algebraic_topology.dold_kan.projections

(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

@@ -30,6 +30,8 @@ By passing to the limit, these endomorphisms `P q` shall be used in `p_infty.lea
 in order to define `P_infty : K[X] ⟶ K[X]`, see `equivalence.lean` for the general
 strategy of proof of the Dold-Kan equivalence.
 
+(See `equivalence.lean` for the general strategy of proof of the Dold-Kan equivalence.)
+
 -/
 
 open category_theory category_theory.category category_theory.limits

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -138,7 +138,7 @@ theorem comp_P_eq_self {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFa
       simp only [v.of_succ.comp_Hσ_eq hnaq, neg_eq_zero, ← assoc]
       have eq :=
         v ⟨a, by linarith⟩ (by simp only [hnaq, Fin.val_mk, Nat.succ_eq_add_one, add_assoc])
-      simp only [Fin.succ_mk] at eq 
+      simp only [Fin.succ_mk] at eq
       simp only [Eq, zero_comp]
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_P_eq_self AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self
 -/

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 -/
-import Mathbin.AlgebraicTopology.DoldKan.Faces
-import Mathbin.CategoryTheory.Idempotents.Basic
+import AlgebraicTopology.DoldKan.Faces
+import CategoryTheory.Idempotents.Basic
 
 #align_import algebraic_topology.dold_kan.projections from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"

bump to nightly-2023-08-06-03

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

b0e28731

Diff

@@ -6,7 +6,7 @@ Authors: Joël Riou
 import Mathbin.AlgebraicTopology.DoldKan.Faces
 import Mathbin.CategoryTheory.Idempotents.Basic
 
-#align_import algebraic_topology.dold_kan.projections from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"
+#align_import algebraic_topology.dold_kan.projections from "leanprover-community/mathlib"@"32a7e535287f9c73f2e4d2aef306a39190f0b504"
 
 /-!
 
@@ -31,6 +31,8 @@ By passing to the limit, these endomorphisms `P q` shall be used in `p_infty.lea
 in order to define `P_infty : K[X] ⟶ K[X]`, see `equivalence.lean` for the general
 strategy of proof of the Dold-Kan equivalence.
 
+(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

@@ -2,15 +2,12 @@
 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.projections
-! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicTopology.DoldKan.Faces
 import Mathbin.CategoryTheory.Idempotents.Basic
 
+#align_import algebraic_topology.dold_kan.projections from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"
+
 /-!
 
 # Construction of projections for the Dold-Kan correspondence

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -79,12 +79,16 @@ def Q (q : ℕ) : K[X] ⟶ K[X] :=
 #align algebraic_topology.dold_kan.Q AlgebraicTopology.DoldKan.Q
 -/
 
+#print AlgebraicTopology.DoldKan.P_add_Q /-
 theorem P_add_Q (q : ℕ) : P q + Q q = 𝟙 K[X] := by rw [Q]; abel
 #align algebraic_topology.dold_kan.P_add_Q AlgebraicTopology.DoldKan.P_add_Q
+-/
 
+#print AlgebraicTopology.DoldKan.P_add_Q_f /-
 theorem P_add_Q_f (q n : ℕ) : (P q).f n + (Q q).f n = 𝟙 (X _[n]) :=
   HomologicalComplex.congr_hom (P_add_Q q) n
 #align algebraic_topology.dold_kan.P_add_Q_f AlgebraicTopology.DoldKan.P_add_Q_f
+-/
 
 #print AlgebraicTopology.DoldKan.Q_zero /-
 @[simp]
@@ -93,9 +97,11 @@ theorem Q_zero : (Q 0 : K[X] ⟶ _) = 0 :=
 #align algebraic_topology.dold_kan.Q_eq_zero AlgebraicTopology.DoldKan.Q_zero
 -/
 
+#print AlgebraicTopology.DoldKan.Q_succ /-
 theorem Q_succ (q : ℕ) : (Q (q + 1) : K[X] ⟶ _) = Q q - P q ≫ hσ q := by unfold Q P;
   simp only [comp_add, comp_id]; abel
 #align algebraic_topology.dold_kan.Q_eq AlgebraicTopology.DoldKan.Q_succ
+-/
 
 #print AlgebraicTopology.DoldKan.Q_f_0_eq /-
 /-- All the `Q q` coincide with `0` in degree 0. -/
@@ -107,13 +113,16 @@ theorem Q_f_0_eq (q : ℕ) : ((Q q).f 0 : X _[0] ⟶ X _[0]) = 0 := by
 
 namespace HigherFacesVanish
 
+#print AlgebraicTopology.DoldKan.HigherFacesVanish.of_P /-
 /-- This lemma expresses the vanishing of
 `(P q).f (n+1) ≫ X.δ k : X _[n+1] ⟶ X _[n]` when `k≠0` and `k≥n-q+2` -/
 theorem of_P : ∀ q n : ℕ, HigherFacesVanish q ((P q).f (n + 1) : X _[n + 1] ⟶ X _[n + 1])
   | 0 => fun n j hj₁ => by exfalso; have hj₂ := Fin.is_lt j; linarith
   | q + 1 => fun n => by unfold P; exact (of_P q n).induction
 #align algebraic_topology.dold_kan.higher_faces_vanish.of_P AlgebraicTopology.DoldKan.HigherFacesVanish.of_P
+-/
 
+#print AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self /-
 @[reassoc]
 theorem comp_P_eq_self {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ) :
     φ ≫ (P q).f (n + 1) = φ := by
@@ -133,9 +142,11 @@ theorem comp_P_eq_self {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFa
       simp only [Fin.succ_mk] at eq 
       simp only [Eq, zero_comp]
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_P_eq_self AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self
+-/
 
 end HigherFacesVanish
 
+#print AlgebraicTopology.DoldKan.comp_P_eq_self_iff /-
 theorem comp_P_eq_self_iff {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} :
     φ ≫ (P q).f (n + 1) = φ ↔ HigherFacesVanish q φ :=
   by
@@ -146,6 +157,7 @@ theorem comp_P_eq_self_iff {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} :
     apply higher_faces_vanish.of_P
   · exact higher_faces_vanish.comp_P_eq_self
 #align algebraic_topology.dold_kan.comp_P_eq_self_iff AlgebraicTopology.DoldKan.comp_P_eq_self_iff
+-/
 
 #print AlgebraicTopology.DoldKan.P_f_idem /-
 @[simp, reassoc]
@@ -196,12 +208,15 @@ def natTransP (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapComp
 #align algebraic_topology.dold_kan.nat_trans_P AlgebraicTopology.DoldKan.natTransP
 -/
 
+#print AlgebraicTopology.DoldKan.P_f_naturality /-
 @[simp, reassoc]
 theorem P_f_naturality (q n : ℕ) {X Y : SimplicialObject C} (f : X ⟶ Y) :
     f.app (op [n]) ≫ (P q).f n = (P q).f n ≫ f.app (op [n]) :=
   HomologicalComplex.congr_hom ((natTransP q).naturality f) n
 #align algebraic_topology.dold_kan.P_f_naturality AlgebraicTopology.DoldKan.P_f_naturality
+-/
 
+#print AlgebraicTopology.DoldKan.Q_f_naturality /-
 @[simp, reassoc]
 theorem Q_f_naturality (q n : ℕ) {X Y : SimplicialObject C} (f : X ⟶ Y) :
     f.app (op [n]) ≫ (Q q).f n = (Q q).f n ≫ f.app (op [n]) :=
@@ -211,6 +226,7 @@ theorem Q_f_naturality (q n : ℕ) {X Y : SimplicialObject C} (f : X ⟶ Y) :
   dsimp
   simp only [comp_id, id_comp]
 #align algebraic_topology.dold_kan.Q_f_naturality AlgebraicTopology.DoldKan.Q_f_naturality
+-/
 
 #print AlgebraicTopology.DoldKan.natTransQ /-
 /-- For each `q`, `Q q` is a natural transformation. -/
@@ -219,6 +235,7 @@ def natTransQ (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapComp
 #align algebraic_topology.dold_kan.nat_trans_Q AlgebraicTopology.DoldKan.natTransQ
 -/
 
+#print AlgebraicTopology.DoldKan.map_P /-
 theorem map_P {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n : ℕ) :
     G.map ((P q : K[X] ⟶ _).f n) = (P q : K[((whiskering C D).obj G).obj X] ⟶ _).f n :=
@@ -230,7 +247,9 @@ theorem map_P {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additiv
     simp only [comp_add, HomologicalComplex.comp_f, HomologicalComplex.add_f_apply, comp_id,
       functor.map_add, functor.map_comp, hq, map_Hσ]
 #align algebraic_topology.dold_kan.map_P AlgebraicTopology.DoldKan.map_P
+-/
 
+#print AlgebraicTopology.DoldKan.map_Q /-
 theorem map_Q {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n : ℕ) :
     G.map ((Q q : K[X] ⟶ _).f n) = (Q q : K[((whiskering C D).obj G).obj X] ⟶ _).f n :=
@@ -239,6 +258,7 @@ theorem map_Q {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additiv
     P_add_Q_f]
   apply G.map_id
 #align algebraic_topology.dold_kan.map_Q AlgebraicTopology.DoldKan.map_Q
+-/
 
 end DoldKan

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -37,8 +37,8 @@ strategy of proof of the Dold-Kan equivalence.
 -/
 
 
-open
-  CategoryTheory CategoryTheory.Category CategoryTheory.Limits CategoryTheory.Preadditive CategoryTheory.SimplicialObject Opposite CategoryTheory.Idempotents
+open CategoryTheory CategoryTheory.Category CategoryTheory.Limits CategoryTheory.Preadditive
+  CategoryTheory.SimplicialObject Opposite CategoryTheory.Idempotents
 
 open scoped Simplicial DoldKan
 
@@ -130,7 +130,7 @@ theorem comp_P_eq_self {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFa
       simp only [v.of_succ.comp_Hσ_eq hnaq, neg_eq_zero, ← assoc]
       have eq :=
         v ⟨a, by linarith⟩ (by simp only [hnaq, Fin.val_mk, Nat.succ_eq_add_one, add_assoc])
-      simp only [Fin.succ_mk] at eq
+      simp only [Fin.succ_mk] at eq 
       simp only [Eq, zero_comp]
 #align algebraic_topology.dold_kan.higher_faces_vanish.comp_P_eq_self AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -40,7 +40,7 @@ strategy of proof of the Dold-Kan equivalence.
 open
   CategoryTheory CategoryTheory.Category CategoryTheory.Limits CategoryTheory.Preadditive CategoryTheory.SimplicialObject Opposite CategoryTheory.Idempotents
 
-open Simplicial DoldKan
+open scoped Simplicial DoldKan
 
 noncomputable section

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -79,15 +79,9 @@ def Q (q : ℕ) : K[X] ⟶ K[X] :=
 #align algebraic_topology.dold_kan.Q AlgebraicTopology.DoldKan.Q
 -/
 
-/- warning: algebraic_topology.dold_kan.P_add_Q -> AlgebraicTopology.DoldKan.P_add_Q is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_add_Q AlgebraicTopology.DoldKan.P_add_Qₓ'. -/
 theorem P_add_Q (q : ℕ) : P q + Q q = 𝟙 K[X] := by rw [Q]; abel
 #align algebraic_topology.dold_kan.P_add_Q AlgebraicTopology.DoldKan.P_add_Q
 
-/- warning: algebraic_topology.dold_kan.P_add_Q_f -> AlgebraicTopology.DoldKan.P_add_Q_f is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_add_Q_f AlgebraicTopology.DoldKan.P_add_Q_fₓ'. -/
 theorem P_add_Q_f (q n : ℕ) : (P q).f n + (Q q).f n = 𝟙 (X _[n]) :=
   HomologicalComplex.congr_hom (P_add_Q q) n
 #align algebraic_topology.dold_kan.P_add_Q_f AlgebraicTopology.DoldKan.P_add_Q_f
@@ -99,9 +93,6 @@ theorem Q_zero : (Q 0 : K[X] ⟶ _) = 0 :=
 #align algebraic_topology.dold_kan.Q_eq_zero AlgebraicTopology.DoldKan.Q_zero
 -/
 
-/- warning: algebraic_topology.dold_kan.Q_eq -> AlgebraicTopology.DoldKan.Q_succ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Q_eq AlgebraicTopology.DoldKan.Q_succₓ'. -/
 theorem Q_succ (q : ℕ) : (Q (q + 1) : K[X] ⟶ _) = Q q - P q ≫ hσ q := by unfold Q P;
   simp only [comp_add, comp_id]; abel
 #align algebraic_topology.dold_kan.Q_eq AlgebraicTopology.DoldKan.Q_succ
@@ -116,12 +107,6 @@ theorem Q_f_0_eq (q : ℕ) : ((Q q).f 0 : X _[0] ⟶ X _[0]) = 0 := by
 
 namespace HigherFacesVanish
 
-/- warning: algebraic_topology.dold_kan.higher_faces_vanish.of_P -> AlgebraicTopology.DoldKan.HigherFacesVanish.of_P 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} (q : Nat) (n : Nat), AlgebraicTopology.DoldKan.HigherFacesVanish.{u1, u2} C _inst_1 _inst_2 X (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))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (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))))) n q (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))))) Nat.hasOne) (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 q) (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.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] {X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1} (q : Nat) (n : Nat), AlgebraicTopology.DoldKan.HigherFacesVanish.{u2, u1} C _inst_1 _inst_2 X (HomologicalComplex.X.{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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u2, u1} 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)))) n q (HomologicalComplex.Hom.f.{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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u2, u1} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u2, u1} C _inst_1 _inst_2 X) (AlgebraicTopology.DoldKan.P.{u2, u1} C _inst_1 _inst_2 X q) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.of_P AlgebraicTopology.DoldKan.HigherFacesVanish.of_Pₓ'. -/
 /-- This lemma expresses the vanishing of
 `(P q).f (n+1) ≫ X.δ k : X _[n+1] ⟶ X _[n]` when `k≠0` and `k≥n-q+2` -/
 theorem of_P : ∀ q n : ℕ, HigherFacesVanish q ((P q).f (n + 1) : X _[n + 1] ⟶ X _[n + 1])
@@ -129,12 +114,6 @@ theorem of_P : ∀ q n : ℕ, HigherFacesVanish q ((P q).f (n + 1) : X _[n + 1]
   | q + 1 => fun n => by unfold P; exact (of_P q n).induction
 #align algebraic_topology.dold_kan.higher_faces_vanish.of_P AlgebraicTopology.DoldKan.HigherFacesVanish.of_P
 
-/- warning: algebraic_topology.dold_kan.higher_faces_vanish.comp_P_eq_self -> AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_P_eq_self AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_selfₓ'. -/
 @[reassoc]
 theorem comp_P_eq_self {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ) :
     φ ≫ (P q).f (n + 1) = φ := by
@@ -157,12 +136,6 @@ theorem comp_P_eq_self {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFa
 
 end HigherFacesVanish
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.comp_P_eq_self_iff AlgebraicTopology.DoldKan.comp_P_eq_self_iffₓ'. -/
 theorem comp_P_eq_self_iff {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} :
     φ ≫ (P q).f (n + 1) = φ ↔ HigherFacesVanish q φ :=
   by
@@ -223,18 +196,12 @@ def natTransP (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapComp
 #align algebraic_topology.dold_kan.nat_trans_P AlgebraicTopology.DoldKan.natTransP
 -/
 
-/- warning: algebraic_topology.dold_kan.P_f_naturality -> AlgebraicTopology.DoldKan.P_f_naturality is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_f_naturality AlgebraicTopology.DoldKan.P_f_naturalityₓ'. -/
 @[simp, reassoc]
 theorem P_f_naturality (q n : ℕ) {X Y : SimplicialObject C} (f : X ⟶ Y) :
     f.app (op [n]) ≫ (P q).f n = (P q).f n ≫ f.app (op [n]) :=
   HomologicalComplex.congr_hom ((natTransP q).naturality f) n
 #align algebraic_topology.dold_kan.P_f_naturality AlgebraicTopology.DoldKan.P_f_naturality
 
-/- warning: algebraic_topology.dold_kan.Q_f_naturality -> AlgebraicTopology.DoldKan.Q_f_naturality is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Q_f_naturality AlgebraicTopology.DoldKan.Q_f_naturalityₓ'. -/
 @[simp, reassoc]
 theorem Q_f_naturality (q n : ℕ) {X Y : SimplicialObject C} (f : X ⟶ Y) :
     f.app (op [n]) ≫ (Q q).f n = (Q q).f n ≫ f.app (op [n]) :=
@@ -252,9 +219,6 @@ def natTransQ (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapComp
 #align algebraic_topology.dold_kan.nat_trans_Q AlgebraicTopology.DoldKan.natTransQ
 -/
 
-/- warning: algebraic_topology.dold_kan.map_P -> AlgebraicTopology.DoldKan.map_P is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.map_P AlgebraicTopology.DoldKan.map_Pₓ'. -/
 theorem map_P {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n : ℕ) :
     G.map ((P q : K[X] ⟶ _).f n) = (P q : K[((whiskering C D).obj G).obj X] ⟶ _).f n :=
@@ -267,9 +231,6 @@ theorem map_P {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additiv
       functor.map_add, functor.map_comp, hq, map_Hσ]
 #align algebraic_topology.dold_kan.map_P AlgebraicTopology.DoldKan.map_P
 
-/- warning: algebraic_topology.dold_kan.map_Q -> AlgebraicTopology.DoldKan.map_Q is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.map_Q AlgebraicTopology.DoldKan.map_Qₓ'. -/
 theorem map_Q {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n : ℕ) :
     G.map ((Q q : K[X] ⟶ _).f n) = (Q q : K[((whiskering C D).obj G).obj X] ⟶ _).f n :=

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -82,10 +82,7 @@ def Q (q : ℕ) : K[X] ⟶ K[X] :=
 /- warning: algebraic_topology.dold_kan.P_add_Q -> AlgebraicTopology.DoldKan.P_add_Q is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_add_Q AlgebraicTopology.DoldKan.P_add_Qₓ'. -/
-theorem P_add_Q (q : ℕ) : P q + Q q = 𝟙 K[X] :=
-  by
-  rw [Q]
-  abel
+theorem P_add_Q (q : ℕ) : P q + Q q = 𝟙 K[X] := by rw [Q]; abel
 #align algebraic_topology.dold_kan.P_add_Q AlgebraicTopology.DoldKan.P_add_Q
 
 /- warning: algebraic_topology.dold_kan.P_add_Q_f -> AlgebraicTopology.DoldKan.P_add_Q_f is a dubious translation:
@@ -105,11 +102,8 @@ theorem Q_zero : (Q 0 : K[X] ⟶ _) = 0 :=
 /- warning: algebraic_topology.dold_kan.Q_eq -> AlgebraicTopology.DoldKan.Q_succ is a dubious translation:
 <too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Q_eq AlgebraicTopology.DoldKan.Q_succₓ'. -/
-theorem Q_succ (q : ℕ) : (Q (q + 1) : K[X] ⟶ _) = Q q - P q ≫ hσ q :=
-  by
-  unfold Q P
-  simp only [comp_add, comp_id]
-  abel
+theorem Q_succ (q : ℕ) : (Q (q + 1) : K[X] ⟶ _) = Q q - P q ≫ hσ q := by unfold Q P;
+  simp only [comp_add, comp_id]; abel
 #align algebraic_topology.dold_kan.Q_eq AlgebraicTopology.DoldKan.Q_succ
 
 #print AlgebraicTopology.DoldKan.Q_f_0_eq /-
@@ -131,13 +125,8 @@ Case conversion may be inaccurate. Consider using '#align algebraic_topology.dol
 /-- This lemma expresses the vanishing of
 `(P q).f (n+1) ≫ X.δ k : X _[n+1] ⟶ X _[n]` when `k≠0` and `k≥n-q+2` -/
 theorem of_P : ∀ q n : ℕ, HigherFacesVanish q ((P q).f (n + 1) : X _[n + 1] ⟶ X _[n + 1])
-  | 0 => fun n j hj₁ => by
-    exfalso
-    have hj₂ := Fin.is_lt j
-    linarith
-  | q + 1 => fun n => by
-    unfold P
-    exact (of_P q n).induction
+  | 0 => fun n j hj₁ => by exfalso; have hj₂ := Fin.is_lt j; linarith
+  | q + 1 => fun n => by unfold P; exact (of_P q n).induction
 #align algebraic_topology.dold_kan.higher_faces_vanish.of_P AlgebraicTopology.DoldKan.HigherFacesVanish.of_P
 
 /- warning: algebraic_topology.dold_kan.higher_faces_vanish.comp_P_eq_self -> AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self is a dubious translation:
@@ -204,19 +193,13 @@ theorem Q_f_idem (q n : ℕ) : ((Q q).f n : X _[n] ⟶ _) ≫ (Q q).f n = (Q q).
 
 #print AlgebraicTopology.DoldKan.P_idem /-
 @[simp, reassoc]
-theorem P_idem (q : ℕ) : (P q : K[X] ⟶ K[X]) ≫ P q = P q :=
-  by
-  ext n
-  exact P_f_idem q n
+theorem P_idem (q : ℕ) : (P q : K[X] ⟶ K[X]) ≫ P q = P q := by ext n; exact P_f_idem q n
 #align algebraic_topology.dold_kan.P_idem AlgebraicTopology.DoldKan.P_idem
 -/
 
 #print AlgebraicTopology.DoldKan.Q_idem /-
 @[simp, reassoc]
-theorem Q_idem (q : ℕ) : (Q q : K[X] ⟶ K[X]) ≫ Q q = Q q :=
-  by
-  ext n
-  exact Q_f_idem q n
+theorem Q_idem (q : ℕ) : (Q q : K[X] ⟶ K[X]) ≫ Q q = Q q := by ext n; exact Q_f_idem q n
 #align algebraic_topology.dold_kan.Q_idem AlgebraicTopology.DoldKan.Q_idem
 -/

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -80,10 +80,7 @@ def Q (q : ℕ) : K[X] ⟶ K[X] :=
 -/
 
 /- warning: algebraic_topology.dold_kan.P_add_Q -> AlgebraicTopology.DoldKan.P_add_Q is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_add_Q AlgebraicTopology.DoldKan.P_add_Qₓ'. -/
 theorem P_add_Q (q : ℕ) : P q + Q q = 𝟙 K[X] :=
   by
@@ -92,10 +89,7 @@ theorem P_add_Q (q : ℕ) : P q + Q q = 𝟙 K[X] :=
 #align algebraic_topology.dold_kan.P_add_Q AlgebraicTopology.DoldKan.P_add_Q
 
 /- warning: algebraic_topology.dold_kan.P_add_Q_f -> AlgebraicTopology.DoldKan.P_add_Q_f is a dubious translation:
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(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))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_add_Q_f AlgebraicTopology.DoldKan.P_add_Q_fₓ'. -/
 theorem P_add_Q_f (q n : ℕ) : (P q).f n + (Q q).f n = 𝟙 (X _[n]) :=
   HomologicalComplex.congr_hom (P_add_Q q) n
@@ -109,10 +103,7 @@ theorem Q_zero : (Q 0 : K[X] ⟶ _) = 0 :=
 -/
 
 /- warning: algebraic_topology.dold_kan.Q_eq -> AlgebraicTopology.DoldKan.Q_succ is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Q_eq AlgebraicTopology.DoldKan.Q_succₓ'. -/
 theorem Q_succ (q : ℕ) : (Q (q + 1) : K[X] ⟶ _) = Q q - P q ≫ hσ q :=
   by
@@ -250,10 +241,7 @@ def natTransP (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapComp
 -/
 
 /- warning: algebraic_topology.dold_kan.P_f_naturality -> AlgebraicTopology.DoldKan.P_f_naturality is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_f_naturality AlgebraicTopology.DoldKan.P_f_naturalityₓ'. -/
 @[simp, reassoc]
 theorem P_f_naturality (q n : ℕ) {X Y : SimplicialObject C} (f : X ⟶ Y) :
@@ -262,10 +250,7 @@ theorem P_f_naturality (q n : ℕ) {X Y : SimplicialObject C} (f : X ⟶ Y) :
 #align algebraic_topology.dold_kan.P_f_naturality AlgebraicTopology.DoldKan.P_f_naturality
 
 /- warning: algebraic_topology.dold_kan.Q_f_naturality -> AlgebraicTopology.DoldKan.Q_f_naturality is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Q_f_naturality AlgebraicTopology.DoldKan.Q_f_naturalityₓ'. -/
 @[simp, reassoc]
 theorem Q_f_naturality (q n : ℕ) {X Y : SimplicialObject C} (f : X ⟶ Y) :
@@ -285,10 +270,7 @@ def natTransQ (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapComp
 -/
 
 /- warning: algebraic_topology.dold_kan.map_P -> AlgebraicTopology.DoldKan.map_P is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.map_P AlgebraicTopology.DoldKan.map_Pₓ'. -/
 theorem map_P {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n : ℕ) :
@@ -303,10 +285,7 @@ theorem map_P {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additiv
 #align algebraic_topology.dold_kan.map_P AlgebraicTopology.DoldKan.map_P
 
 /- warning: algebraic_topology.dold_kan.map_Q -> AlgebraicTopology.DoldKan.map_Q is a dubious translation:
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(CategoryTheory.Functor.{u2, u3, u1, u4} C _inst_1 D _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max (max u1 u2) u4) u3} (CategoryTheory.Functor.{u2, u3, u1, u4} C _inst_1 D _inst_3) (CategoryTheory.Functor.category.{u2, u3, u1, u4} C _inst_1 D _inst_3))) (CategoryTheory.Functor.{u2, u3, max u1 u2, max u4 u3} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.{u3, u4} D _inst_3) (CategoryTheory.instCategorySimplicialObject.{u3, u4} D _inst_3)) (CategoryTheory.CategoryStruct.toQuiver.{max (max u1 u2) u3, max (max (max u1 u2) u4) u3} (CategoryTheory.Functor.{u2, u3, max u1 u2, max u4 u3} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.{u3, u4} D _inst_3) (CategoryTheory.instCategorySimplicialObject.{u3, u4} D _inst_3)) (CategoryTheory.Category.toCategoryStruct.{max (max u1 u2) u3, max (max (max u1 u2) u4) u3} (CategoryTheory.Functor.{u2, u3, max u1 u2, max u4 u3} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.{u3, u4} D _inst_3) (CategoryTheory.instCategorySimplicialObject.{u3, u4} D _inst_3)) (CategoryTheory.Functor.category.{u2, u3, max u1 u2, max u4 u3} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.{u3, u4} D _inst_3) (CategoryTheory.instCategorySimplicialObject.{u3, u4} D _inst_3)))) (CategoryTheory.Functor.toPrefunctor.{max u1 u3, max (max u1 u2) u3, max (max (max u1 u2) u4) u3, max (max (max u1 u2) u4) u3} (CategoryTheory.Functor.{u2, u3, u1, u4} C _inst_1 D _inst_3) (CategoryTheory.Functor.category.{u2, u3, u1, u4} C _inst_1 D _inst_3) (CategoryTheory.Functor.{u2, u3, max u1 u2, max u4 u3} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.{u3, u4} D _inst_3) (CategoryTheory.instCategorySimplicialObject.{u3, u4} D _inst_3)) (CategoryTheory.Functor.category.{u2, u3, max u1 u2, max u4 u3} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.{u3, u4} D _inst_3) (CategoryTheory.instCategorySimplicialObject.{u3, u4} D _inst_3)) (CategoryTheory.SimplicialObject.whiskering.{u2, u1, u4, u3} C _inst_1 D _inst_3)) G)) X)) (AlgebraicTopology.DoldKan.Q.{u4, u3} D _inst_3 _inst_4 (Prefunctor.obj.{succ u2, succ u3, max u1 u2, max u4 u3} (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) 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(CategoryTheory.Functor.{u2, u3, u1, u4} C _inst_1 D _inst_3) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max (max u1 u2) u4) u3} (CategoryTheory.Functor.{u2, u3, u1, u4} C _inst_1 D _inst_3) (CategoryTheory.Functor.category.{u2, u3, u1, u4} C _inst_1 D _inst_3))) (CategoryTheory.Functor.{u2, u3, max u1 u2, max u4 u3} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.{u3, u4} D _inst_3) (CategoryTheory.instCategorySimplicialObject.{u3, u4} D _inst_3)) (CategoryTheory.CategoryStruct.toQuiver.{max (max u1 u2) u3, max (max (max u1 u2) u4) u3} (CategoryTheory.Functor.{u2, u3, max u1 u2, max u4 u3} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.{u3, u4} D _inst_3) (CategoryTheory.instCategorySimplicialObject.{u3, u4} D _inst_3)) (CategoryTheory.Category.toCategoryStruct.{max (max u1 u2) u3, max (max (max u1 u2) u4) u3} (CategoryTheory.Functor.{u2, u3, max u1 u2, max u4 u3} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.{u3, u4} D _inst_3) (CategoryTheory.instCategorySimplicialObject.{u3, u4} D _inst_3)) (CategoryTheory.Functor.category.{u2, u3, max u1 u2, max u4 u3} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.{u3, u4} D _inst_3) (CategoryTheory.instCategorySimplicialObject.{u3, u4} D _inst_3)))) (CategoryTheory.Functor.toPrefunctor.{max u1 u3, max (max u1 u2) u3, max (max (max u1 u2) u4) u3, max (max (max u1 u2) u4) u3} (CategoryTheory.Functor.{u2, u3, u1, u4} C _inst_1 D _inst_3) (CategoryTheory.Functor.category.{u2, u3, u1, u4} C _inst_1 D _inst_3) (CategoryTheory.Functor.{u2, u3, max u1 u2, max u4 u3} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.{u3, u4} D _inst_3) (CategoryTheory.instCategorySimplicialObject.{u3, u4} D _inst_3)) (CategoryTheory.Functor.category.{u2, u3, max u1 u2, max u4 u3} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.{u3, u4} D _inst_3) (CategoryTheory.instCategorySimplicialObject.{u3, u4} D _inst_3)) (CategoryTheory.SimplicialObject.whiskering.{u2, u1, u4, u3} C _inst_1 D _inst_3)) G)) X) q) n)
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.map_Q AlgebraicTopology.DoldKan.map_Qₓ'. -/
 theorem map_Q {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n : ℕ) :

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -155,7 +155,7 @@ lean 3 declaration is
 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} {Y : C} {n : Nat} {q : Nat} {φ : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Y (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.HigherFacesVanish.{u1, u2} C _inst_1 _inst_2 X Y n q φ) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Y (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))))) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) Y (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.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)))) φ (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 q) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) φ)
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_P_eq_self AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_selfₓ'. -/
-@[reassoc.1]
+@[reassoc]
 theorem comp_P_eq_self {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ) :
     φ ≫ (P q).f (n + 1) = φ := by
   induction' q with q hq
@@ -195,7 +195,7 @@ theorem comp_P_eq_self_iff {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} :
 #align algebraic_topology.dold_kan.comp_P_eq_self_iff AlgebraicTopology.DoldKan.comp_P_eq_self_iff
 
 #print AlgebraicTopology.DoldKan.P_f_idem /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem P_f_idem (q n : ℕ) : ((P q).f n : X _[n] ⟶ _) ≫ (P q).f n = (P q).f n :=
   by
   cases n
@@ -205,14 +205,14 @@ theorem P_f_idem (q n : ℕ) : ((P q).f n : X _[n] ⟶ _) ≫ (P q).f n = (P q).
 -/
 
 #print AlgebraicTopology.DoldKan.Q_f_idem /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem Q_f_idem (q n : ℕ) : ((Q q).f n : X _[n] ⟶ _) ≫ (Q q).f n = (Q q).f n :=
   idem_of_id_sub_idem _ (P_f_idem q n)
 #align algebraic_topology.dold_kan.Q_f_idem AlgebraicTopology.DoldKan.Q_f_idem
 -/
 
 #print AlgebraicTopology.DoldKan.P_idem /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem P_idem (q : ℕ) : (P q : K[X] ⟶ K[X]) ≫ P q = P q :=
   by
   ext n
@@ -221,7 +221,7 @@ theorem P_idem (q : ℕ) : (P q : K[X] ⟶ K[X]) ≫ P q = P q :=
 -/
 
 #print AlgebraicTopology.DoldKan.Q_idem /-
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem Q_idem (q : ℕ) : (Q q : K[X] ⟶ K[X]) ≫ Q q = Q q :=
   by
   ext n
@@ -255,7 +255,7 @@ lean 3 declaration is
 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] (q : Nat) (n : Nat) {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {Y : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (f : 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 Y), 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 n))) (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 Y) n)) (CategoryTheory.CategoryStruct.comp.{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 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 Y) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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 Y) n) (CategoryTheory.NatTrans.app.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Y f (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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 Y) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 Y) (AlgebraicTopology.DoldKan.P.{u1, u2} C _inst_1 _inst_2 Y q) n)) (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) n) (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) 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 Y) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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 q) n) (CategoryTheory.NatTrans.app.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Y f (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_f_naturality AlgebraicTopology.DoldKan.P_f_naturalityₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem P_f_naturality (q n : ℕ) {X Y : SimplicialObject C} (f : X ⟶ Y) :
     f.app (op [n]) ≫ (P q).f n = (P q).f n ≫ f.app (op [n]) :=
   HomologicalComplex.congr_hom ((natTransP q).naturality f) n
@@ -267,7 +267,7 @@ lean 3 declaration is
 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] (q : Nat) (n : Nat) {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {Y : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (f : 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 Y), 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 n))) (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 Y) n)) (CategoryTheory.CategoryStruct.comp.{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 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 Y) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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 Y) n) (CategoryTheory.NatTrans.app.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Y f (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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 Y) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 Y) (AlgebraicTopology.DoldKan.Q.{u1, u2} C _inst_1 _inst_2 Y q) n)) (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) n) (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) 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 Y) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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.Q.{u1, u2} C _inst_1 _inst_2 X q) n) (CategoryTheory.NatTrans.app.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X Y f (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))))
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Q_f_naturality AlgebraicTopology.DoldKan.Q_f_naturalityₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem Q_f_naturality (q n : ℕ) {X Y : SimplicialObject C} (f : X ⟶ Y) :
     f.app (op [n]) ≫ (Q q).f n = (Q q).f n ≫ f.app (op [n]) :=
   by

bump to nightly-2023-04-22-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/52932b3a083d4142e78a15dc928084a22fea9ba0

21a90077

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.projections
-! leanprover-community/mathlib commit ed98c07faf6d9de3e52771d5b00394c4294ccb4d
+! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.CategoryTheory.Idempotents.Basic
 
 # Construction of projections for the Dold-Kan correspondence
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 TODO (@joelriou) continue adding the various files referenced below
 
 In this file, we construct endomorphisms `P q : K[X] ⟶ K[X]` for all

bump to nightly-2023-04-20-16

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

3940090c

Diff

@@ -47,62 +47,96 @@ namespace DoldKan
 
 variable {C : Type _} [Category C] [Preadditive C] {X : SimplicialObject C}
 
+#print AlgebraicTopology.DoldKan.P /-
 /-- This is the inductive definition of the projections `P q : K[X] ⟶ K[X]`,
 with `P 0 := 𝟙 _` and `P (q+1) := P q ≫ (𝟙 _ + Hσ q)`. -/
-noncomputable def p : ℕ → (K[X] ⟶ K[X])
+noncomputable def P : ℕ → (K[X] ⟶ K[X])
   | 0 => 𝟙 _
   | q + 1 => P q ≫ (𝟙 _ + hσ q)
-#align algebraic_topology.dold_kan.P AlgebraicTopology.DoldKan.p
+#align algebraic_topology.dold_kan.P AlgebraicTopology.DoldKan.P
+-/
 
+#print AlgebraicTopology.DoldKan.P_f_0_eq /-
 /-- All the `P q` coincide with `𝟙 _` in degree 0. -/
 @[simp]
-theorem p_f_0_eq (q : ℕ) : ((p q).f 0 : X _[0] ⟶ X _[0]) = 𝟙 _ :=
+theorem P_f_0_eq (q : ℕ) : ((P q).f 0 : X _[0] ⟶ X _[0]) = 𝟙 _ :=
   by
   induction' q with q hq
   · rfl
   · unfold P
     simp only [HomologicalComplex.add_f_apply, HomologicalComplex.comp_f, HomologicalComplex.id_f,
       id_comp, hq, Hσ_eq_zero, add_zero]
-#align algebraic_topology.dold_kan.P_f_0_eq AlgebraicTopology.DoldKan.p_f_0_eq
+#align algebraic_topology.dold_kan.P_f_0_eq AlgebraicTopology.DoldKan.P_f_0_eq
+-/
 
+#print AlgebraicTopology.DoldKan.Q /-
 /-- `Q q` is the complement projection associated to `P q` -/
-def q (q : ℕ) : K[X] ⟶ K[X] :=
-  𝟙 _ - p q
-#align algebraic_topology.dold_kan.Q AlgebraicTopology.DoldKan.q
+def Q (q : ℕ) : K[X] ⟶ K[X] :=
+  𝟙 _ - P q
+#align algebraic_topology.dold_kan.Q AlgebraicTopology.DoldKan.Q
+-/
 
-theorem p_add_q (q : ℕ) : p q + q q = 𝟙 K[X] :=
+/- warning: algebraic_topology.dold_kan.P_add_Q -> AlgebraicTopology.DoldKan.P_add_Q 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} (q : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, max u1 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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{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))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{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))))) Nat.hasOne)))) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X)) (HAdd.hAdd.{u2, u2, u2} (Quiver.Hom.{succ u2, max u1 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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{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))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{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))))) Nat.hasOne)))) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X)) (Quiver.Hom.{succ u2, max u1 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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{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))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{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))))) Nat.hasOne)))) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X)) (Quiver.Hom.{succ u2, max u1 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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{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))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{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))))) Nat.hasOne)))) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X)) (instHAdd.{u2} (Quiver.Hom.{succ u2, max u1 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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{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))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{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))))) Nat.hasOne)))) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X)) (HomologicalComplex.Quiver.Hom.hasAdd.{u2, u1, 0} Nat 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) (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 q) (AlgebraicTopology.DoldKan.Q.{u1, u2} C _inst_1 _inst_2 X q)) (CategoryTheory.CategoryStruct.id.{u2, max u1 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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{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))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{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 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+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} (q : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, max u2 u1} (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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{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.{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)) (HAdd.hAdd.{u2, u2, u2} (Quiver.Hom.{succ u2, max u2 u1} (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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{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.Category.toCategoryStruct.{u2, max u1 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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat 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)) (Quiver.Hom.{succ u2, max u2 u1} (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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{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.Category.toCategoryStruct.{u2, max u1 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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat 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)) (Quiver.Hom.{succ u2, max u2 u1} (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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_add_Q AlgebraicTopology.DoldKan.P_add_Qₓ'. -/
+theorem P_add_Q (q : ℕ) : P q + Q q = 𝟙 K[X] :=
   by
   rw [Q]
   abel
-#align algebraic_topology.dold_kan.P_add_Q AlgebraicTopology.DoldKan.p_add_q
-
-theorem p_add_q_f (q n : ℕ) : (p q).f n + (q q).f n = 𝟙 (X _[n]) :=
-  HomologicalComplex.congr_hom (p_add_q q) n
-#align algebraic_topology.dold_kan.P_add_Q_f AlgebraicTopology.DoldKan.p_add_q_f
-
+#align algebraic_topology.dold_kan.P_add_Q AlgebraicTopology.DoldKan.P_add_Q
+
+/- warning: algebraic_topology.dold_kan.P_add_Q_f -> AlgebraicTopology.DoldKan.P_add_Q_f is a dubious translation:
+lean 3 declaration is
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SimplexCategory (SimplexCategory.mk n))))
+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} (q : Nat) (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} 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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 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(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))))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_add_Q_f AlgebraicTopology.DoldKan.P_add_Q_fₓ'. -/
+theorem P_add_Q_f (q n : ℕ) : (P q).f n + (Q q).f n = 𝟙 (X _[n]) :=
+  HomologicalComplex.congr_hom (P_add_Q q) n
+#align algebraic_topology.dold_kan.P_add_Q_f AlgebraicTopology.DoldKan.P_add_Q_f
+
+#print AlgebraicTopology.DoldKan.Q_zero /-
 @[simp]
-theorem q_eq_zero : (q 0 : K[X] ⟶ _) = 0 :=
+theorem Q_zero : (Q 0 : K[X] ⟶ _) = 0 :=
   sub_self _
-#align algebraic_topology.dold_kan.Q_eq_zero AlgebraicTopology.DoldKan.q_eq_zero
+#align algebraic_topology.dold_kan.Q_eq_zero AlgebraicTopology.DoldKan.Q_zero
+-/
 
-theorem q_eq (q : ℕ) : (q (q + 1) : K[X] ⟶ _) = q q - p q ≫ hσ q :=
+/- warning: algebraic_topology.dold_kan.Q_eq -> AlgebraicTopology.DoldKan.Q_succ is a dubious translation:
+lean 3 declaration is
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+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} (q : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, max u2 u1} (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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat 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(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.Q.{u1, u2} C _inst_1 _inst_2 X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) q (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HSub.hSub.{u2, u2, u2} (Quiver.Hom.{succ u2, max u2 u1} (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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{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.Category.toCategoryStruct.{u2, max u1 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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat 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)) (Quiver.Hom.{succ u2, max u2 u1} (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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat 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)) (Quiver.Hom.{succ u2, max u2 u1} (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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{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.Category.toCategoryStruct.{u2, max u1 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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat 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)) (instHSub.{u2} (Quiver.Hom.{succ u2, max u2 u1} (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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{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.Category.toCategoryStruct.{u2, max u1 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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat 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)) (HomologicalComplex.instSubHomHomologicalComplexPreadditiveHasZeroMorphismsToQuiverToCategoryStructInstCategoryHomologicalComplex.{u2, u1, 0} Nat 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.Q.{u1, u2} C _inst_1 _inst_2 X q) (CategoryTheory.CategoryStruct.comp.{u2, max u2 u1} (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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (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 (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat 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.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.DoldKan.P.{u1, u2} C _inst_1 _inst_2 X q) (AlgebraicTopology.DoldKan.Hσ.{u1, u2} C _inst_1 _inst_2 X q)))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Q_eq AlgebraicTopology.DoldKan.Q_succₓ'. -/
+theorem Q_succ (q : ℕ) : (Q (q + 1) : K[X] ⟶ _) = Q q - P q ≫ hσ q :=
   by
   unfold Q P
   simp only [comp_add, comp_id]
   abel
-#align algebraic_topology.dold_kan.Q_eq AlgebraicTopology.DoldKan.q_eq
+#align algebraic_topology.dold_kan.Q_eq AlgebraicTopology.DoldKan.Q_succ
 
+#print AlgebraicTopology.DoldKan.Q_f_0_eq /-
 /-- All the `Q q` coincide with `0` in degree 0. -/
 @[simp]
-theorem q_f_0_eq (q : ℕ) : ((q q).f 0 : X _[0] ⟶ X _[0]) = 0 := by
+theorem Q_f_0_eq (q : ℕ) : ((Q q).f 0 : X _[0] ⟶ X _[0]) = 0 := by
   simp only [HomologicalComplex.sub_f_apply, HomologicalComplex.id_f, Q, P_f_0_eq, sub_self]
-#align algebraic_topology.dold_kan.Q_f_0_eq AlgebraicTopology.DoldKan.q_f_0_eq
+#align algebraic_topology.dold_kan.Q_f_0_eq AlgebraicTopology.DoldKan.Q_f_0_eq
+-/
 
 namespace HigherFacesVanish
 
+/- warning: algebraic_topology.dold_kan.higher_faces_vanish.of_P -> AlgebraicTopology.DoldKan.HigherFacesVanish.of_P 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} (q : Nat) (n : Nat), AlgebraicTopology.DoldKan.HigherFacesVanish.{u1, u2} C _inst_1 _inst_2 X (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))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (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))))) n q (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))))) Nat.hasOne) (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 q) (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.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] {X : CategoryTheory.SimplicialObject.{u1, u2} C _inst_1} (q : Nat) (n : Nat), AlgebraicTopology.DoldKan.HigherFacesVanish.{u2, u1} C _inst_1 _inst_2 X (HomologicalComplex.X.{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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u2, u1} 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)))) n q (HomologicalComplex.Hom.f.{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)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u2, u1} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u2, u1} C _inst_1 _inst_2 X) (AlgebraicTopology.DoldKan.P.{u2, u1} C _inst_1 _inst_2 X q) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.of_P AlgebraicTopology.DoldKan.HigherFacesVanish.of_Pₓ'. -/
 /-- This lemma expresses the vanishing of
 `(P q).f (n+1) ≫ X.δ k : X _[n+1] ⟶ X _[n]` when `k≠0` and `k≥n-q+2` -/
-theorem of_p : ∀ q n : ℕ, HigherFacesVanish q ((p q).f (n + 1) : X _[n + 1] ⟶ X _[n + 1])
+theorem of_P : ∀ q n : ℕ, HigherFacesVanish q ((P q).f (n + 1) : X _[n + 1] ⟶ X _[n + 1])
   | 0 => fun n j hj₁ => by
     exfalso
     have hj₂ := Fin.is_lt j
@@ -110,11 +144,17 @@ theorem of_p : ∀ q n : ℕ, HigherFacesVanish q ((p q).f (n + 1) : X _[n + 1]
   | q + 1 => fun n => by
     unfold P
     exact (of_P q n).induction
-#align algebraic_topology.dold_kan.higher_faces_vanish.of_P AlgebraicTopology.DoldKan.HigherFacesVanish.of_p
-
+#align algebraic_topology.dold_kan.higher_faces_vanish.of_P AlgebraicTopology.DoldKan.HigherFacesVanish.of_P
+
+/- warning: algebraic_topology.dold_kan.higher_faces_vanish.comp_P_eq_self -> AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self 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} {Y : C} {n : Nat} {q : Nat} {φ : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Y (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.HigherFacesVanish.{u1, u2} C _inst_1 _inst_2 X Y n q φ) -> (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Y (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))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (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.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) Y (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))))))) (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))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (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))))) φ (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))))) Nat.hasOne) (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 q) (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)))))) φ)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.higher_faces_vanish.comp_P_eq_self AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_selfₓ'. -/
 @[reassoc.1]
-theorem comp_p_eq_self {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ) :
-    φ ≫ (p q).f (n + 1) = φ := by
+theorem comp_P_eq_self {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFacesVanish q φ) :
+    φ ≫ (P q).f (n + 1) = φ := by
   induction' q with q hq
   · unfold P
     apply comp_id
@@ -130,12 +170,18 @@ theorem comp_p_eq_self {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFa
         v ⟨a, by linarith⟩ (by simp only [hnaq, Fin.val_mk, Nat.succ_eq_add_one, add_assoc])
       simp only [Fin.succ_mk] at eq
       simp only [Eq, zero_comp]
-#align algebraic_topology.dold_kan.higher_faces_vanish.comp_P_eq_self AlgebraicTopology.DoldKan.HigherFacesVanish.comp_p_eq_self
+#align algebraic_topology.dold_kan.higher_faces_vanish.comp_P_eq_self AlgebraicTopology.DoldKan.HigherFacesVanish.comp_P_eq_self
 
 end HigherFacesVanish
 
-theorem comp_p_eq_self_iff {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} :
-    φ ≫ (p q).f (n + 1) = φ ↔ HigherFacesVanish q φ :=
+/- warning: algebraic_topology.dold_kan.comp_P_eq_self_iff -> AlgebraicTopology.DoldKan.comp_P_eq_self_iff 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} {Y : C} {n : Nat} {q : Nat} {φ : Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Y (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)))))))}, Iff (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) Y (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))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (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.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) Y (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))))))) (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))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (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))))) φ (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))))) Nat.hasOne) (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 q) (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)))))) φ) (AlgebraicTopology.DoldKan.HigherFacesVanish.{u1, u2} C _inst_1 _inst_2 X Y n q φ)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.comp_P_eq_self_iff AlgebraicTopology.DoldKan.comp_P_eq_self_iffₓ'. -/
+theorem comp_P_eq_self_iff {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} :
+    φ ≫ (P q).f (n + 1) = φ ↔ HigherFacesVanish q φ :=
   by
   constructor
   · intro hφ
@@ -143,40 +189,49 @@ theorem comp_p_eq_self_iff {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} :
     apply higher_faces_vanish.of_comp
     apply higher_faces_vanish.of_P
   · exact higher_faces_vanish.comp_P_eq_self
-#align algebraic_topology.dold_kan.comp_P_eq_self_iff AlgebraicTopology.DoldKan.comp_p_eq_self_iff
+#align algebraic_topology.dold_kan.comp_P_eq_self_iff AlgebraicTopology.DoldKan.comp_P_eq_self_iff
 
+#print AlgebraicTopology.DoldKan.P_f_idem /-
 @[simp, reassoc.1]
-theorem p_f_idem (q n : ℕ) : ((p q).f n : X _[n] ⟶ _) ≫ (p q).f n = (p q).f n :=
+theorem P_f_idem (q n : ℕ) : ((P q).f n : X _[n] ⟶ _) ≫ (P q).f n = (P q).f n :=
   by
   cases n
   · rw [P_f_0_eq q, comp_id]
-  · exact (higher_faces_vanish.of_P q n).comp_p_eq_self
-#align algebraic_topology.dold_kan.P_f_idem AlgebraicTopology.DoldKan.p_f_idem
+  · exact (higher_faces_vanish.of_P q n).comp_P_eq_self
+#align algebraic_topology.dold_kan.P_f_idem AlgebraicTopology.DoldKan.P_f_idem
+-/
 
+#print AlgebraicTopology.DoldKan.Q_f_idem /-
 @[simp, reassoc.1]
-theorem q_f_idem (q n : ℕ) : ((q q).f n : X _[n] ⟶ _) ≫ (q q).f n = (q q).f n :=
-  idem_of_id_sub_idem _ (p_f_idem q n)
-#align algebraic_topology.dold_kan.Q_f_idem AlgebraicTopology.DoldKan.q_f_idem
+theorem Q_f_idem (q n : ℕ) : ((Q q).f n : X _[n] ⟶ _) ≫ (Q q).f n = (Q q).f n :=
+  idem_of_id_sub_idem _ (P_f_idem q n)
+#align algebraic_topology.dold_kan.Q_f_idem AlgebraicTopology.DoldKan.Q_f_idem
+-/
 
+#print AlgebraicTopology.DoldKan.P_idem /-
 @[simp, reassoc.1]
-theorem p_idem (q : ℕ) : (p q : K[X] ⟶ K[X]) ≫ p q = p q :=
+theorem P_idem (q : ℕ) : (P q : K[X] ⟶ K[X]) ≫ P q = P q :=
   by
   ext n
   exact P_f_idem q n
-#align algebraic_topology.dold_kan.P_idem AlgebraicTopology.DoldKan.p_idem
+#align algebraic_topology.dold_kan.P_idem AlgebraicTopology.DoldKan.P_idem
+-/
 
+#print AlgebraicTopology.DoldKan.Q_idem /-
 @[simp, reassoc.1]
-theorem q_idem (q : ℕ) : (q q : K[X] ⟶ K[X]) ≫ q q = q q :=
+theorem Q_idem (q : ℕ) : (Q q : K[X] ⟶ K[X]) ≫ Q q = Q q :=
   by
   ext n
   exact Q_f_idem q n
-#align algebraic_topology.dold_kan.Q_idem AlgebraicTopology.DoldKan.q_idem
+#align algebraic_topology.dold_kan.Q_idem AlgebraicTopology.DoldKan.Q_idem
+-/
 
+#print AlgebraicTopology.DoldKan.natTransP /-
 /-- For each `q`, `P q` is a natural transformation. -/
 @[simps]
 def natTransP (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapComplex C
     where
-  app X := p q
+  app X := P q
   naturality' X Y f := by
     induction' q with q hq
     · unfold P
@@ -189,31 +244,52 @@ def natTransP (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapComp
       congr 1
       exact (nat_trans_Hσ q).naturality' f
 #align algebraic_topology.dold_kan.nat_trans_P AlgebraicTopology.DoldKan.natTransP
+-/
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.P_f_naturality AlgebraicTopology.DoldKan.P_f_naturalityₓ'. -/
 @[simp, reassoc.1]
-theorem p_f_naturality (q n : ℕ) {X Y : SimplicialObject C} (f : X ⟶ Y) :
-    f.app (op [n]) ≫ (p q).f n = (p q).f n ≫ f.app (op [n]) :=
+theorem P_f_naturality (q n : ℕ) {X Y : SimplicialObject C} (f : X ⟶ Y) :
+    f.app (op [n]) ≫ (P q).f n = (P q).f n ≫ f.app (op [n]) :=
   HomologicalComplex.congr_hom ((natTransP q).naturality f) n
-#align algebraic_topology.dold_kan.P_f_naturality AlgebraicTopology.DoldKan.p_f_naturality
-
+#align algebraic_topology.dold_kan.P_f_naturality AlgebraicTopology.DoldKan.P_f_naturality
+
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Q_f_naturality AlgebraicTopology.DoldKan.Q_f_naturalityₓ'. -/
 @[simp, reassoc.1]
-theorem q_f_naturality (q n : ℕ) {X Y : SimplicialObject C} (f : X ⟶ Y) :
-    f.app (op [n]) ≫ (q q).f n = (q q).f n ≫ f.app (op [n]) :=
+theorem Q_f_naturality (q n : ℕ) {X Y : SimplicialObject C} (f : X ⟶ Y) :
+    f.app (op [n]) ≫ (Q q).f n = (Q q).f n ≫ f.app (op [n]) :=
   by
   simp only [Q, HomologicalComplex.sub_f_apply, HomologicalComplex.id_f, comp_sub, P_f_naturality,
     sub_comp, sub_left_inj]
   dsimp
   simp only [comp_id, id_comp]
-#align algebraic_topology.dold_kan.Q_f_naturality AlgebraicTopology.DoldKan.q_f_naturality
+#align algebraic_topology.dold_kan.Q_f_naturality AlgebraicTopology.DoldKan.Q_f_naturality
 
+#print AlgebraicTopology.DoldKan.natTransQ /-
 /-- For each `q`, `Q q` is a natural transformation. -/
 @[simps]
-def natTransQ (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapComplex C where app X := q q
+def natTransQ (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapComplex C where app X := Q q
 #align algebraic_topology.dold_kan.nat_trans_Q AlgebraicTopology.DoldKan.natTransQ
+-/
 
-theorem map_p {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
+/- warning: algebraic_topology.dold_kan.map_P -> AlgebraicTopology.DoldKan.map_P 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.map_P AlgebraicTopology.DoldKan.map_Pₓ'. -/
+theorem map_P {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n : ℕ) :
-    G.map ((p q : K[X] ⟶ _).f n) = (p q : K[((whiskering C D).obj G).obj X] ⟶ _).f n :=
+    G.map ((P q : K[X] ⟶ _).f n) = (P q : K[((whiskering C D).obj G).obj X] ⟶ _).f n :=
   by
   induction' q with q hq
   · unfold P
@@ -221,16 +297,22 @@ theorem map_p {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additiv
   · unfold P
     simp only [comp_add, HomologicalComplex.comp_f, HomologicalComplex.add_f_apply, comp_id,
       functor.map_add, functor.map_comp, hq, map_Hσ]
-#align algebraic_topology.dold_kan.map_P AlgebraicTopology.DoldKan.map_p
-
-theorem map_q {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
+#align algebraic_topology.dold_kan.map_P AlgebraicTopology.DoldKan.map_P
+
+/- warning: algebraic_topology.dold_kan.map_Q -> AlgebraicTopology.DoldKan.map_Q is a dubious translation:
+lean 3 declaration is
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_inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.{u3, u4} D _inst_3) (CategoryTheory.instCategorySimplicialObject.{u3, u4} D _inst_3)) (CategoryTheory.Functor.category.{u2, u3, max u1 u2, max u4 u3} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.{u3, u4} D _inst_3) (CategoryTheory.instCategorySimplicialObject.{u3, u4} D _inst_3)) (CategoryTheory.SimplicialObject.whiskering.{u2, u1, u4, u3} C _inst_1 D _inst_3)) G)) X) q) n)
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.map_Q AlgebraicTopology.DoldKan.map_Qₓ'. -/
+theorem map_Q {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n : ℕ) :
-    G.map ((q q : K[X] ⟶ _).f n) = (q q : K[((whiskering C D).obj G).obj X] ⟶ _).f n :=
+    G.map ((Q q : K[X] ⟶ _).f n) = (Q q : K[((whiskering C D).obj G).obj X] ⟶ _).f n :=
   by
   rw [← add_right_inj (G.map ((P q : K[X] ⟶ _).f n)), ← G.map_add, map_P G X q n, P_add_Q_f,
     P_add_Q_f]
   apply G.map_id
-#align algebraic_topology.dold_kan.map_Q AlgebraicTopology.DoldKan.map_q
+#align algebraic_topology.dold_kan.map_Q AlgebraicTopology.DoldKan.map_Q
 
 end DoldKan

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

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

@@ -51,7 +51,7 @@ noncomputable def P : ℕ → (K[X] ⟶ K[X])
 set_option linter.uppercaseLean3 false in
 #align algebraic_topology.dold_kan.P AlgebraicTopology.DoldKan.P
 
--- porting note: `P_zero` and `P_succ` have been added to ease the port, because
+-- Porting note: `P_zero` and `P_succ` have been added to ease the port, because
 -- `unfold P` would sometimes unfold to a `match` rather than the induction formula
 lemma P_zero : (P 0 : K[X] ⟶ K[X]) = 𝟙 _ := rfl
 lemma P_succ (q : ℕ) : (P (q+1) : K[X] ⟶ K[X]) = P q ≫ (𝟙 _ + Hσ q) := rfl

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

@@ -107,10 +107,7 @@ namespace HigherFacesVanish
 /-- This lemma expresses the vanishing of
 `(P q).f (n+1) ≫ X.δ k : X _[n+1] ⟶ X _[n]` when `k≠0` and `k≥n-q+2` -/
 theorem of_P : ∀ q n : ℕ, HigherFacesVanish q ((P q).f (n + 1) : X _[n + 1] ⟶ X _[n + 1])
-  | 0 => fun n j hj₁ => by
-    exfalso
-    have hj₂ := Fin.is_lt j
-    linarith
+  | 0 => fun n j hj₁ => by omega
   | q + 1 => fun n => by
     simp only [P_succ]
     exact (of_P q n).induction
@@ -128,9 +125,9 @@ theorem comp_P_eq_self {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFa
     by_cases hqn : n < q
     · exact v.of_succ.comp_Hσ_eq_zero hqn
     · obtain ⟨a, ha⟩ := Nat.le.dest (not_lt.mp hqn)
-      have hnaq : n = a + q := by linarith
+      have hnaq : n = a + q := by omega
       simp only [v.of_succ.comp_Hσ_eq hnaq, neg_eq_zero, ← assoc]
-      have eq := v ⟨a, by linarith⟩ (by
+      have eq := v ⟨a, by omega⟩ (by
         simp only [hnaq, Nat.succ_eq_add_one, add_assoc]
         rfl)
       simp only [Fin.succ_mk] at eq

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

cf01bdac

Diff

@@ -6,7 +6,7 @@ Authors: Joël Riou
 import Mathlib.AlgebraicTopology.DoldKan.Faces
 import Mathlib.CategoryTheory.Idempotents.Basic
 
-#align_import algebraic_topology.dold_kan.projections from "leanprover-community/mathlib"@"ed98c07faf6d9de3e52771d5b00394c4294ccb4d"
+#align_import algebraic_topology.dold_kan.projections 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

@@ -23,8 +23,9 @@ and `P_f_naturality`) and are compatible with the application
 of additive functors (see `map_P`).
 
 By passing to the limit, these endomorphisms `P q` shall be used in `PInfty.lean`
-in order to define `PInfty : K[X] ⟶ K[X]`, see `Equivalence.lean` for the general
-strategy of proof of the Dold-Kan equivalence.
+in order to define `PInfty : K[X] ⟶ K[X]`.
+
+(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

@@ -40,7 +40,7 @@ namespace AlgebraicTopology
 
 namespace DoldKan
 
-variable {C : Type _} [Category C] [Preadditive C] {X : SimplicialObject C}
+variable {C : Type*} [Category C] [Preadditive C] {X : SimplicialObject C}
 
 /-- This is the inductive definition of the projections `P q : K[X] ⟶ K[X]`,
 with `P 0 := 𝟙 _` and `P (q+1) := P q ≫ (𝟙 _ + Hσ q)`. -/
@@ -216,7 +216,7 @@ def natTransQ (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapComp
 set_option linter.uppercaseLean3 false in
 #align algebraic_topology.dold_kan.nat_trans_Q AlgebraicTopology.DoldKan.natTransQ
 
-theorem map_P {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
+theorem map_P {D : Type*} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n : ℕ) :
     G.map ((P q : K[X] ⟶ _).f n) = (P q : K[((whiskering C D).obj G).obj X] ⟶ _).f n := by
   induction' q with q hq
@@ -227,7 +227,7 @@ theorem map_P {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additiv
 set_option linter.uppercaseLean3 false in
 #align algebraic_topology.dold_kan.map_P AlgebraicTopology.DoldKan.map_P
 
-theorem map_Q {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
+theorem map_Q {D : Type*} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n : ℕ) :
     G.map ((Q q : K[X] ⟶ _).f n) = (Q q : K[((whiskering C D).obj G).obj X] ⟶ _).f n := by
   rw [← add_right_inj (G.map ((P q : K[X] ⟶ _).f n)), ← G.map_add, map_P G X q n, P_add_Q_f,

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

@@ -2,15 +2,12 @@
 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.projections
-! leanprover-community/mathlib commit ed98c07faf6d9de3e52771d5b00394c4294ccb4d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicTopology.DoldKan.Faces
 import Mathlib.CategoryTheory.Idempotents.Basic
 
+#align_import algebraic_topology.dold_kan.projections from "leanprover-community/mathlib"@"ed98c07faf6d9de3e52771d5b00394c4294ccb4d"
+
 /-!
 
 # Construction of projections for the Dold-Kan correspondence

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

@@ -129,7 +129,7 @@ theorem comp_P_eq_self {Y : C} {n q : ℕ} {φ : Y ⟶ X _[n + 1]} (v : HigherFa
       comp_id, ← assoc, hq v.of_succ, add_right_eq_self]
     by_cases hqn : n < q
     · exact v.of_succ.comp_Hσ_eq_zero hqn
-    . obtain ⟨a, ha⟩ := Nat.le.dest (not_lt.mp hqn)
+    · obtain ⟨a, ha⟩ := Nat.le.dest (not_lt.mp hqn)
       have hnaq : n = a + q := by linarith
       simp only [v.of_succ.comp_Hσ_eq hnaq, neg_eq_zero, ← assoc]
       have eq := v ⟨a, by linarith⟩ (by

chore: formatting issues (#4947)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

5068808d

Diff

@@ -56,7 +56,7 @@ set_option linter.uppercaseLean3 false in
 -- porting note: `P_zero` and `P_succ` have been added to ease the port, because
 -- `unfold P` would sometimes unfold to a `match` rather than the induction formula
 lemma P_zero : (P 0 : K[X] ⟶ K[X]) = 𝟙 _ := rfl
-lemma P_succ (q : ℕ): (P (q+1) : K[X] ⟶ K[X]) = P q ≫ (𝟙 _ + Hσ q) := rfl
+lemma P_succ (q : ℕ) : (P (q+1) : K[X] ⟶ K[X]) = P q ≫ (𝟙 _ + Hσ q) := rfl
 
 /-- All the `P q` coincide with `𝟙 _` in degree 0. -/
 @[simp]