PR contents

(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

@@ -21,6 +21,8 @@ In this file, it is shown that the functors
 `N₂ : karoubi (simplicial_object C) ⥤ karoubi (chain_complex C ℕ))`
 reflect isomorphisms for any preadditive category `C`.
 
+(See `equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
+
 -/
 
 open category_theory

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-14-09

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

f736ea6b

Diff

@@ -45,7 +45,9 @@ variable {C : Type _} [Category C] [Preadditive C]
 
 open MorphComponents
 
-instance : ReflectsIsomorphisms (N₁ : SimplicialObject C ⥤ Karoubi (ChainComplex C ℕ)) :=
+instance :
+    CategoryTheory.Functor.ReflectsIsomorphisms
+      (N₁ : SimplicialObject C ⥤ Karoubi (ChainComplex C ℕ)) :=
   ⟨fun X Y f => by
     intro
     -- restating the result in a way that allows induction on the degree n
@@ -115,7 +117,9 @@ theorem compatibility_N₂_N₁_karoubi :
 /-- We deduce that `N₂ : karoubi (simplicial_object C) ⥤ karoubi (chain_complex C ℕ))`
 reflects isomorphisms from the fact that
 `N₁ : simplicial_object (karoubi C) ⥤ karoubi (chain_complex (karoubi C) ℕ)` does. -/
-instance : ReflectsIsomorphisms (N₂ : Karoubi (SimplicialObject C) ⥤ Karoubi (ChainComplex C ℕ)) :=
+instance :
+    CategoryTheory.Functor.ReflectsIsomorphisms
+      (N₂ : Karoubi (SimplicialObject C) ⥤ Karoubi (ChainComplex C ℕ)) :=
   ⟨fun X Y f => by
     intro
     -- The following functor `F` reflects isomorphism because it is

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -59,7 +59,7 @@ instance : ReflectsIsomorphisms (N₁ : SimplicialObject C ⥤ Karoubi (ChainCom
     have h₃ := fun n =>
       karoubi.homological_complex.p_comm_f_assoc (inv (N₁.map f)) n (f.app (op [n]))
     simp only [N₁_map_f, karoubi.comp_f, HomologicalComplex.comp_f,
-      alternating_face_map_complex.map_f, N₁_obj_p, karoubi.id_eq, assoc] at h₁ h₂ h₃ 
+      alternating_face_map_complex.map_f, N₁_obj_p, karoubi.id_eq, assoc] at h₁ h₂ h₃
     -- we have to construct an inverse to f in degree n, by induction on n
     intro n
     induction' n with n hn
@@ -67,8 +67,8 @@ instance : ReflectsIsomorphisms (N₁ : SimplicialObject C ⥤ Karoubi (ChainCom
     · use(inv (N₁.map f)).f.f 0
       have h₁₀ := h₁ 0
       have h₂₀ := h₂ 0
-      dsimp at h₁₀ h₂₀ 
-      simp only [id_comp, comp_id] at h₁₀ h₂₀ 
+      dsimp at h₁₀ h₂₀
+      simp only [id_comp, comp_id] at h₁₀ h₂₀
       tauto
     -- induction step
     · haveI := hn

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ 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 Mathbin.AlgebraicTopology.DoldKan.Decomposition
-import Mathbin.CategoryTheory.Idempotents.HomologicalComplex
-import Mathbin.CategoryTheory.Idempotents.KaroubiKaroubi
+import AlgebraicTopology.DoldKan.FunctorN
+import AlgebraicTopology.DoldKan.Decomposition
+import CategoryTheory.Idempotents.HomologicalComplex
+import CategoryTheory.Idempotents.KaroubiKaroubi
 
 #align_import algebraic_topology.dold_kan.n_reflects_iso from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"

bump to nightly-2023-08-06-03

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

b0e28731

Diff

@@ -8,7 +8,7 @@ import Mathbin.AlgebraicTopology.DoldKan.Decomposition
 import Mathbin.CategoryTheory.Idempotents.HomologicalComplex
 import Mathbin.CategoryTheory.Idempotents.KaroubiKaroubi
 
-#align_import algebraic_topology.dold_kan.n_reflects_iso from "leanprover-community/mathlib"@"4f81bc21e32048db7344b7867946e992cf5f68cc"
+#align_import algebraic_topology.dold_kan.n_reflects_iso from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 
 /-!
 
@@ -22,6 +22,8 @@ In this file, it is shown that the functors
 `N₂ : karoubi (simplicial_object C) ⥤ karoubi (chain_complex C ℕ))`
 reflect isomorphisms for any preadditive category `C`.
 
+(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

@@ -62,7 +62,7 @@ instance : ReflectsIsomorphisms (N₁ : SimplicialObject C ⥤ Karoubi (ChainCom
     intro n
     induction' n with n hn
     -- degree 0
-    · use (inv (N₁.map f)).f.f 0
+    · use(inv (N₁.map f)).f.f 0
       have h₁₀ := h₁ 0
       have h₂₀ := h₂ 0
       dsimp at h₁₀ h₂₀

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 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.n_reflects_iso
-! leanprover-community/mathlib commit 4f81bc21e32048db7344b7867946e992cf5f68cc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicTopology.DoldKan.FunctorN
 import Mathbin.AlgebraicTopology.DoldKan.Decomposition
 import Mathbin.CategoryTheory.Idempotents.HomologicalComplex
 import Mathbin.CategoryTheory.Idempotents.KaroubiKaroubi
 
+#align_import algebraic_topology.dold_kan.n_reflects_iso from "leanprover-community/mathlib"@"4f81bc21e32048db7344b7867946e992cf5f68cc"
+
 /-!
 
 # N₁ and N₂ reflects isomorphisms

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -81,6 +81,7 @@ instance : ReflectsIsomorphisms (N₁ : SimplicialObject C ⥤ Karoubi (ChainCom
         simplicial_object.σ_naturality, h₁, h₂, h₃]
       tauto⟩
 
+#print AlgebraicTopology.DoldKan.compatibility_N₂_N₁_karoubi /-
 theorem compatibility_N₂_N₁_karoubi :
     N₂ ⋙ (karoubiChainComplexEquivalence C ℕ).Functor =
       karoubiFunctorCategoryEmbedding SimplexCategoryᵒᵖ C ⋙
@@ -110,6 +111,7 @@ theorem compatibility_N₂_N₁_karoubi :
       karoubi_chain_complex_equivalence_functor_obj_X_p, N₂_obj_p_f, eq_to_hom_refl,
       P_infty_f_naturality_assoc, app_comp_p, P_infty_f_idem_assoc]
 #align algebraic_topology.dold_kan.compatibility_N₂_N₁_karoubi AlgebraicTopology.DoldKan.compatibility_N₂_N₁_karoubi
+-/
 
 /-- We deduce that `N₂ : karoubi (simplicial_object C) ⥤ karoubi (chain_complex C ℕ))`
 reflects isomorphisms from the fact that

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -60,7 +60,7 @@ instance : ReflectsIsomorphisms (N₁ : SimplicialObject C ⥤ Karoubi (ChainCom
     have h₃ := fun n =>
       karoubi.homological_complex.p_comm_f_assoc (inv (N₁.map f)) n (f.app (op [n]))
     simp only [N₁_map_f, karoubi.comp_f, HomologicalComplex.comp_f,
-      alternating_face_map_complex.map_f, N₁_obj_p, karoubi.id_eq, assoc] at h₁ h₂ h₃
+      alternating_face_map_complex.map_f, N₁_obj_p, karoubi.id_eq, assoc] at h₁ h₂ h₃ 
     -- we have to construct an inverse to f in degree n, by induction on n
     intro n
     induction' n with n hn
@@ -68,8 +68,8 @@ instance : ReflectsIsomorphisms (N₁ : SimplicialObject C ⥤ Karoubi (ChainCom
     · use (inv (N₁.map f)).f.f 0
       have h₁₀ := h₁ 0
       have h₂₀ := h₂ 0
-      dsimp at h₁₀ h₂₀
-      simp only [id_comp, comp_id] at h₁₀ h₂₀
+      dsimp at h₁₀ h₂₀ 
+      simp only [id_comp, comp_id] at h₁₀ h₂₀ 
       tauto
     -- induction step
     · haveI := hn
@@ -98,7 +98,7 @@ theorem compatibility_N₂_N₁_karoubi :
       ext
       have h := (alternating_face_map_complex.map P.p).comm (n + 1) n
       dsimp [N₂, karoubi_chain_complex_equivalence, karoubi_karoubi.inverse,
-        karoubi_homological_complex_equivalence.functor.obj] at h⊢
+        karoubi_homological_complex_equivalence.functor.obj] at h ⊢
       simp only [karoubi.comp_f, assoc, karoubi.eq_to_hom_f, eq_to_hom_refl, id_comp, comp_id,
         karoubi_alternating_face_map_complex_d, karoubi_P_infty_f, ←
         HomologicalComplex.Hom.comm_assoc, ← h, app_idem_assoc]

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -36,7 +36,7 @@ open CategoryTheory.Idempotents
 
 open Opposite
 
-open Simplicial
+open scoped Simplicial
 
 namespace AlgebraicTopology

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -81,9 +81,6 @@ instance : ReflectsIsomorphisms (N₁ : SimplicialObject C ⥤ Karoubi (ChainCom
         simplicial_object.σ_naturality, h₁, h₂, h₃]
       tauto⟩
 
-/- warning: algebraic_topology.dold_kan.compatibility_N₂_N₁_karoubi -> AlgebraicTopology.DoldKan.compatibility_N₂_N₁_karoubi is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility_N₂_N₁_karoubi AlgebraicTopology.DoldKan.compatibility_N₂_N₁_karoubiₓ'. -/
 theorem compatibility_N₂_N₁_karoubi :
     N₂ ⋙ (karoubiChainComplexEquivalence C ℕ).Functor =
       karoubiFunctorCategoryEmbedding SimplexCategoryᵒᵖ C ⋙

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -82,10 +82,7 @@ instance : ReflectsIsomorphisms (N₁ : SimplicialObject C ⥤ Karoubi (ChainCom
       tauto⟩
 
 /- warning: algebraic_topology.dold_kan.compatibility_N₂_N₁_karoubi -> AlgebraicTopology.DoldKan.compatibility_N₂_N₁_karoubi is a dubious translation:
-lean 3 declaration is
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Nat.canonicallyOrderedCommSemiring))) (HomologicalComplex.{u1, max u2 u1, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, max u2 u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _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))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, max u2 u1, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, max u2 u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _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.Equivalence.functor.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u1} (ChainComplex.{u1, max u1 u2, 0} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _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.{u1, max u1 u2, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _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)))) (ChainComplex.{u1, max u1 u2, 0} (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _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.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u1} (ChainComplex.{u1, max u1 u2, 0} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _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.{u1, max u1 u2, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _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)))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, max u1 u2, 0} Nat (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _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.karoubiChainComplexEquivalence.{max u1 u2, u1, 0} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _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.Functor.mapHomologicalComplex.{u1, max u2 u1, 0, max u2 u1, u1} Nat (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u2 u1, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{max u2 u1, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _inst_1 _inst_2)) (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Equivalence.inverse.{u1, u1, max u2 u1, max u2 u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u2 u1, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.KaroubiKaroubi.equivalence.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.KaroubiKaroubi.equivalence.additive_inverse.{u2, u1} C _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.compatibility_N₂_N₁_karoubi AlgebraicTopology.DoldKan.compatibility_N₂_N₁_karoubiₓ'. -/
 theorem compatibility_N₂_N₁_karoubi :
     N₂ ⋙ (karoubiChainComplexEquivalence C ℕ).Functor =

bump to nightly-2023-04-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e281deff072232a3c5b3e90034bd65dde396312

8c574543

Diff

@@ -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.n_reflects_iso
-! leanprover-community/mathlib commit 88bca0ce5d22ebfd9e73e682e51d60ea13b48347
+! leanprover-community/mathlib commit 4f81bc21e32048db7344b7867946e992cf5f68cc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.CategoryTheory.Idempotents.KaroubiKaroubi
 
 # N₁ and N₂ reflects isomorphisms
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file, it is shown that the functors
 `N₁ : simplicial_object C ⥤ karoubi (chain_complex C ℕ)` and
 `N₂ : karoubi (simplicial_object C) ⥤ karoubi (chain_complex C ℕ))`

bump to nightly-2023-04-21-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/246f6f7989ff86bd07e1b014846f11304f33cf9e

f5635fc7

Diff

@@ -78,7 +78,13 @@ instance : ReflectsIsomorphisms (N₁ : SimplicialObject C ⥤ Karoubi (ChainCom
         simplicial_object.σ_naturality, h₁, h₂, h₃]
       tauto⟩
 
-theorem compatibility_n₂_n₁_karoubi :
+/- warning: algebraic_topology.dold_kan.compatibility_N₂_N₁_karoubi -> AlgebraicTopology.DoldKan.compatibility_N₂_N₁_karoubi is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _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, max u1 u2, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _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.comp.{u2, u2, u2, max u2 u1, max u1 u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{max u2 u1, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{max u2 u1, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _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, max u1 u2, 0} Nat (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} 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(CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _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)) (ChainComplex.{u2, max u1 u2, 0} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (CategoryTheory.Equivalence.functor.{u2, u2, max u1 u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (ChainComplex.{u2, max u1 u2, 0} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _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, max u1 u2, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _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.Idempotents.Karoubi.CategoryTheory.category.{max u1 u2, u2} (ChainComplex.{u2, max u1 u2, 0} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _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, max u1 u2, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _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))) (ChainComplex.{u2, max u1 u2, 0} (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _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, max u1 u2, 0} Nat (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _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.Idempotents.karoubiChainComplexEquivalence.{max u1 u2, u2, 0} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _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.Functor.mapHomologicalComplex.{u2, max u1 u2, 0, max u1 u2, u2} Nat (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Equivalence.inverse.{u2, u2, max u1 u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.KaroubiKaroubi.equivalence.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.KaroubiKaroubi.equivalence.additive_inverse.{u1, u2} C _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)))))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1], Eq.{max (succ u2) (succ u1)} (CategoryTheory.Functor.{u1, u1, max u1 u2, max u2 u1} (CategoryTheory.Idempotents.Karoubi.{max u2 u1, u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u2 u1, u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (ChainComplex.{u1, max u1 u2, 0} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, max u2 u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _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.{u1, max u2 u1, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, max u2 u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _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.comp.{u1, u1, u1, max u1 u2, max u1 u2, max u2 u1} (CategoryTheory.Idempotents.Karoubi.{max u2 u1, u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u2 u1, u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.{max u2 u1, u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _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.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _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)))) 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_inst_1)) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _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))) 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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.compatibility_N₂_N₁_karoubi AlgebraicTopology.DoldKan.compatibility_N₂_N₁_karoubiₓ'. -/
+theorem compatibility_N₂_N₁_karoubi :
     N₂ ⋙ (karoubiChainComplexEquivalence C ℕ).Functor =
       karoubiFunctorCategoryEmbedding SimplexCategoryᵒᵖ C ⋙
         N₁ ⋙
@@ -106,7 +112,7 @@ theorem compatibility_n₂_n₁_karoubi :
       assoc, comp_id, P_infty_f_naturality, app_p_comp,
       karoubi_chain_complex_equivalence_functor_obj_X_p, N₂_obj_p_f, eq_to_hom_refl,
       P_infty_f_naturality_assoc, app_comp_p, P_infty_f_idem_assoc]
-#align algebraic_topology.dold_kan.compatibility_N₂_N₁_karoubi AlgebraicTopology.DoldKan.compatibility_n₂_n₁_karoubi
+#align algebraic_topology.dold_kan.compatibility_N₂_N₁_karoubi AlgebraicTopology.DoldKan.compatibility_N₂_N₁_karoubi
 
 /-- We deduce that `N₂ : karoubi (simplicial_object C) ⥤ karoubi (chain_complex C ℕ))`
 reflects isomorphisms from the fact that

bump to nightly-2023-04-20-20

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

e863e061

Diff

@@ -43,7 +43,7 @@ variable {C : Type _} [Category C] [Preadditive C]
 
 open MorphComponents
 
-instance : ReflectsIsomorphisms (n₁ : SimplicialObject C ⥤ Karoubi (ChainComplex C ℕ)) :=
+instance : ReflectsIsomorphisms (N₁ : SimplicialObject C ⥤ Karoubi (ChainComplex C ℕ)) :=
   ⟨fun X Y f => by
     intro
     -- restating the result in a way that allows induction on the degree n
@@ -79,9 +79,9 @@ instance : ReflectsIsomorphisms (n₁ : SimplicialObject C ⥤ Karoubi (ChainCom
       tauto⟩
 
 theorem compatibility_n₂_n₁_karoubi :
-    n₂ ⋙ (karoubiChainComplexEquivalence C ℕ).Functor =
+    N₂ ⋙ (karoubiChainComplexEquivalence C ℕ).Functor =
       karoubiFunctorCategoryEmbedding SimplexCategoryᵒᵖ C ⋙
-        n₁ ⋙
+        N₁ ⋙
           (karoubiChainComplexEquivalence (Karoubi C) ℕ).Functor ⋙
             Functor.mapHomologicalComplex (KaroubiKaroubi.equivalence C).inverse _ :=
   by
@@ -111,7 +111,7 @@ theorem compatibility_n₂_n₁_karoubi :
 /-- We deduce that `N₂ : karoubi (simplicial_object C) ⥤ karoubi (chain_complex C ℕ))`
 reflects isomorphisms from the fact that
 `N₁ : simplicial_object (karoubi C) ⥤ karoubi (chain_complex (karoubi C) ℕ)` does. -/
-instance : ReflectsIsomorphisms (n₂ : Karoubi (SimplicialObject C) ⥤ Karoubi (ChainComplex C ℕ)) :=
+instance : ReflectsIsomorphisms (N₂ : Karoubi (SimplicialObject C) ⥤ Karoubi (ChainComplex C ℕ)) :=
   ⟨fun X Y f => by
     intro
     -- The following functor `F` reflects isomorphism because it is

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

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

@@ -34,7 +34,7 @@ variable {C : Type*} [Category C] [Preadditive C]
 
 open MorphComponents
 
-instance : ReflectsIsomorphisms (N₁ : SimplicialObject C ⥤ Karoubi (ChainComplex C ℕ)) :=
+instance : (N₁ : SimplicialObject C ⥤ Karoubi (ChainComplex C ℕ)).ReflectsIsomorphisms :=
   ⟨fun {X Y} f => by
     intro
     -- restating the result in a way that allows induction on the degree n
@@ -96,7 +96,7 @@ set_option linter.uppercaseLean3 false in
 /-- We deduce that `N₂ : Karoubi (SimplicialObject C) ⥤ Karoubi (ChainComplex C ℕ))`
 reflects isomorphisms from the fact that
 `N₁ : SimplicialObject (Karoubi C) ⥤ Karoubi (ChainComplex (Karoubi C) ℕ)` does. -/
-instance : ReflectsIsomorphisms (N₂ : Karoubi (SimplicialObject C) ⥤ Karoubi (ChainComplex C ℕ)) :=
+instance : (N₂ : Karoubi (SimplicialObject C) ⥤ Karoubi (ChainComplex C ℕ)).ReflectsIsomorphisms :=
   ⟨fun f => by
     intro
     -- The following functor `F` reflects isomorphism because it is
@@ -110,10 +110,10 @@ instance : ReflectsIsomorphisms (N₂ : Karoubi (SimplicialObject C) ⥤ Karoubi
     let F := F₁ ⋙ F₂ ⋙ F₃ ⋙ F₄
     -- Porting note: we have to help Lean4 find the `ReflectsIsomorphisms` instances
     -- could this be fixed by setting better instance priorities?
-    haveI : ReflectsIsomorphisms F₁ := reflectsIsomorphisms_of_full_and_faithful _
-    haveI : ReflectsIsomorphisms F₂ := by infer_instance
-    haveI : ReflectsIsomorphisms F₃ := reflectsIsomorphisms_of_full_and_faithful _
-    haveI : ReflectsIsomorphisms ((KaroubiKaroubi.equivalence C).inverse) :=
+    haveI : F₁.ReflectsIsomorphisms := reflectsIsomorphisms_of_full_and_faithful _
+    haveI : F₂.ReflectsIsomorphisms := by infer_instance
+    haveI : F₃.ReflectsIsomorphisms := reflectsIsomorphisms_of_full_and_faithful _
+    haveI : ((KaroubiKaroubi.equivalence C).inverse).ReflectsIsomorphisms :=
       reflectsIsomorphisms_of_full_and_faithful _
     have : IsIso (F.map f) := by
       simp only [F]

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

converts "--porting note" into "-- Porting note";
converts "porting note" into "Porting note".

8be0b69c

Diff

@@ -108,7 +108,7 @@ instance : ReflectsIsomorphisms (N₂ : Karoubi (SimplicialObject C) ⥤ Karoubi
     let F₄ := Functor.mapHomologicalComplex (KaroubiKaroubi.equivalence C).inverse
       (ComplexShape.down ℕ)
     let F := F₁ ⋙ F₂ ⋙ F₃ ⋙ F₄
-    -- porting note: we have to help Lean4 find the `ReflectsIsomorphisms` instances
+    -- Porting note: we have to help Lean4 find the `ReflectsIsomorphisms` instances
     -- could this be fixed by setting better instance priorities?
     haveI : ReflectsIsomorphisms F₁ := reflectsIsomorphisms_of_full_and_faithful _
     haveI : ReflectsIsomorphisms F₂ := by infer_instance

chore: prepare Lean version bump with explicit simp (#10999)

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

38bce757

Diff

@@ -116,7 +116,7 @@ instance : ReflectsIsomorphisms (N₂ : Karoubi (SimplicialObject C) ⥤ Karoubi
     haveI : ReflectsIsomorphisms ((KaroubiKaroubi.equivalence C).inverse) :=
       reflectsIsomorphisms_of_full_and_faithful _
     have : IsIso (F.map f) := by
-      simp only
+      simp only [F]
       rw [← compatibility_N₂_N₁_karoubi, Functor.comp_map]
       apply Functor.map_isIso
     exact isIso_of_reflects_iso f F⟩

chore: bump to v4.3.0-rc2 (#8366)

PR contents

This is the supremum of

#8284
#8056
#8023
#8332
#8226 (already approved)
#7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

switching to using explicit lemmas that have the intended level of application
(config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

40b64f79

Diff

@@ -63,7 +63,7 @@ instance : ReflectsIsomorphisms (N₁ : SimplicialObject C ⥤ Karoubi (ChainCom
               b := fun i => inv (f.app (op [n])) ≫ X.σ i }
       simp only [MorphComponents.id, ← id_φ, ← preComp_φ, preComp, ← postComp_φ, postComp,
         PInfty_f_naturality_assoc, IsIso.hom_inv_id_assoc, assoc, IsIso.inv_hom_id_assoc,
-        SimplicialObject.σ_naturality, h₁, h₂, h₃]⟩
+        SimplicialObject.σ_naturality, h₁, h₂, h₃, and_self]⟩
 
 theorem compatibility_N₂_N₁_karoubi :
     N₂ ⋙ (karoubiChainComplexEquivalence C ℕ).functor =

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

cf01bdac

Diff

@@ -8,7 +8,7 @@ import Mathlib.AlgebraicTopology.DoldKan.Decomposition
 import Mathlib.CategoryTheory.Idempotents.HomologicalComplex
 import Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi
 
-#align_import algebraic_topology.dold_kan.n_reflects_iso from "leanprover-community/mathlib"@"88bca0ce5d22ebfd9e73e682e51d60ea13b48347"
+#align_import algebraic_topology.dold_kan.n_reflects_iso from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 
 /-!

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

@@ -19,6 +19,8 @@ In this file, it is shown that the functors
 `N₂ : Karoubi (SimplicialObject C) ⥤ Karoubi (ChainComplex C ℕ))`
 reflect isomorphisms for any preadditive category `C`.
 
+(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

@@ -28,7 +28,7 @@ namespace AlgebraicTopology
 
 namespace DoldKan
 
-variable {C : Type _} [Category C] [Preadditive C]
+variable {C : Type*} [Category C] [Preadditive C]
 
 open MorphComponents

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

@@ -2,17 +2,14 @@
 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.n_reflects_iso
-! leanprover-community/mathlib commit 88bca0ce5d22ebfd9e73e682e51d60ea13b48347
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicTopology.DoldKan.FunctorN
 import Mathlib.AlgebraicTopology.DoldKan.Decomposition
 import Mathlib.CategoryTheory.Idempotents.HomologicalComplex
 import Mathlib.CategoryTheory.Idempotents.KaroubiKaroubi
 
+#align_import algebraic_topology.dold_kan.n_reflects_iso from "leanprover-community/mathlib"@"88bca0ce5d22ebfd9e73e682e51d60ea13b48347"
+
 /-!
 
 # N₁ and N₂ reflects isomorphisms

chore: bump to nightly-2023-07-01 (#5409)

depends on: https://github.com/leanprover/std4/pull/163
depends on: #5584
depends on: #5715
depends on: #5729
depends on: https://github.com/leanprover/std4/pull/173

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

906f7221

Diff

@@ -74,9 +74,9 @@ theorem compatibility_N₂_N₁_karoubi :
   refine' CategoryTheory.Functor.ext (fun P => _) fun P Q f => _
   · refine' HomologicalComplex.ext _ _
     · ext n
+      · rfl
       · dsimp
         simp only [karoubi_PInfty_f, comp_id, PInfty_f_naturality, id_comp, eqToHom_refl]
-      · rfl
     · rintro _ n (rfl : n + 1 = _)
       ext
       have h := (AlternatingFaceMapComplex.map P.p).comm (n + 1) n

chore: fix focusing dots (#5708)

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

cb02d09e

Diff

@@ -76,7 +76,7 @@ theorem compatibility_N₂_N₁_karoubi :
     · ext n
       · dsimp
         simp only [karoubi_PInfty_f, comp_id, PInfty_f_naturality, id_comp, eqToHom_refl]
-      . rfl
+      · rfl
     · rintro _ n (rfl : n + 1 = _)
       ext
       have h := (AlternatingFaceMapComplex.map P.p).comm (n + 1) n