algebraic_topology.dold_kan.decomposition

(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

@@ -29,6 +29,8 @@ role in the proof that the functor
 `N₁ : simplicial_object C ⥤ karoubi (chain_complex C ℕ))`
 reflects isomorphisms.
 
+(See `equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
+
 -/
 
 open category_theory category_theory.category category_theory.preadditive opposite

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 -/
-import Mathbin.AlgebraicTopology.DoldKan.PInfty
+import AlgebraicTopology.DoldKan.PInfty
 
 #align_import algebraic_topology.dold_kan.decomposition from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"

bump to nightly-2023-08-06-03

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

b0e28731

Diff

@@ -5,7 +5,7 @@ Authors: Joël Riou
 -/
 import Mathbin.AlgebraicTopology.DoldKan.PInfty
 
-#align_import algebraic_topology.dold_kan.decomposition from "leanprover-community/mathlib"@"4f81bc21e32048db7344b7867946e992cf5f68cc"
+#align_import algebraic_topology.dold_kan.decomposition from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 
 /-!
 
@@ -30,6 +30,8 @@ role in the proof that the functor
 `N₁ : simplicial_object C ⥤ karoubi (chain_complex C ℕ))`
 reflects isomorphisms.
 
+(See `equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
+
 -/

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
-
-! This file was ported from Lean 3 source module algebraic_topology.dold_kan.decomposition
-! 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.PInfty
 
+#align_import algebraic_topology.dold_kan.decomposition from "leanprover-community/mathlib"@"4f81bc21e32048db7344b7867946e992cf5f68cc"
+
 /-!
 
 # Decomposition of the Q endomorphisms

bump to nightly-2023-07-05-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/5dc6092d09e5e489106865241986f7f2ad28d4c8

3fd81375

Diff

@@ -58,7 +58,7 @@ the $y_i$ are in degree $n$. -/
 theorem decomposition_Q (n q : ℕ) :
     ((Q q).f (n + 1) : X _[n + 1] ⟶ X _[n + 1]) =
       ∑ i : Fin (n + 1) in Finset.filter (fun i : Fin (n + 1) => (i : ℕ) < q) Finset.univ,
-        (P i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev :=
+        (P i).f (n + 1) ≫ X.δ i.revPerm.succ ≫ X.σ i.revPerm :=
   by
   induction' q with q hq
   ·
@@ -110,7 +110,7 @@ variable {X} {n : ℕ} {Z Z' : C} (f : MorphComponents X n Z) (g : X' ⟶ X) (h
 #print AlgebraicTopology.DoldKan.MorphComponents.φ /-
 /-- The morphism `X _[n+1] ⟶ Z ` associated to `f : morph_components X n Z`. -/
 def φ {Z : C} (f : MorphComponents X n Z) : X _[n + 1] ⟶ Z :=
-  PInfty.f (n + 1) ≫ f.a + ∑ i : Fin (n + 1), (P i).f (n + 1) ≫ X.δ i.rev.succ ≫ f.b i.rev
+  PInfty.f (n + 1) ≫ f.a + ∑ i : Fin (n + 1), (P i).f (n + 1) ≫ X.δ i.revPerm.succ ≫ f.b i.revPerm
 #align algebraic_topology.dold_kan.morph_components.φ AlgebraicTopology.DoldKan.MorphComponents.φ
 -/

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -48,6 +48,7 @@ namespace DoldKan
 
 variable {C : Type _} [Category C] [Preadditive C] {X X' : SimplicialObject C}
 
+#print AlgebraicTopology.DoldKan.decomposition_Q /-
 /-- In each positive degree, this lemma decomposes the idempotent endomorphism
 `Q q` as a sum of morphisms which are postcompositions with suitable degeneracies.
 As `Q q` is the complement projection to `P q`, this implies that in the case of
@@ -85,9 +86,11 @@ theorem decomposition_Q (n q : ℕ) :
           neg_neg]
       · simp only [Finset.mem_filter, Fin.val_mk, lt_self_iff_false, and_false_iff, not_false_iff]
 #align algebraic_topology.dold_kan.decomposition_Q AlgebraicTopology.DoldKan.decomposition_Q
+-/
 
 variable (X)
 
+#print AlgebraicTopology.DoldKan.MorphComponents /-
 /-- The structure `morph_components` is an ad hoc structure that is used in
 the proof that `N₁ : simplicial_object C ⥤ karoubi (chain_complex C ℕ))`
 reflects isomorphisms. The fields are the data that are needed in order to
@@ -98,6 +101,7 @@ structure MorphComponents (n : ℕ) (Z : C) where
   a : X _[n + 1] ⟶ Z
   b : Fin (n + 1) → (X _[n] ⟶ Z)
 #align algebraic_topology.dold_kan.morph_components AlgebraicTopology.DoldKan.MorphComponents
+-/
 
 namespace MorphComponents
 
@@ -123,6 +127,7 @@ def id : MorphComponents X n (X _[n + 1])
 #align algebraic_topology.dold_kan.morph_components.id AlgebraicTopology.DoldKan.MorphComponents.id
 -/
 
+#print AlgebraicTopology.DoldKan.MorphComponents.id_φ /-
 @[simp]
 theorem id_φ : (id X n).φ = 𝟙 _ :=
   by
@@ -133,15 +138,18 @@ theorem id_φ : (id X n).φ = 𝟙 _ :=
     ext i
     simpa only [Finset.mem_univ, Finset.mem_filter, true_and_iff, true_iff_iff] using Fin.is_lt i
 #align algebraic_topology.dold_kan.morph_components.id_φ AlgebraicTopology.DoldKan.MorphComponents.id_φ
+-/
 
 variable {X n}
 
+#print AlgebraicTopology.DoldKan.MorphComponents.postComp /-
 /-- A `morph_components` can be postcomposed with a morphism. -/
 @[simps]
 def postComp : MorphComponents X n Z' where
   a := f.a ≫ h
   b i := f.b i ≫ h
 #align algebraic_topology.dold_kan.morph_components.post_comp AlgebraicTopology.DoldKan.MorphComponents.postComp
+-/
 
 #print AlgebraicTopology.DoldKan.MorphComponents.postComp_φ /-
 @[simp]
@@ -152,6 +160,7 @@ theorem postComp_φ : (f.postComp h).φ = f.φ ≫ h :=
 #align algebraic_topology.dold_kan.morph_components.post_comp_φ AlgebraicTopology.DoldKan.MorphComponents.postComp_φ
 -/
 
+#print AlgebraicTopology.DoldKan.MorphComponents.preComp /-
 /-- A `morph_components` can be precomposed with a morphism of simplicial objects. -/
 @[simps]
 def preComp : MorphComponents X' n Z
@@ -159,6 +168,7 @@ def preComp : MorphComponents X' n Z
   a := g.app (op [n + 1]) ≫ f.a
   b i := g.app (op [n]) ≫ f.b i
 #align algebraic_topology.dold_kan.morph_components.pre_comp AlgebraicTopology.DoldKan.MorphComponents.preComp
+-/
 
 #print AlgebraicTopology.DoldKan.MorphComponents.preComp_φ /-
 @[simp]

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -129,7 +129,7 @@ theorem id_φ : (id X n).φ = 𝟙 _ :=
   simp only [← P_add_Q_f (n + 1) (n + 1), φ]
   congr 1
   · simp only [id, P_infty_f, P_f_idem]
-  · convert(decomposition_Q n (n + 1)).symm
+  · convert (decomposition_Q n (n + 1)).symm
     ext i
     simpa only [Finset.mem_univ, Finset.mem_filter, true_and_iff, true_iff_iff] using Fin.is_lt i
 #align algebraic_topology.dold_kan.morph_components.id_φ AlgebraicTopology.DoldKan.MorphComponents.id_φ

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -38,7 +38,7 @@ reflects isomorphisms.
 
 open CategoryTheory CategoryTheory.Category CategoryTheory.Preadditive Opposite
 
-open BigOperators Simplicial
+open scoped BigOperators Simplicial
 
 noncomputable section

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -48,9 +48,6 @@ namespace DoldKan
 
 variable {C : Type _} [Category C] [Preadditive C] {X X' : SimplicialObject C}
 
-/- warning: algebraic_topology.dold_kan.decomposition_Q -> AlgebraicTopology.DoldKan.decomposition_Q is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.decomposition_Q AlgebraicTopology.DoldKan.decomposition_Qₓ'. -/
 /-- In each positive degree, this lemma decomposes the idempotent endomorphism
 `Q q` as a sum of morphisms which are postcompositions with suitable degeneracies.
 As `Q q` is the complement projection to `P q`, this implies that in the case of
@@ -91,12 +88,6 @@ theorem decomposition_Q (n q : ℕ) :
 
 variable (X)
 
-/- warning: algebraic_topology.dold_kan.morph_components -> AlgebraicTopology.DoldKan.MorphComponents is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1], (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) -> Nat -> C -> Type.{u2}
-but is expected to have type
-  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C], (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) -> Nat -> C -> Type.{u2}
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.morph_components AlgebraicTopology.DoldKan.MorphComponentsₓ'. -/
 /-- The structure `morph_components` is an ad hoc structure that is used in
 the proof that `N₁ : simplicial_object C ⥤ karoubi (chain_complex C ℕ))`
 reflects isomorphisms. The fields are the data that are needed in order to
@@ -132,12 +123,6 @@ def id : MorphComponents X n (X _[n + 1])
 #align algebraic_topology.dold_kan.morph_components.id AlgebraicTopology.DoldKan.MorphComponents.id
 -/
 
-/- warning: algebraic_topology.dold_kan.morph_components.id_φ -> AlgebraicTopology.DoldKan.MorphComponents.id_φ 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.morph_components.id_φ AlgebraicTopology.DoldKan.MorphComponents.id_φₓ'. -/
 @[simp]
 theorem id_φ : (id X n).φ = 𝟙 _ :=
   by
@@ -151,12 +136,6 @@ theorem id_φ : (id X n).φ = 𝟙 _ :=
 
 variable {X n}
 
-/- warning: algebraic_topology.dold_kan.morph_components.post_comp -> AlgebraicTopology.DoldKan.MorphComponents.postComp is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {n : Nat} {Z : C} {Z' : C}, (AlgebraicTopology.DoldKan.MorphComponents.{u1, u2} C _inst_1 _inst_2 X n Z) -> (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Z Z') -> (AlgebraicTopology.DoldKan.MorphComponents.{u1, u2} C _inst_1 _inst_2 X n Z')
-but is expected to have type
-  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] {_inst_2 : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {X : Nat} {n : C} {Z : C}, (AlgebraicTopology.DoldKan.MorphComponents.{u1, u2} C _inst_1 _inst_2 X n) -> (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) n Z) -> (AlgebraicTopology.DoldKan.MorphComponents.{u1, u2} C _inst_1 _inst_2 X Z)
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.morph_components.post_comp AlgebraicTopology.DoldKan.MorphComponents.postCompₓ'. -/
 /-- A `morph_components` can be postcomposed with a morphism. -/
 @[simps]
 def postComp : MorphComponents X n Z' where
@@ -173,12 +152,6 @@ theorem postComp_φ : (f.postComp h).φ = f.φ ≫ h :=
 #align algebraic_topology.dold_kan.morph_components.post_comp_φ AlgebraicTopology.DoldKan.MorphComponents.postComp_φ
 -/
 
-/- warning: algebraic_topology.dold_kan.morph_components.pre_comp -> AlgebraicTopology.DoldKan.MorphComponents.preComp is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {X' : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {n : Nat} {Z : C}, (AlgebraicTopology.DoldKan.MorphComponents.{u1, u2} C _inst_1 _inst_2 X n Z) -> (Quiver.Hom.{succ u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1))) X' X) -> (AlgebraicTopology.DoldKan.MorphComponents.{u1, u2} C _inst_1 _inst_2 X' n Z)
-but is expected to have type
-  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] {_inst_2 : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {X' : Nat} {n : C}, (AlgebraicTopology.DoldKan.MorphComponents.{u1, u2} C _inst_1 _inst_2 X' n) -> (Quiver.Hom.{succ u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1))) X _inst_2) -> (AlgebraicTopology.DoldKan.MorphComponents.{u1, u2} C _inst_1 X X' n)
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.morph_components.pre_comp AlgebraicTopology.DoldKan.MorphComponents.preCompₓ'. -/
 /-- A `morph_components` can be precomposed with a morphism of simplicial objects. -/
 @[simps]
 def preComp : MorphComponents X' n Z

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -66,8 +66,7 @@ theorem decomposition_Q (n q : ℕ) :
   ·
     simp only [Q_eq_zero, HomologicalComplex.zero_f_apply, Nat.not_lt_zero, Finset.filter_False,
       Finset.sum_empty]
-  · by_cases hqn : q + 1 ≤ n + 1
-    swap
+  · by_cases hqn : q + 1 ≤ n + 1; swap
     · rw [Q_is_eventually_constant (show n + 1 ≤ q by linarith), hq]
       congr
       ext

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -49,10 +49,7 @@ namespace DoldKan
 variable {C : Type _} [Category C] [Preadditive C] {X X' : SimplicialObject C}
 
 /- warning: algebraic_topology.dold_kan.decomposition_Q -> AlgebraicTopology.DoldKan.decomposition_Q is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.decomposition_Q AlgebraicTopology.DoldKan.decomposition_Qₓ'. -/
 /-- In each positive degree, this lemma decomposes the idempotent endomorphism
 `Q q` as a sum of morphisms which are postcompositions with suitable degeneracies.

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -52,7 +52,7 @@ variable {C : Type _} [Category C] [Preadditive C] {X X' : SimplicialObject C}
 lean 3 declaration is
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 but is expected to have type
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(CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (AddCommGroup.toAddCommMonoid.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))) (Finset.filter.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => LT.lt.{0} Nat instLTNat (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i) q) (fun (a : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Nat.decLt (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) a) q) (Finset.univ.{0} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin.fintype (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (fun (i : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _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)))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _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)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.DoldKan.P.{u1, u2} C _inst_1 _inst_2 X (Fin.val (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) i)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _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)))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.SimplicialObject.δ.{u2, u1} C _inst_1 X n (Fin.succ (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (FunLike.coe.{1, 1, 1} (Equiv.Perm.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (Equiv.instFunLikeEquiv.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin.rev (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i))) (CategoryTheory.SimplicialObject.σ.{u2, u1} C _inst_1 X n (FunLike.coe.{1, 1, 1} (Equiv.Perm.{1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (fun (_x : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) _x) (Equiv.instFunLikeEquiv.{1, 1} (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (Fin (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (Fin.rev (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) i)))))
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.decomposition_Q AlgebraicTopology.DoldKan.decomposition_Qₓ'. -/
 /-- In each positive degree, this lemma decomposes the idempotent endomorphism
 `Q q` as a sum of morphisms which are postcompositions with suitable degeneracies.

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.decomposition
-! leanprover-community/mathlib commit 9af20344b24ef1801b599d296aaed8b9fffdc360
+! leanprover-community/mathlib commit 4f81bc21e32048db7344b7867946e992cf5f68cc
 ! 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.PInfty
 
 # Decomposition of the Q endomorphisms
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file, we obtain a lemma `decomposition_Q` which expresses
 explicitly the projection `(Q q).f (n+1) : X _[n+1] ⟶ X _[n+1]`
 (`X : simplicial_object C` with `C` a preadditive category) as

bump to nightly-2023-04-21-06

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

901cd3e2

Diff

@@ -45,13 +45,19 @@ namespace DoldKan
 
 variable {C : Type _} [Category C] [Preadditive C] {X X' : SimplicialObject C}
 
+/- warning: algebraic_topology.dold_kan.decomposition_Q -> AlgebraicTopology.DoldKan.decomposition_Q 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.decomposition_Q AlgebraicTopology.DoldKan.decomposition_Qₓ'. -/
 /-- In each positive degree, this lemma decomposes the idempotent endomorphism
 `Q q` as a sum of morphisms which are postcompositions with suitable degeneracies.
 As `Q q` is the complement projection to `P q`, this implies that in the case of
 simplicial abelian groups, any $(n+1)$-simplex $x$ can be decomposed as
 $x = x' + \sum (i=0}^{q-1} σ_{n-i}(y_i)$ where $x'$ is in the image of `P q` and
 the $y_i$ are in degree $n$. -/
-theorem decomposition_q (n q : ℕ) :
+theorem decomposition_Q (n q : ℕ) :
     ((Q q).f (n + 1) : X _[n + 1] ⟶ X _[n + 1]) =
       ∑ i : Fin (n + 1) in Finset.filter (fun i : Fin (n + 1) => (i : ℕ) < q) Finset.univ,
         (P i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev :=
@@ -82,10 +88,16 @@ theorem decomposition_q (n q : ℕ) :
         simpa only [Fin.val_mk, (higher_faces_vanish.of_P q n).comp_Hσ_eq hnaq', q'.rev_eq hnaq',
           neg_neg]
       · simp only [Finset.mem_filter, Fin.val_mk, lt_self_iff_false, and_false_iff, not_false_iff]
-#align algebraic_topology.dold_kan.decomposition_Q AlgebraicTopology.DoldKan.decomposition_q
+#align algebraic_topology.dold_kan.decomposition_Q AlgebraicTopology.DoldKan.decomposition_Q
 
 variable (X)
 
+/- warning: algebraic_topology.dold_kan.morph_components -> AlgebraicTopology.DoldKan.MorphComponents is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1], (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) -> Nat -> C -> Type.{u2}
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C], (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) -> Nat -> C -> Type.{u2}
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.morph_components AlgebraicTopology.DoldKan.MorphComponentsₓ'. -/
 /-- The structure `morph_components` is an ad hoc structure that is used in
 the proof that `N₁ : simplicial_object C ⥤ karoubi (chain_complex C ℕ))`
 reflects isomorphisms. The fields are the data that are needed in order to
@@ -101,13 +113,16 @@ namespace MorphComponents
 
 variable {X} {n : ℕ} {Z Z' : C} (f : MorphComponents X n Z) (g : X' ⟶ X) (h : Z ⟶ Z')
 
+#print AlgebraicTopology.DoldKan.MorphComponents.φ /-
 /-- The morphism `X _[n+1] ⟶ Z ` associated to `f : morph_components X n Z`. -/
 def φ {Z : C} (f : MorphComponents X n Z) : X _[n + 1] ⟶ Z :=
   PInfty.f (n + 1) ≫ f.a + ∑ i : Fin (n + 1), (P i).f (n + 1) ≫ X.δ i.rev.succ ≫ f.b i.rev
 #align algebraic_topology.dold_kan.morph_components.φ AlgebraicTopology.DoldKan.MorphComponents.φ
+-/
 
 variable (X n)
 
+#print AlgebraicTopology.DoldKan.MorphComponents.id /-
 /-- the canonical `morph_components` whose associated morphism is the identity
 (see `F_id`) thanks to `decomposition_Q n (n+1)` -/
 @[simps]
@@ -116,7 +131,14 @@ def id : MorphComponents X n (X _[n + 1])
   a := PInfty.f (n + 1)
   b i := X.σ i
 #align algebraic_topology.dold_kan.morph_components.id AlgebraicTopology.DoldKan.MorphComponents.id
+-/
 
+/- warning: algebraic_topology.dold_kan.morph_components.id_φ -> AlgebraicTopology.DoldKan.MorphComponents.id_φ is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (AlgebraicTopology.DoldKan.MorphComponents.φ.{u1, u2} C _inst_1 _inst_2 X n (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (AlgebraicTopology.DoldKan.MorphComponents.id.{u1, u2} C _inst_1 _inst_2 X n)) (CategoryTheory.CategoryStruct.id.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (AlgebraicTopology.DoldKan.MorphComponents.φ.{u1, u2} C _inst_1 _inst_2 X n (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (AlgebraicTopology.DoldKan.MorphComponents.id.{u1, u2} C _inst_1 _inst_2 X n)) (CategoryTheory.CategoryStruct.id.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (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.morph_components.id_φ AlgebraicTopology.DoldKan.MorphComponents.id_φₓ'. -/
 @[simp]
 theorem id_φ : (id X n).φ = 𝟙 _ :=
   by
@@ -130,6 +152,12 @@ theorem id_φ : (id X n).φ = 𝟙 _ :=
 
 variable {X n}
 
+/- warning: algebraic_topology.dold_kan.morph_components.post_comp -> AlgebraicTopology.DoldKan.MorphComponents.postComp is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {n : Nat} {Z : C} {Z' : C}, (AlgebraicTopology.DoldKan.MorphComponents.{u1, u2} C _inst_1 _inst_2 X n Z) -> (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Z Z') -> (AlgebraicTopology.DoldKan.MorphComponents.{u1, u2} C _inst_1 _inst_2 X n Z')
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] {_inst_2 : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {X : Nat} {n : C} {Z : C}, (AlgebraicTopology.DoldKan.MorphComponents.{u1, u2} C _inst_1 _inst_2 X n) -> (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) n Z) -> (AlgebraicTopology.DoldKan.MorphComponents.{u1, u2} C _inst_1 _inst_2 X Z)
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.morph_components.post_comp AlgebraicTopology.DoldKan.MorphComponents.postCompₓ'. -/
 /-- A `morph_components` can be postcomposed with a morphism. -/
 @[simps]
 def postComp : MorphComponents X n Z' where
@@ -137,13 +165,21 @@ def postComp : MorphComponents X n Z' where
   b i := f.b i ≫ h
 #align algebraic_topology.dold_kan.morph_components.post_comp AlgebraicTopology.DoldKan.MorphComponents.postComp
 
+#print AlgebraicTopology.DoldKan.MorphComponents.postComp_φ /-
 @[simp]
 theorem postComp_φ : (f.postComp h).φ = f.φ ≫ h :=
   by
   unfold φ post_comp
   simp only [add_comp, sum_comp, assoc]
 #align algebraic_topology.dold_kan.morph_components.post_comp_φ AlgebraicTopology.DoldKan.MorphComponents.postComp_φ
+-/
 
+/- warning: algebraic_topology.dold_kan.morph_components.pre_comp -> AlgebraicTopology.DoldKan.MorphComponents.preComp is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {X' : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {n : Nat} {Z : C}, (AlgebraicTopology.DoldKan.MorphComponents.{u1, u2} C _inst_1 _inst_2 X n Z) -> (Quiver.Hom.{succ u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1))) X' X) -> (AlgebraicTopology.DoldKan.MorphComponents.{u1, u2} C _inst_1 _inst_2 X' n Z)
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] {_inst_2 : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {X' : Nat} {n : C}, (AlgebraicTopology.DoldKan.MorphComponents.{u1, u2} C _inst_1 _inst_2 X' n) -> (Quiver.Hom.{succ u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1))) X _inst_2) -> (AlgebraicTopology.DoldKan.MorphComponents.{u1, u2} C _inst_1 X X' n)
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.morph_components.pre_comp AlgebraicTopology.DoldKan.MorphComponents.preCompₓ'. -/
 /-- A `morph_components` can be precomposed with a morphism of simplicial objects. -/
 @[simps]
 def preComp : MorphComponents X' n Z
@@ -152,6 +188,7 @@ def preComp : MorphComponents X' n Z
   b i := g.app (op [n]) ≫ f.b i
 #align algebraic_topology.dold_kan.morph_components.pre_comp AlgebraicTopology.DoldKan.MorphComponents.preComp
 
+#print AlgebraicTopology.DoldKan.MorphComponents.preComp_φ /-
 @[simp]
 theorem preComp_φ : (f.preComp g).φ = g.app (op [n + 1]) ≫ f.φ :=
   by
@@ -161,6 +198,7 @@ theorem preComp_φ : (f.preComp g).φ = g.app (op [n + 1]) ≫ f.φ :=
   · simp only [P_f_naturality_assoc]
   · simp only [comp_sum, P_f_naturality_assoc, simplicial_object.δ_naturality_assoc]
 #align algebraic_topology.dold_kan.morph_components.pre_comp_φ AlgebraicTopology.DoldKan.MorphComponents.preComp_φ
+-/
 
 end MorphComponents

bump to nightly-2023-04-20-20

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

e863e061

Diff

@@ -103,7 +103,7 @@ variable {X} {n : ℕ} {Z Z' : C} (f : MorphComponents X n Z) (g : X' ⟶ X) (h
 
 /-- The morphism `X _[n+1] ⟶ Z ` associated to `f : morph_components X n Z`. -/
 def φ {Z : C} (f : MorphComponents X n Z) : X _[n + 1] ⟶ Z :=
-  pInfty.f (n + 1) ≫ f.a + ∑ i : Fin (n + 1), (P i).f (n + 1) ≫ X.δ i.rev.succ ≫ f.b i.rev
+  PInfty.f (n + 1) ≫ f.a + ∑ i : Fin (n + 1), (P i).f (n + 1) ≫ X.δ i.rev.succ ≫ f.b i.rev
 #align algebraic_topology.dold_kan.morph_components.φ AlgebraicTopology.DoldKan.MorphComponents.φ
 
 variable (X n)
@@ -113,7 +113,7 @@ variable (X n)
 @[simps]
 def id : MorphComponents X n (X _[n + 1])
     where
-  a := pInfty.f (n + 1)
+  a := PInfty.f (n + 1)
   b i := X.σ i
 #align algebraic_topology.dold_kan.morph_components.id AlgebraicTopology.DoldKan.MorphComponents.id

bump to nightly-2023-04-20-16

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

3940090c

Diff

@@ -52,9 +52,9 @@ simplicial abelian groups, any $(n+1)$-simplex $x$ can be decomposed as
 $x = x' + \sum (i=0}^{q-1} σ_{n-i}(y_i)$ where $x'$ is in the image of `P q` and
 the $y_i$ are in degree $n$. -/
 theorem decomposition_q (n q : ℕ) :
-    ((q q).f (n + 1) : X _[n + 1] ⟶ X _[n + 1]) =
+    ((Q q).f (n + 1) : X _[n + 1] ⟶ X _[n + 1]) =
       ∑ i : Fin (n + 1) in Finset.filter (fun i : Fin (n + 1) => (i : ℕ) < q) Finset.univ,
-        (p i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev :=
+        (P i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ i.rev :=
   by
   induction' q with q hq
   ·
@@ -103,7 +103,7 @@ variable {X} {n : ℕ} {Z Z' : C} (f : MorphComponents X n Z) (g : X' ⟶ X) (h
 
 /-- The morphism `X _[n+1] ⟶ Z ` associated to `f : morph_components X n Z`. -/
 def φ {Z : C} (f : MorphComponents X n Z) : X _[n + 1] ⟶ Z :=
-  pInfty.f (n + 1) ≫ f.a + ∑ i : Fin (n + 1), (p i).f (n + 1) ≫ X.δ i.rev.succ ≫ f.b i.rev
+  pInfty.f (n + 1) ≫ f.a + ∑ i : Fin (n + 1), (P i).f (n + 1) ≫ X.δ i.rev.succ ≫ f.b i.rev
 #align algebraic_topology.dold_kan.morph_components.φ AlgebraicTopology.DoldKan.MorphComponents.φ
 
 variable (X n)

bump to nightly-2023-04-20-12

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

ffd433f8

Diff

@@ -79,7 +79,7 @@ theorem decomposition_q (n q : ℕ) :
           Nat.lt_succ_iff_lt_or_eq, Fin.ext_iff]
         tauto
       · have hnaq' : n = a + q := by linarith
-        simpa only [Fin.val_mk, (higher_faces_vanish.of_P q n).comp_hσ_eq hnaq', q'.rev_eq hnaq',
+        simpa only [Fin.val_mk, (higher_faces_vanish.of_P q n).comp_Hσ_eq hnaq', q'.rev_eq hnaq',
           neg_neg]
       · simp only [Finset.mem_filter, Fin.val_mk, lt_self_iff_false, and_false_iff, not_false_iff]
 #align algebraic_topology.dold_kan.decomposition_Q AlgebraicTopology.DoldKan.decomposition_q

bump to nightly-2023-03-17-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

c85864d4

Diff

@@ -123,7 +123,7 @@ theorem id_φ : (id X n).φ = 𝟙 _ :=
   simp only [← P_add_Q_f (n + 1) (n + 1), φ]
   congr 1
   · simp only [id, P_infty_f, P_f_idem]
-  · convert (decomposition_Q n (n + 1)).symm
+  · convert(decomposition_Q n (n + 1)).symm
     ext i
     simpa only [Finset.mem_univ, Finset.mem_filter, true_and_iff, true_iff_iff] using Fin.is_lt i
 #align algebraic_topology.dold_kan.morph_components.id_φ AlgebraicTopology.DoldKan.MorphComponents.id_φ

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

chore: classify porting notes referring to missing linters (#12098)

Reference the newly created issues #12094 and #12096, as well as the pre-existing #5171. Change all references to #10927 to #5171. Some of these changes were not labelled as "porting note"; change this for good measure.

c5b5490c

Diff

@@ -84,7 +84,7 @@ set_option linter.uppercaseLean3 false in
 
 variable (X)
 
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 /-- The structure `MorphComponents` is an ad hoc structure that is used in
 the proof that `N₁ : SimplicialObject C ⥤ Karoubi (ChainComplex C ℕ))`
 reflects isomorphisms. The fields are the data that are needed in order to

refactor: optimize proofs with omega (#11093)

I ran tryAtEachStep on all files under Mathlib to find all locations where omega succeeds. For each that was a linarith without an only, I tried replacing it with omega, and I verified that elaboration time got smaller. (In almost all cases, there was a noticeable speedup.) I also replaced some slow aesops along the way.

37bc4aba

Diff

@@ -58,11 +58,11 @@ theorem decomposition_Q (n q : ℕ) :
       Finset.filter_False, Finset.sum_empty]
   · by_cases hqn : q + 1 ≤ n + 1
     swap
-    · rw [Q_is_eventually_constant (show n + 1 ≤ q by linarith), hq]
+    · rw [Q_is_eventually_constant (show n + 1 ≤ q by omega), hq]
       congr 1
       ext ⟨x, hx⟩
       simp only [Nat.succ_eq_add_one, Finset.mem_filter, Finset.mem_univ, true_and]
-      constructor <;> intro <;> linarith
+      omega
     · cases' Nat.le.dest (Nat.succ_le_succ_iff.mp hqn) with a ha
       rw [Q_succ, HomologicalComplex.sub_f_apply, HomologicalComplex.comp_f, hq]
       symm
@@ -70,7 +70,7 @@ theorem decomposition_Q (n q : ℕ) :
       let q' : Fin (n + 1) := ⟨q, Nat.succ_le_iff.mp hqn⟩
       rw [← @Finset.add_sum_erase _ _ _ _ _ _ q' (by simp)]
       congr
-      · have hnaq' : n = a + q := by linarith
+      · have hnaq' : n = a + q := by omega
         simp only [Fin.val_mk, (HigherFacesVanish.of_P q n).comp_Hσ_eq hnaq',
           q'.rev_eq hnaq', neg_neg]
         rfl

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

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

38bce757

Diff

@@ -75,7 +75,7 @@ theorem decomposition_Q (n q : ℕ) :
           q'.rev_eq hnaq', neg_neg]
         rfl
       · ext ⟨i, hi⟩
-        simp only [Nat.succ_eq_add_one, Nat.lt_succ_iff_lt_or_eq, Finset.mem_univ,
+        simp only [q', Nat.succ_eq_add_one, Nat.lt_succ_iff_lt_or_eq, Finset.mem_univ,
           forall_true_left, Finset.mem_filter, lt_self_iff_false, or_true, and_self, not_true,
           Finset.mem_erase, ne_eq, Fin.mk.injEq, true_and]
         aesop

chore: classify removed @[nolint has_nonempty_instance] porting notes (#10929)

Classifies by adding issue number (#10927) to porting notes claiming removed @[nolint has_nonempty_instance].

2599c3bb

Diff

@@ -84,7 +84,7 @@ set_option linter.uppercaseLean3 false in
 
 variable (X)
 
--- porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 /-- The structure `MorphComponents` is an ad hoc structure that is used in
 the proof that `N₁ : SimplicialObject C ⥤ Karoubi (ChainComplex C ℕ))`
 reflects isomorphisms. The fields are the data that are needed in order to

chore: remove trailing space in backticks (#7617)

This will improve spaces in the mathlib4 docs.

9106dcf8

Diff

@@ -100,7 +100,7 @@ namespace MorphComponents
 
 variable {X} {n : ℕ} {Z Z' : C} (f : MorphComponents X n Z) (g : X' ⟶ X) (h : Z ⟶ Z')
 
-/-- The morphism `X _[n+1] ⟶ Z ` associated to `f : MorphComponents X n Z`. -/
+/-- The morphism `X _[n+1] ⟶ Z` associated to `f : MorphComponents X n Z`. -/
 def φ {Z : C} (f : MorphComponents X n Z) : X _[n + 1] ⟶ Z :=
   PInfty.f (n + 1) ≫ f.a + ∑ i : Fin (n + 1), (P i).f (n + 1) ≫ X.δ i.rev.succ ≫
     f.b (Fin.rev i)

chore: replace Fin.castIso and Fin.revPerm with Fin.cast and Fin.rev for the bump of Std (#5847)

Some theorems in Data.Fin.Basic are copied to Std at the recent commit in Std. These are written using Fin.cast and Fin.rev, so declarations using Fin.castIso and Fin.revPerm in Mathlib should be rewritten.

Co-authored-by: Pol'tta / Miyahara Kō <52843868+Komyyy@users.noreply.github.com> Co-authored-by: Johan Commelin <johan@commelin.net>

45b31dda

Diff

@@ -52,7 +52,7 @@ the $y_i$ are in degree $n$. -/
 theorem decomposition_Q (n q : ℕ) :
     ((Q q).f (n + 1) : X _[n + 1] ⟶ X _[n + 1]) =
       ∑ i : Fin (n + 1) in Finset.filter (fun i : Fin (n + 1) => (i : ℕ) < q) Finset.univ,
-        (P i).f (n + 1) ≫ X.δ i.revPerm.succ ≫ X.σ (Fin.revPerm i) := by
+        (P i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ (Fin.rev i) := by
   induction' q with q hq
   · simp only [Nat.zero_eq, Q_zero, HomologicalComplex.zero_f_apply, Nat.not_lt_zero,
       Finset.filter_False, Finset.sum_empty]
@@ -72,7 +72,7 @@ theorem decomposition_Q (n q : ℕ) :
       congr
       · have hnaq' : n = a + q := by linarith
         simp only [Fin.val_mk, (HigherFacesVanish.of_P q n).comp_Hσ_eq hnaq',
-          q'.revPerm_eq hnaq', neg_neg]
+          q'.rev_eq hnaq', neg_neg]
         rfl
       · ext ⟨i, hi⟩
         simp only [Nat.succ_eq_add_one, Nat.lt_succ_iff_lt_or_eq, Finset.mem_univ,
@@ -102,8 +102,8 @@ variable {X} {n : ℕ} {Z Z' : C} (f : MorphComponents X n Z) (g : X' ⟶ X) (h
 
 /-- The morphism `X _[n+1] ⟶ Z ` associated to `f : MorphComponents X n Z`. -/
 def φ {Z : C} (f : MorphComponents X n Z) : X _[n + 1] ⟶ Z :=
-  PInfty.f (n + 1) ≫ f.a + ∑ i : Fin (n + 1), (P i).f (n + 1) ≫ X.δ i.revPerm.succ ≫
-    f.b (Fin.revPerm i)
+  PInfty.f (n + 1) ≫ f.a + ∑ i : Fin (n + 1), (P i).f (n + 1) ≫ X.δ i.rev.succ ≫
+    f.b (Fin.rev i)
 #align algebraic_topology.dold_kan.morph_components.φ AlgebraicTopology.DoldKan.MorphComponents.φ
 
 variable (X n)

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

cf01bdac

Diff

@@ -5,7 +5,7 @@ Authors: Joël Riou
 -/
 import Mathlib.AlgebraicTopology.DoldKan.PInfty
 
-#align_import algebraic_topology.dold_kan.decomposition from "leanprover-community/mathlib"@"9af20344b24ef1801b599d296aaed8b9fffdc360"
+#align_import algebraic_topology.dold_kan.decomposition 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

@@ -27,6 +27,8 @@ role in the proof that the functor
 `N₁ : SimplicialObject C ⥤ Karoubi (ChainComplex C ℕ))`
 reflects isomorphisms.
 
+(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

@@ -39,7 +39,7 @@ namespace AlgebraicTopology
 
 namespace DoldKan
 
-variable {C : Type _} [Category C] [Preadditive C] {X X' : SimplicialObject C}
+variable {C : Type*} [Category C] [Preadditive C] {X X' : SimplicialObject C}
 
 /-- In each positive degree, this lemma decomposes the idempotent endomorphism
 `Q q` as a sum of morphisms which are postcompositions with suitable degeneracies.

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
-
-! This file was ported from Lean 3 source module algebraic_topology.dold_kan.decomposition
-! leanprover-community/mathlib commit 9af20344b24ef1801b599d296aaed8b9fffdc360
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicTopology.DoldKan.PInfty
 
+#align_import algebraic_topology.dold_kan.decomposition from "leanprover-community/mathlib"@"9af20344b24ef1801b599d296aaed8b9fffdc360"
+
 /-!
 
 # Decomposition of the Q endomorphisms

chore: rename Fin.rev to Fin.revPerm (#5715)

24d17585

Diff

@@ -53,7 +53,7 @@ the $y_i$ are in degree $n$. -/
 theorem decomposition_Q (n q : ℕ) :
     ((Q q).f (n + 1) : X _[n + 1] ⟶ X _[n + 1]) =
       ∑ i : Fin (n + 1) in Finset.filter (fun i : Fin (n + 1) => (i : ℕ) < q) Finset.univ,
-        (P i).f (n + 1) ≫ X.δ i.rev.succ ≫ X.σ (Fin.rev i) := by
+        (P i).f (n + 1) ≫ X.δ i.revPerm.succ ≫ X.σ (Fin.revPerm i) := by
   induction' q with q hq
   · simp only [Nat.zero_eq, Q_zero, HomologicalComplex.zero_f_apply, Nat.not_lt_zero,
       Finset.filter_False, Finset.sum_empty]
@@ -73,7 +73,7 @@ theorem decomposition_Q (n q : ℕ) :
       congr
       · have hnaq' : n = a + q := by linarith
         simp only [Fin.val_mk, (HigherFacesVanish.of_P q n).comp_Hσ_eq hnaq',
-          q'.rev_eq hnaq', neg_neg]
+          q'.revPerm_eq hnaq', neg_neg]
         rfl
       · ext ⟨i, hi⟩
         simp only [Nat.succ_eq_add_one, Nat.lt_succ_iff_lt_or_eq, Finset.mem_univ,
@@ -103,7 +103,8 @@ variable {X} {n : ℕ} {Z Z' : C} (f : MorphComponents X n Z) (g : X' ⟶ X) (h
 
 /-- The morphism `X _[n+1] ⟶ Z ` associated to `f : MorphComponents X n Z`. -/
 def φ {Z : C} (f : MorphComponents X n Z) : X _[n + 1] ⟶ Z :=
-  PInfty.f (n + 1) ≫ f.a + ∑ i : Fin (n + 1), (P i).f (n + 1) ≫ X.δ i.rev.succ ≫ f.b (Fin.rev i)
+  PInfty.f (n + 1) ≫ f.a + ∑ i : Fin (n + 1), (P i).f (n + 1) ≫ X.δ i.revPerm.succ ≫
+    f.b (Fin.revPerm i)
 #align algebraic_topology.dold_kan.morph_components.φ AlgebraicTopology.DoldKan.MorphComponents.φ
 
 variable (X n)

chore: remove occurrences of semicolon after space (#5713)

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

c795bd35

Diff

@@ -121,7 +121,7 @@ theorem id_φ : (id X n).φ = 𝟙 _ := by
   simp only [← P_add_Q_f (n + 1) (n + 1), φ]
   congr 1
   · simp only [id, PInfty_f, P_f_idem]
-  · exact Eq.trans (by congr ; simp) (decomposition_Q n (n + 1)).symm
+  · exact Eq.trans (by congr; simp) (decomposition_Q n (n + 1)).symm
 #align algebraic_topology.dold_kan.morph_components.id_φ AlgebraicTopology.DoldKan.MorphComponents.id_φ
 
 variable {X 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

@@ -75,7 +75,7 @@ theorem decomposition_Q (n q : ℕ) :
         simp only [Fin.val_mk, (HigherFacesVanish.of_P q n).comp_Hσ_eq hnaq',
           q'.rev_eq hnaq', neg_neg]
         rfl
-      . ext ⟨i, hi⟩
+      · ext ⟨i, hi⟩
         simp only [Nat.succ_eq_add_one, Nat.lt_succ_iff_lt_or_eq, Finset.mem_univ,
           forall_true_left, Finset.mem_filter, lt_self_iff_false, or_true, and_self, not_true,
           Finset.mem_erase, ne_eq, Fin.mk.injEq, true_and]
@@ -121,7 +121,7 @@ theorem id_φ : (id X n).φ = 𝟙 _ := by
   simp only [← P_add_Q_f (n + 1) (n + 1), φ]
   congr 1
   · simp only [id, PInfty_f, P_f_idem]
-  . exact Eq.trans (by congr ; simp) (decomposition_Q n (n + 1)).symm
+  · exact Eq.trans (by congr ; simp) (decomposition_Q n (n + 1)).symm
 #align algebraic_topology.dold_kan.morph_components.id_φ AlgebraicTopology.DoldKan.MorphComponents.id_φ
 
 variable {X n}