusion_of_Moore_complex_map_f,
       factor_thru_arrow_assoc, ← alternating_face_map_complex_obj_d]
     exact P_infty.comm' (n + 1) n rfl
-#align algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex AlgebraicTopology.DoldKan.pInftyToNormalizedMooreComplex
+#align algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex
+-/
 
+/- warning: algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex_comp_inclusion_of_Moore_complex_map -> AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex_comp_inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMapₓ'. -/
 @[simp, reassoc.1]
-theorem pInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap (X : SimplicialObject A) :
-    pInftyToNormalizedMooreComplex X ≫ inclusionOfMooreComplexMap X = PInfty := by tidy
-#align algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex_comp_inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.pInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap
+theorem PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap (X : SimplicialObject A) :
+    PInftyToNormalizedMooreComplex X ≫ inclusionOfMooreComplexMap X = PInfty := by tidy
+#align algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex_comp_inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap
 
+#print AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_naturality /-
 @[simp, reassoc.1]
-theorem pInftyToNormalizedMooreComplex_naturality {X Y : SimplicialObject A} (f : X ⟶ Y) :
-    AlternatingFaceMapComplex.map f ≫ pInftyToNormalizedMooreComplex Y =
-      pInftyToNormalizedMooreComplex X ≫ NormalizedMooreComplex.map f :=
+theorem PInftyToNormalizedMooreComplex_naturality {X Y : SimplicialObject A} (f : X ⟶ Y) :
+    AlternatingFaceMapComplex.map f ≫ PInftyToNormalizedMooreComplex Y =
+      PInftyToNormalizedMooreComplex X ≫ NormalizedMooreComplex.map f :=
   by tidy
-#align algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex_naturality AlgebraicTopology.DoldKan.pInftyToNormalizedMooreComplex_naturality
+#align algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex_naturality AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex_naturality
+-/
 
+#print AlgebraicTopology.DoldKan.PInfty_comp_PInftyToNormalizedMooreComplex /-
 @[simp, reassoc.1]
-theorem pInfty_comp_pInftyToNormalizedMooreComplex (X : SimplicialObject A) :
-    PInfty ≫ pInftyToNormalizedMooreComplex X = pInftyToNormalizedMooreComplex X := by tidy
-#align algebraic_topology.dold_kan.P_infty_comp_P_infty_to_normalized_Moore_complex AlgebraicTopology.DoldKan.pInfty_comp_pInftyToNormalizedMooreComplex
+theorem PInfty_comp_PInftyToNormalizedMooreComplex (X : SimplicialObject A) :
+    PInfty ≫ PInftyToNormalizedMooreComplex X = PInftyToNormalizedMooreComplex X := by tidy
+#align algebraic_topology.dold_kan.P_infty_comp_P_infty_to_normalized_Moore_complex AlgebraicTopology.DoldKan.PInfty_comp_PInftyToNormalizedMooreComplex
+-/
 
+/- warning: algebraic_topology.dold_kan.inclusion_of_Moore_complex_map_comp_P_infty -> AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} A] [_inst_2 : CategoryTheory.Abelian.{u2, u1} A _inst_1] (X : CategoryTheory.SimplicialObject.{u2, u1} A _inst_1), Eq.{succ u2} (Quiver.Hom.{succ u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) (CategoryTheory.Functor.obj.{u2, u2, max u2 u1, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} A _inst_1) (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (AlgebraicTopology.normalizedMooreComplex.{u1, u2} A _inst_1 _inst_2) X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2) X)) (CategoryTheory.CategoryStruct.comp.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne))) (CategoryTheory.Functor.obj.{u2, u2, max u2 u1, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} A _inst_1) (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (AlgebraicTopology.normalizedMooreComplex.{u1, u2} A _inst_1 _inst_2) X) (CategoryTheory.Functor.obj.{u2, u2, max u2 u1, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} A _inst_1) (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (AlgebraicTopology.alternatingFaceMapComplex.{u1, u2} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2) X) (AlgebraicTopology.inclusionOfMooreComplexMap.{u1, u2} A _inst_1 _inst_2 X) (AlgebraicTopology.DoldKan.PInfty.{u1, u2} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2) X)) (AlgebraicTopology.inclusionOfMooreComplexMap.{u1, u2} A _inst_1 _inst_2 X)
+but is expected to have type
+  forall {A : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} A] [_inst_2 : CategoryTheory.Abelian.{u2, u1} A _inst_1] (X : CategoryTheory.SimplicialObject.{u2, u1} A _inst_1), Eq.{succ u2} (Quiver.Hom.{succ u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u2, succ u2, max u1 u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} A _inst_1))) (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, max u1 u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} A _inst_1) (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (AlgebraicTopology.normalizedMooreComplex.{u1, u2} A _inst_1 _inst_2)) X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2) X)) (CategoryTheory.CategoryStruct.comp.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (Prefunctor.obj.{succ u2, succ u2, max u1 u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} A _inst_1))) (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.inclusion_of_Moore_complex_map_comp_P_infty AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInftyₓ'. -/
 @[simp, reassoc.1]
-theorem inclusionOfMooreComplexMap_comp_pInfty (X : SimplicialObject A) :
+theorem inclusionOfMooreComplexMap_comp_PInfty (X : SimplicialObject A) :
     inclusionOfMooreComplexMap X ≫ PInfty = inclusionOfMooreComplexMap X :=
   by
   ext n
@@ -106,18 +136,24 @@ theorem inclusionOfMooreComplexMap_comp_pInfty (X : SimplicialObject A) :
   · dsimp
     simp only [comp_id]
   · exact (higher_faces_vanish.inclusion_of_Moore_complex_map n).comp_P_eq_self
-#align algebraic_topology.dold_kan.inclusion_of_Moore_complex_map_comp_P_infty AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_pInfty
+#align algebraic_topology.dold_kan.inclusion_of_Moore_complex_map_comp_P_infty AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_PInfty
 
 instance : Mono (inclusionOfMooreComplexMap X) :=
   ⟨fun Y f₁ f₂ hf => by
     ext n
     exact HomologicalComplex.congr_hom hf n⟩
 
+/- warning: algebraic_topology.dold_kan.split_mono_inclusion_of_Moore_complex_map -> AlgebraicTopology.DoldKan.splitMonoInclusionOfMooreComplexMap is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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(CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (AlgebraicTopology.alternatingFaceMapComplex.{u1, u2} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2))) X) (AlgebraicTopology.inclusionOfMooreComplexMap.{u1, u2} A _inst_1 _inst_2 X)
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.split_mono_inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.splitMonoInclusionOfMooreComplexMapₓ'. -/
 /-- `inclusion_of_Moore_complex_map X` is a split mono. -/
 def splitMonoInclusionOfMooreComplexMap (X : SimplicialObject A) :
     SplitMono (inclusionOfMooreComplexMap X)
     where
-  retraction := pInftyToNormalizedMooreComplex X
+  retraction := PInftyToNormalizedMooreComplex X
   id' := by
     simp only [← cancel_mono (inclusion_of_Moore_complex_map X), assoc, id_comp,
       P_infty_to_normalized_Moore_complex_comp_inclusion_of_Moore_complex_map,
@@ -126,15 +162,21 @@ def splitMonoInclusionOfMooreComplexMap (X : SimplicialObject A) :
 
 variable (A)
 
+/- warning: algebraic_topology.dold_kan.N₁_iso_normalized_Moore_complex_comp_to_karoubi -> AlgebraicTopology.DoldKan.N₁_iso_normalizedMooreComplex_comp_toKaroubi is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall (A : Type.{u1}) [_inst_1 : CategoryTheory.Category.{u2, u1} A] [_inst_2 : CategoryTheory.Abelian.{u2, u1} A _inst_1], CategoryTheory.Iso.{max u1 u2, max u2 u1} (CategoryTheory.Functor.{u2, u2, max u1 u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} A _inst_1) (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) 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Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (AlgebraicTopology.DoldKan.N₁.{u1, u2} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (CategoryTheory.Functor.comp.{u2, u2, u2, max u2 u1, max u1 u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} A _inst_1) (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (AlgebraicTopology.normalizedMooreComplex.{u1, u2} A _inst_1 _inst_2) (CategoryTheory.Idempotents.toKaroubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.N₁_iso_normalized_Moore_complex_comp_to_karoubi AlgebraicTopology.DoldKan.N₁_iso_normalizedMooreComplex_comp_toKaroubiₓ'. -/
 /-- When the category `A` is abelian,
 the functor `N₁ : simplicial_object A ⥤ karoubi (chain_complex A ℕ)` defined
 using `P_infty` identifies to the composition of the normalized Moore complex functor
 and the inclusion in the Karoubi envelope. -/
-def n₁IsoNormalizedMooreComplexCompToKaroubi : N₁ ≅ normalizedMooreComplex A ⋙ toKaroubi _
+def N₁_iso_normalizedMooreComplex_comp_toKaroubi : N₁ ≅ normalizedMooreComplex A ⋙ toKaroubi _
     where
   Hom :=
     { app := fun X =>
-        { f := pInftyToNormalizedMooreComplex X
+        { f := PInftyToNormalizedMooreComplex X
           comm := by erw [comp_id, P_infty_comp_P_infty_to_normalized_Moore_complex] }
       naturality' := fun X Y f => by
         simp only [functor.comp_map, normalized_Moore_complex_map,
@@ -162,7 +204,7 @@ def n₁IsoNormalizedMooreComplexCompToKaroubi : N₁ ≅ normalizedMooreComplex
       inclusion_of_Moore_complex_map_comp_P_infty]
     dsimp only [functor.comp_obj, to_karoubi]
     rw [id_comp]
-#align algebraic_topology.dold_kan.N₁_iso_normalized_Moore_complex_comp_to_karoubi AlgebraicTopology.DoldKan.n₁IsoNormalizedMooreComplexCompToKaroubi
+#align algebraic_topology.dold_kan.N₁_iso_normalized_Moore_complex_comp_to_karoubi AlgebraicTopology.DoldKan.N₁_iso_normalizedMooreComplex_comp_toKaroubi
 
 end DoldKan
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

@@ -57,7 +57,7 @@ theorem HigherFacesVanish.inclusionOfMooreComplexMap (n : ℕ) :
 #align algebraic_topology.dold_kan.higher_faces_vanish.inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.HigherFacesVanish.inclusionOfMooreComplexMap
 
 theorem factors_normalized_Moore_complex_pInfty (n : ℕ) :
-    Subobject.Factors (NormalizedMooreComplex.objX X n) (pInfty.f n) :=
+    Subobject.Factors (NormalizedMooreComplex.objX X n) (PInfty.f n) :=
   by
   cases n
   · apply top_factors
@@ -82,7 +82,7 @@ def pInftyToNormalizedMooreComplex (X : SimplicialObject A) : K[X] ⟶ N[X] :=
 
 @[simp, reassoc.1]
 theorem pInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap (X : SimplicialObject A) :
-    pInftyToNormalizedMooreComplex X ≫ inclusionOfMooreComplexMap X = pInfty := by tidy
+    pInftyToNormalizedMooreComplex X ≫ inclusionOfMooreComplexMap X = PInfty := by tidy
 #align algebraic_topology.dold_kan.P_infty_to_normalized_Moore_complex_comp_inclusion_of_Moore_complex_map AlgebraicTopology.DoldKan.pInftyToNormalizedMooreComplex_comp_inclusionOfMooreComplexMap
 
 @[simp, reassoc.1]
@@ -94,12 +94,12 @@ theorem pInftyToNormalizedMooreComplex_naturality {X Y : SimplicialObject A} (f
 
 @[simp, reassoc.1]
 theorem pInfty_comp_pInftyToNormalizedMooreComplex (X : SimplicialObject A) :
-    pInfty ≫ pInftyToNormalizedMooreComplex X = pInftyToNormalizedMooreComplex X := by tidy
+    PInfty ≫ pInftyToNormalizedMooreComplex X = pInftyToNormalizedMooreComplex X := by tidy
 #align algebraic_topology.dold_kan.P_infty_comp_P_infty_to_normalized_Moore_complex AlgebraicTopology.DoldKan.pInfty_comp_pInftyToNormalizedMooreComplex
 
 @[simp, reassoc.1]
 theorem inclusionOfMooreComplexMap_comp_pInfty (X : SimplicialObject A) :
-    inclusionOfMooreComplexMap X ≫ pInfty = inclusionOfMooreComplexMap X :=
+    inclusionOfMooreComplexMap X ≫ PInfty = inclusionOfMooreComplexMap X :=
   by
   ext n
   cases n
@@ -130,7 +130,7 @@ variable (A)
 the functor `N₁ : simplicial_object A ⥤ karoubi (chain_complex A ℕ)` defined
 using `P_infty` identifies to the composition of the normalized Moore complex functor
 and the inclusion in the Karoubi envelope. -/
-def n₁IsoNormalizedMooreComplexCompToKaroubi : n₁ ≅ normalizedMooreComplex A ⋙ toKaroubi _
+def n₁IsoNormalizedMooreComplexCompToKaroubi : N₁ ≅ normalizedMooreComplex A ⋙ toKaroubi _
     where
   Hom :=
     { app := fun X =>

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

@@ -105,7 +105,7 @@ theorem inclusionOfMooreComplexMap_comp_pInfty (X : SimplicialObject A) :
   cases n
   · dsimp
     simp only [comp_id]
-  · exact (higher_faces_vanish.inclusion_of_Moore_complex_map n).comp_p_eq_self
+  · exact (higher_faces_vanish.inclusion_of_Moore_complex_map n).comp_P_eq_self
 #align algebraic_topology.dold_kan.inclusion_of_Moore_complex_map_comp_P_infty AlgebraicTopology.DoldKan.inclusionOfMooreComplexMap_comp_pInfty
 
 instance : Mono (inclusionOfMooreComplexMap X) :=

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

And fix some names in comments where this revealed issues

@@ -18,7 +18,7 @@ defined in `FunctorN.lean` and the composition of
 `normalizedMooreComplex A` with the inclusion
 `ChainComplex A ℕ ⥤ Karoubi (ChainComplex A ℕ)`.
 
-This isomorphism shall be used in `equivalence.lean` in order to obtain
+This isomorphism shall be used in `Equivalence.lean` in order to obtain
 the Dold-Kan equivalence
 `CategoryTheory.Abelian.DoldKan.equivalence : SimplicialObject A ≌ ChainComplex A ℕ`
 with a functor (definitionally) equal to `normalizedMooreComplex A`.

@@ -5,7 +5,7 @@ Authors: Joël Riou
 -/
 import Mathlib.AlgebraicTopology.DoldKan.FunctorN
 
-#align_import algebraic_topology.dold_kan.normalized from "leanprover-community/mathlib"@"d1d69e99ed34c95266668af4e288fc1c598b9a7f"
+#align_import algebraic_topology.dold_kan.normalized from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 
 /-!
 

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>

@@ -23,6 +23,8 @@ the Dold-Kan equivalence
 `CategoryTheory.Abelian.DoldKan.equivalence : SimplicialObject A ≌ ChainComplex A ℕ`
 with a functor (definitionally) equal to `normalizedMooreComplex A`.
 
+(See `Equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
+
 -/
 
 

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

This has nice performance benefits.

@@ -37,7 +37,7 @@ namespace DoldKan
 
 universe v
 
-variable {A : Type _} [Category A] [Abelian A] {X : SimplicialObject A}
+variable {A : Type*} [Category A] [Abelian A] {X : SimplicialObject A}
 
 theorem HigherFacesVanish.inclusionOfMooreComplexMap (n : ℕ) :
     HigherFacesVanish (n + 1) ((inclusionOfMooreComplexMap X).f (n + 1)) := fun j _ => by

• depends on: #5966

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

@@ -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.normalized
-! leanprover-community/mathlib commit d1d69e99ed34c95266668af4e288fc1c598b9a7f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicTopology.DoldKan.FunctorN
 
+#align_import algebraic_topology.dold_kan.normalized from "leanprover-community/mathlib"@"d1d69e99ed34c95266668af4e288fc1c598b9a7f"
+
 /-!
 
 # Comparison with the normalized Moore complex functor