algebraic_topology.alternating_face_map_complex

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

88bca0ce

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

86d1873c

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -122,7 +122,7 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 :=
   · -- φ : S → Sᶜ is surjective
     rintro ⟨i', j'⟩ hij'
     simp only [true_and_iff, Finset.mem_univ, Finset.compl_filter, not_le, Finset.mem_filter] at
-      hij' 
+      hij'
     refine' ⟨(j'.pred _, Fin.castSuccEmb i'), _, _⟩
     · intro H
       simpa only [H, Nat.not_lt_zero, Fin.val_zero] using hij'
@@ -323,8 +323,8 @@ def inclusionOfMooreComplexMap (X : SimplicialObject A) :
     simp only [add_zero]
     -- finally, we study the remaining term which is induced by X.δ 0
     let eq := def_t 0
-    rw [show (-1 : ℤ) ^ ((0 : Fin (n + 2)) : ℕ) = 1 by ring] at eq 
-    rw [one_smul] at eq 
+    rw [show (-1 : ℤ) ^ ((0 : Fin (n + 2)) : ℕ) = 1 by ring] at eq
+    rw [one_smul] at eq
     rw [Eq]
     cases n <;> dsimp <;> simp
 #align algebraic_topology.inclusion_of_Moore_complex_map AlgebraicTopology.inclusionOfMooreComplexMap

86d1873c

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,12 +3,12 @@ Copyright (c) 2021 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou, Adam Topaz, Johan Commelin
 -/
-import Mathbin.Algebra.Homology.Additive
-import Mathbin.AlgebraicTopology.MooreComplex
-import Mathbin.Algebra.BigOperators.Fin
-import Mathbin.CategoryTheory.Preadditive.Opposite
-import Mathbin.CategoryTheory.Idempotents.FunctorCategories
-import Mathbin.Tactic.EquivRw
+import Algebra.Homology.Additive
+import AlgebraicTopology.MooreComplex
+import Algebra.BigOperators.Fin
+import CategoryTheory.Preadditive.Opposite
+import CategoryTheory.Idempotents.FunctorCategories
+import Tactic.EquivRw
 
 #align_import algebraic_topology.alternating_face_map_complex from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"

86d1873c

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou, Adam Topaz, Johan Commelin
-
-! This file was ported from Lean 3 source module algebraic_topology.alternating_face_map_complex
-! 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.Algebra.Homology.Additive
 import Mathbin.AlgebraicTopology.MooreComplex
@@ -15,6 +10,8 @@ import Mathbin.CategoryTheory.Preadditive.Opposite
 import Mathbin.CategoryTheory.Idempotents.FunctorCategories
 import Mathbin.Tactic.EquivRw
 
+#align_import algebraic_topology.alternating_face_map_complex from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"
+
 /-!
 
 # The alternating face map complex of a simplicial object in a preadditive category

86d1873c

bump to nightly-2023-07-16-17

mathlib commit https://github.com/leanprover-community/mathlib/commit/2fe465deb81bcd7ccafa065bb686888a82f15372

6db63fa6

Diff

@@ -115,13 +115,13 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 :=
       mul_one, Fin.coe_castLT, Fin.val_succ, pow_one, mul_neg, neg_neg]
     let jj : Fin (n + 2) := (φ (i, j) hij).1
     have ineq : jj ≤ i := by rw [← Fin.val_fin_le]; simpa using hij
-    rw [CategoryTheory.SimplicialObject.δ_comp_δ X ineq, Fin.castSuccEmb_castLT, mul_comm]
+    rw [CategoryTheory.SimplicialObject.δ_comp_δ X ineq, Fin.castSucc_castLT, mul_comm]
   · -- φ : S → Sᶜ is injective
     rintro ⟨i, j⟩ ⟨i', j'⟩ hij hij' h
     rw [Prod.mk.inj_iff]
     refine' ⟨by simpa using congr_arg Prod.snd h, _⟩
     have h1 := congr_arg Fin.castSuccEmb (congr_arg Prod.fst h)
-    simpa [Fin.castSuccEmb_castLT] using h1
+    simpa [Fin.castSucc_castLT] using h1
   · -- φ : S → Sᶜ is surjective
     rintro ⟨i', j'⟩ hij'
     simp only [true_and_iff, Finset.mem_univ, Finset.compl_filter, not_le, Finset.mem_filter] at
@@ -130,9 +130,9 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 :=
     · intro H
       simpa only [H, Nat.not_lt_zero, Fin.val_zero] using hij'
     ·
-      simpa only [true_and_iff, Finset.mem_univ, Fin.coe_castSuccEmb, Fin.coe_pred,
+      simpa only [true_and_iff, Finset.mem_univ, Fin.coe_castSucc, Fin.coe_pred,
         Finset.mem_filter] using Nat.le_pred_of_lt hij'
-    · simp only [Prod.mk.inj_iff, Fin.succ_pred, Fin.castLT_castSuccEmb]
+    · simp only [Prod.mk.inj_iff, Fin.succ_pred, Fin.castLT_castSucc]
       constructor <;> rfl
 #align algebraic_topology.alternating_face_map_complex.d_squared AlgebraicTopology.AlternatingFaceMapComplex.d_squared
 -/

86d1873c

bump to nightly-2023-07-06-11

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

a2f50eda

Diff

@@ -115,24 +115,24 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 :=
       mul_one, Fin.coe_castLT, Fin.val_succ, pow_one, mul_neg, neg_neg]
     let jj : Fin (n + 2) := (φ (i, j) hij).1
     have ineq : jj ≤ i := by rw [← Fin.val_fin_le]; simpa using hij
-    rw [CategoryTheory.SimplicialObject.δ_comp_δ X ineq, Fin.castSucc_castLT, mul_comm]
+    rw [CategoryTheory.SimplicialObject.δ_comp_δ X ineq, Fin.castSuccEmb_castLT, mul_comm]
   · -- φ : S → Sᶜ is injective
     rintro ⟨i, j⟩ ⟨i', j'⟩ hij hij' h
     rw [Prod.mk.inj_iff]
     refine' ⟨by simpa using congr_arg Prod.snd h, _⟩
-    have h1 := congr_arg Fin.castSucc (congr_arg Prod.fst h)
-    simpa [Fin.castSucc_castLT] using h1
+    have h1 := congr_arg Fin.castSuccEmb (congr_arg Prod.fst h)
+    simpa [Fin.castSuccEmb_castLT] using h1
   · -- φ : S → Sᶜ is surjective
     rintro ⟨i', j'⟩ hij'
     simp only [true_and_iff, Finset.mem_univ, Finset.compl_filter, not_le, Finset.mem_filter] at
       hij' 
-    refine' ⟨(j'.pred _, Fin.castSucc i'), _, _⟩
+    refine' ⟨(j'.pred _, Fin.castSuccEmb i'), _, _⟩
     · intro H
       simpa only [H, Nat.not_lt_zero, Fin.val_zero] using hij'
     ·
-      simpa only [true_and_iff, Finset.mem_univ, Fin.coe_castSucc, Fin.coe_pred,
+      simpa only [true_and_iff, Finset.mem_univ, Fin.coe_castSuccEmb, Fin.coe_pred,
         Finset.mem_filter] using Nat.le_pred_of_lt hij'
-    · simp only [Prod.mk.inj_iff, Fin.succ_pred, Fin.castLT_castSucc]
+    · simp only [Prod.mk.inj_iff, Fin.succ_pred, Fin.castLT_castSuccEmb]
       constructor <;> rfl
 #align algebraic_topology.alternating_face_map_complex.d_squared AlgebraicTopology.AlternatingFaceMapComplex.d_squared
 -/

86d1873c

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -69,13 +69,16 @@ variable (X : SimplicialObject C)
 
 variable (Y : SimplicialObject C)
 
+#print AlgebraicTopology.AlternatingFaceMapComplex.objD /-
 /-- The differential on the alternating face map complex is the alternate
 sum of the face maps -/
 @[simp]
 def objD (n : ℕ) : X _[n + 1] ⟶ X _[n] :=
   ∑ i : Fin (n + 2), (-1 : ℤ) ^ (i : ℕ) • X.δ i
 #align algebraic_topology.alternating_face_map_complex.obj_d AlgebraicTopology.AlternatingFaceMapComplex.objD
+-/
 
+#print AlgebraicTopology.AlternatingFaceMapComplex.d_squared /-
 /-- ## The chain complex relation `d ≫ d`
 -/
 theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 :=
@@ -132,6 +135,7 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 :=
     · simp only [Prod.mk.inj_iff, Fin.succ_pred, Fin.castLT_castSucc]
       constructor <;> rfl
 #align algebraic_topology.alternating_face_map_complex.d_squared AlgebraicTopology.AlternatingFaceMapComplex.d_squared
+-/
 
 /-!
 ## Construction of the alternating face map complex functor
@@ -145,16 +149,20 @@ def obj : ChainComplex C ℕ :=
 #align algebraic_topology.alternating_face_map_complex.obj AlgebraicTopology.AlternatingFaceMapComplex.obj
 -/
 
+#print AlgebraicTopology.AlternatingFaceMapComplex.obj_X /-
 @[simp]
 theorem obj_X (X : SimplicialObject C) (n : ℕ) : (AlternatingFaceMapComplex.obj X).pt n = X _[n] :=
   rfl
 #align algebraic_topology.alternating_face_map_complex.obj_X AlgebraicTopology.AlternatingFaceMapComplex.obj_X
+-/
 
+#print AlgebraicTopology.AlternatingFaceMapComplex.obj_d_eq /-
 @[simp]
 theorem obj_d_eq (X : SimplicialObject C) (n : ℕ) :
     (AlternatingFaceMapComplex.obj X).d (n + 1) n = ∑ i : Fin (n + 2), (-1 : ℤ) ^ (i : ℕ) • X.δ i :=
   by apply ChainComplex.of_d
 #align algebraic_topology.alternating_face_map_complex.obj_d_eq AlgebraicTopology.AlternatingFaceMapComplex.obj_d_eq
+-/
 
 variable {X} {Y}
 
@@ -195,24 +203,31 @@ def alternatingFaceMapComplex : SimplicialObject C ⥤ ChainComplex C ℕ
 
 variable {C}
 
+#print AlgebraicTopology.alternatingFaceMapComplex_obj_X /-
 @[simp]
 theorem alternatingFaceMapComplex_obj_X (X : SimplicialObject C) (n : ℕ) :
     ((alternatingFaceMapComplex C).obj X).pt n = X _[n] :=
   rfl
 #align algebraic_topology.alternating_face_map_complex_obj_X AlgebraicTopology.alternatingFaceMapComplex_obj_X
+-/
 
+#print AlgebraicTopology.alternatingFaceMapComplex_obj_d /-
 @[simp]
 theorem alternatingFaceMapComplex_obj_d (X : SimplicialObject C) (n : ℕ) :
     ((alternatingFaceMapComplex C).obj X).d (n + 1) n = AlternatingFaceMapComplex.objD X n := by
   apply ChainComplex.of_d
 #align algebraic_topology.alternating_face_map_complex_obj_d AlgebraicTopology.alternatingFaceMapComplex_obj_d
+-/
 
+#print AlgebraicTopology.alternatingFaceMapComplex_map_f /-
 @[simp]
 theorem alternatingFaceMapComplex_map_f {X Y : SimplicialObject C} (f : X ⟶ Y) (n : ℕ) :
     ((alternatingFaceMapComplex C).map f).f n = f.app (op [n]) :=
   rfl
 #align algebraic_topology.alternating_face_map_complex_map_f AlgebraicTopology.alternatingFaceMapComplex_map_f
+-/
 
+#print AlgebraicTopology.map_alternatingFaceMapComplex /-
 theorem map_alternatingFaceMapComplex {D : Type _} [Category D] [Preadditive D] (F : C ⥤ D)
     [F.Additive] :
     alternatingFaceMapComplex C ⋙ F.mapHomologicalComplex _ =
@@ -234,7 +249,9 @@ theorem map_alternatingFaceMapComplex {D : Type _} [Category D] [Preadditive D]
     · ext n
       rfl
 #align algebraic_topology.map_alternating_face_map_complex AlgebraicTopology.map_alternatingFaceMapComplex
+-/
 
+#print AlgebraicTopology.karoubi_alternatingFaceMapComplex_d /-
 theorem karoubi_alternatingFaceMapComplex_d (P : Karoubi (SimplicialObject C)) (n : ℕ) :
     ((AlternatingFaceMapComplex.obj (KaroubiFunctorCategoryEmbedding.obj P)).d (n + 1) n).f =
       P.p.app (op [n + 1]) ≫ (AlternatingFaceMapComplex.obj P.pt).d (n + 1) n :=
@@ -243,6 +260,7 @@ theorem karoubi_alternatingFaceMapComplex_d (P : Karoubi (SimplicialObject C)) (
   simpa only [alternating_face_map_complex.obj_d_eq, karoubi.sum_hom, preadditive.comp_sum,
     karoubi.zsmul_hom, preadditive.comp_zsmul]
 #align algebraic_topology.karoubi_alternating_face_map_complex_d AlgebraicTopology.karoubi_alternatingFaceMapComplex_d
+-/
 
 namespace AlternatingFaceMapComplex
 
@@ -274,6 +292,7 @@ end AlternatingFaceMapComplex
 
 variable {A : Type _} [Category A] [Abelian A]
 
+#print AlgebraicTopology.inclusionOfMooreComplexMap /-
 /-- The inclusion map of the Moore complex in the alternating face map complex -/
 def inclusionOfMooreComplexMap (X : SimplicialObject A) :
     (normalizedMooreComplex A).obj X ⟶ (alternatingFaceMapComplex A).obj X :=
@@ -312,12 +331,15 @@ def inclusionOfMooreComplexMap (X : SimplicialObject A) :
     rw [Eq]
     cases n <;> dsimp <;> simp
 #align algebraic_topology.inclusion_of_Moore_complex_map AlgebraicTopology.inclusionOfMooreComplexMap
+-/
 
+#print AlgebraicTopology.inclusionOfMooreComplexMap_f /-
 @[simp]
 theorem inclusionOfMooreComplexMap_f (X : SimplicialObject A) (n : ℕ) :
     (inclusionOfMooreComplexMap X).f n = (NormalizedMooreComplex.objX X n).arrow :=
   ChainComplex.ofHom_f _ _ _ _ _ _ _ _ n
 #align algebraic_topology.inclusion_of_Moore_complex_map_f AlgebraicTopology.inclusionOfMooreComplexMap_f
+-/
 
 variable (A)
 
@@ -334,23 +356,29 @@ namespace AlternatingCofaceMapComplex
 
 variable (X Y : CosimplicialObject C)
 
+#print AlgebraicTopology.AlternatingCofaceMapComplex.objD /-
 /-- The differential on the alternating coface map complex is the alternate
 sum of the coface maps -/
 @[simp]
 def objD (n : ℕ) : X.obj [n] ⟶ X.obj [n + 1] :=
   ∑ i : Fin (n + 2), (-1 : ℤ) ^ (i : ℕ) • X.δ i
 #align algebraic_topology.alternating_coface_map_complex.obj_d AlgebraicTopology.AlternatingCofaceMapComplex.objD
+-/
 
+#print AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_d /-
 theorem d_eq_unop_d (n : ℕ) :
     objD X n =
       (AlternatingFaceMapComplex.objD ((cosimplicialSimplicialEquiv C).Functor.obj (op X))
           n).unop :=
   by simpa only [obj_d, alternating_face_map_complex.obj_d, unop_sum, unop_zsmul]
 #align algebraic_topology.alternating_coface_map_complex.d_eq_unop_d AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_d
+-/
 
+#print AlgebraicTopology.AlternatingCofaceMapComplex.d_squared /-
 theorem d_squared (n : ℕ) : objD X n ≫ objD X (n + 1) = 0 := by
   simp only [d_eq_unop_d, ← unop_comp, alternating_face_map_complex.d_squared, unop_zero]
 #align algebraic_topology.alternating_coface_map_complex.d_squared AlgebraicTopology.AlternatingCofaceMapComplex.d_squared
+-/
 
 #print AlgebraicTopology.AlternatingCofaceMapComplex.obj /-
 /-- The alternating coface map complex, on objects -/

86d1873c

bump to nightly-2023-06-10-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

3fdc57bc

Diff

@@ -92,7 +92,7 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 :=
   let P := Fin (n + 2) × Fin (n + 3)
   let S := finset.univ.filter fun ij : P => (ij.2 : ℕ) ≤ (ij.1 : ℕ)
   let term := fun ij : P => d_l ij.2 ≫ d_r ij.1
-  erw [show (∑ ij : P, term ij) = (∑ ij in S, term ij) + ∑ ij in Sᶜ, term ij by
+  erw [show ∑ ij : P, term ij = ∑ ij in S, term ij + ∑ ij in Sᶜ, term ij by
       rw [Finset.sum_add_sum_compl]]
   rw [← eq_neg_iff_add_eq_zero, ← Finset.sum_neg_distrib]
   /- we are reduced to showing that two sums are equal, and this is obtained

86d1873c

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -104,7 +104,7 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 :=
   · -- φ(S) is contained in Sᶜ
     intro ij hij
     simp only [Finset.mem_univ, Finset.compl_filter, Finset.mem_filter, true_and_iff, Fin.val_succ,
-      Fin.coe_castLT] at hij⊢
+      Fin.coe_castLT] at hij ⊢
     linarith
   · -- identification of corresponding terms in both sums
     rintro ⟨i, j⟩ hij
@@ -122,7 +122,7 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 :=
   · -- φ : S → Sᶜ is surjective
     rintro ⟨i', j'⟩ hij'
     simp only [true_and_iff, Finset.mem_univ, Finset.compl_filter, not_le, Finset.mem_filter] at
-      hij'
+      hij' 
     refine' ⟨(j'.pred _, Fin.castSucc i'), _, _⟩
     · intro H
       simpa only [H, Nat.not_lt_zero, Fin.val_zero] using hij'
@@ -307,8 +307,8 @@ def inclusionOfMooreComplexMap (X : SimplicialObject A) :
     simp only [add_zero]
     -- finally, we study the remaining term which is induced by X.δ 0
     let eq := def_t 0
-    rw [show (-1 : ℤ) ^ ((0 : Fin (n + 2)) : ℕ) = 1 by ring] at eq
-    rw [one_smul] at eq
+    rw [show (-1 : ℤ) ^ ((0 : Fin (n + 2)) : ℕ) = 1 by ring] at eq 
+    rw [one_smul] at eq 
     rw [Eq]
     cases n <;> dsimp <;> simp
 #align algebraic_topology.inclusion_of_Moore_complex_map AlgebraicTopology.inclusionOfMooreComplexMap

86d1873c

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -48,9 +48,9 @@ open CategoryTheory.Preadditive CategoryTheory.Category CategoryTheory.Idempoten
 
 open Opposite
 
-open BigOperators
+open scoped BigOperators
 
-open Simplicial
+open scoped Simplicial
 
 noncomputable section

86d1873c

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -69,12 +69,6 @@ variable (X : SimplicialObject C)
 
 variable (Y : SimplicialObject C)
 
-/- warning: algebraic_topology.alternating_face_map_complex.obj_d -> AlgebraicTopology.AlternatingFaceMapComplex.objD is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (n : Nat), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk 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) (n : Nat), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex.obj_d AlgebraicTopology.AlternatingFaceMapComplex.objDₓ'. -/
 /-- The differential on the alternating face map complex is the alternate
 sum of the face maps -/
 @[simp]
@@ -82,9 +76,6 @@ def objD (n : ℕ) : X _[n + 1] ⟶ X _[n] :=
   ∑ i : Fin (n + 2), (-1 : ℤ) ^ (i : ℕ) • X.δ i
 #align algebraic_topology.alternating_face_map_complex.obj_d AlgebraicTopology.AlternatingFaceMapComplex.objD
 
-/- warning: algebraic_topology.alternating_face_map_complex.d_squared -> AlgebraicTopology.AlternatingFaceMapComplex.d_squared is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex.d_squared AlgebraicTopology.AlternatingFaceMapComplex.d_squaredₓ'. -/
 /-- ## The chain complex relation `d ≫ d`
 -/
 theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 :=
@@ -154,20 +145,11 @@ def obj : ChainComplex C ℕ :=
 #align algebraic_topology.alternating_face_map_complex.obj AlgebraicTopology.AlternatingFaceMapComplex.obj
 -/
 
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex.obj_X AlgebraicTopology.AlternatingFaceMapComplex.obj_Xₓ'. -/
 @[simp]
 theorem obj_X (X : SimplicialObject C) (n : ℕ) : (AlternatingFaceMapComplex.obj X).pt n = X _[n] :=
   rfl
 #align algebraic_topology.alternating_face_map_complex.obj_X AlgebraicTopology.AlternatingFaceMapComplex.obj_X
 
-/- warning: algebraic_topology.alternating_face_map_complex.obj_d_eq -> AlgebraicTopology.AlternatingFaceMapComplex.obj_d_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex.obj_d_eq AlgebraicTopology.AlternatingFaceMapComplex.obj_d_eqₓ'. -/
 @[simp]
 theorem obj_d_eq (X : SimplicialObject C) (n : ℕ) :
     (AlternatingFaceMapComplex.obj X).d (n + 1) n = ∑ i : Fin (n + 2), (-1 : ℤ) ^ (i : ℕ) • X.δ i :=
@@ -213,39 +195,24 @@ def alternatingFaceMapComplex : SimplicialObject C ⥤ ChainComplex C ℕ
 
 variable {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)))
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 @[simp]
 theorem alternatingFaceMapComplex_obj_X (X : SimplicialObject C) (n : ℕ) :
     ((alternatingFaceMapComplex C).obj X).pt n = X _[n] :=
   rfl
 #align algebraic_topology.alternating_face_map_complex_obj_X AlgebraicTopology.alternatingFaceMapComplex_obj_X
 
-/- warning: algebraic_topology.alternating_face_map_complex_obj_d -> AlgebraicTopology.alternatingFaceMapComplex_obj_d is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex_obj_d AlgebraicTopology.alternatingFaceMapComplex_obj_dₓ'. -/
 @[simp]
 theorem alternatingFaceMapComplex_obj_d (X : SimplicialObject C) (n : ℕ) :
     ((alternatingFaceMapComplex C).obj X).d (n + 1) n = AlternatingFaceMapComplex.objD X n := by
   apply ChainComplex.of_d
 #align algebraic_topology.alternating_face_map_complex_obj_d AlgebraicTopology.alternatingFaceMapComplex_obj_d
 
-/- warning: algebraic_topology.alternating_face_map_complex_map_f -> AlgebraicTopology.alternatingFaceMapComplex_map_f is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex_map_f AlgebraicTopology.alternatingFaceMapComplex_map_fₓ'. -/
 @[simp]
 theorem alternatingFaceMapComplex_map_f {X Y : SimplicialObject C} (f : X ⟶ Y) (n : ℕ) :
     ((alternatingFaceMapComplex C).map f).f n = f.app (op [n]) :=
   rfl
 #align algebraic_topology.alternating_face_map_complex_map_f AlgebraicTopology.alternatingFaceMapComplex_map_f
 
-/- warning: algebraic_topology.map_alternating_face_map_complex -> AlgebraicTopology.map_alternatingFaceMapComplex is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.map_alternating_face_map_complex AlgebraicTopology.map_alternatingFaceMapComplexₓ'. -/
 theorem map_alternatingFaceMapComplex {D : Type _} [Category D] [Preadditive D] (F : C ⥤ D)
     [F.Additive] :
     alternatingFaceMapComplex C ⋙ F.mapHomologicalComplex _ =
@@ -268,9 +235,6 @@ theorem map_alternatingFaceMapComplex {D : Type _} [Category D] [Preadditive D]
       rfl
 #align algebraic_topology.map_alternating_face_map_complex AlgebraicTopology.map_alternatingFaceMapComplex
 
-/- warning: algebraic_topology.karoubi_alternating_face_map_complex_d -> AlgebraicTopology.karoubi_alternatingFaceMapComplex_d is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.karoubi_alternating_face_map_complex_d AlgebraicTopology.karoubi_alternatingFaceMapComplex_dₓ'. -/
 theorem karoubi_alternatingFaceMapComplex_d (P : Karoubi (SimplicialObject C)) (n : ℕ) :
     ((AlternatingFaceMapComplex.obj (KaroubiFunctorCategoryEmbedding.obj P)).d (n + 1) n).f =
       P.p.app (op [n + 1]) ≫ (AlternatingFaceMapComplex.obj P.pt).d (n + 1) n :=
@@ -310,9 +274,6 @@ end AlternatingFaceMapComplex
 
 variable {A : Type _} [Category A] [Abelian A]
 
-/- warning: algebraic_topology.inclusion_of_Moore_complex_map -> AlgebraicTopology.inclusionOfMooreComplexMap is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.inclusion_of_Moore_complex_map AlgebraicTopology.inclusionOfMooreComplexMapₓ'. -/
 /-- The inclusion map of the Moore complex in the alternating face map complex -/
 def inclusionOfMooreComplexMap (X : SimplicialObject A) :
     (normalizedMooreComplex A).obj X ⟶ (alternatingFaceMapComplex A).obj X :=
@@ -352,9 +313,6 @@ def inclusionOfMooreComplexMap (X : SimplicialObject A) :
     cases n <;> dsimp <;> simp
 #align algebraic_topology.inclusion_of_Moore_complex_map AlgebraicTopology.inclusionOfMooreComplexMap
 
-/- warning: algebraic_topology.inclusion_of_Moore_complex_map_f -> AlgebraicTopology.inclusionOfMooreComplexMap_f is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.inclusion_of_Moore_complex_map_f AlgebraicTopology.inclusionOfMooreComplexMap_fₓ'. -/
 @[simp]
 theorem inclusionOfMooreComplexMap_f (X : SimplicialObject A) (n : ℕ) :
     (inclusionOfMooreComplexMap X).f n = (NormalizedMooreComplex.objX X n).arrow :=
@@ -376,12 +334,6 @@ namespace AlternatingCofaceMapComplex
 
 variable (X Y : CosimplicialObject C)
 
-/- warning: algebraic_topology.alternating_coface_map_complex.obj_d -> AlgebraicTopology.AlternatingCofaceMapComplex.objD is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_coface_map_complex.obj_d AlgebraicTopology.AlternatingCofaceMapComplex.objDₓ'. -/
 /-- The differential on the alternating coface map complex is the alternate
 sum of the coface maps -/
 @[simp]
@@ -389,9 +341,6 @@ def objD (n : ℕ) : X.obj [n] ⟶ X.obj [n + 1] :=
   ∑ i : Fin (n + 2), (-1 : ℤ) ^ (i : ℕ) • X.δ i
 #align algebraic_topology.alternating_coface_map_complex.obj_d AlgebraicTopology.AlternatingCofaceMapComplex.objD
 
-/- warning: algebraic_topology.alternating_coface_map_complex.d_eq_unop_d -> AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_d is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_coface_map_complex.d_eq_unop_d AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_dₓ'. -/
 theorem d_eq_unop_d (n : ℕ) :
     objD X n =
       (AlternatingFaceMapComplex.objD ((cosimplicialSimplicialEquiv C).Functor.obj (op X))
@@ -399,9 +348,6 @@ theorem d_eq_unop_d (n : ℕ) :
   by simpa only [obj_d, alternating_face_map_complex.obj_d, unop_sum, unop_zsmul]
 #align algebraic_topology.alternating_coface_map_complex.d_eq_unop_d AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_d
 
-/- warning: algebraic_topology.alternating_coface_map_complex.d_squared -> AlgebraicTopology.AlternatingCofaceMapComplex.d_squared is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_coface_map_complex.d_squared AlgebraicTopology.AlternatingCofaceMapComplex.d_squaredₓ'. -/
 theorem d_squared (n : ℕ) : objD X n ≫ objD X (n + 1) = 0 := by
   simp only [d_eq_unop_d, ← unop_comp, alternating_face_map_complex.d_squared, unop_zero]
 #align algebraic_topology.alternating_coface_map_complex.d_squared AlgebraicTopology.AlternatingCofaceMapComplex.d_squared

86d1873c

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -95,9 +95,7 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 :=
   let d_l := fun j : Fin (n + 3) => (-1 : ℤ) ^ (j : ℕ) • X.δ j
   let d_r := fun i : Fin (n + 2) => (-1 : ℤ) ^ (i : ℕ) • X.δ i
   rw [show (fun i => (∑ j : Fin (n + 3), d_l j) ≫ d_r i) = fun i => ∑ j : Fin (n + 3), d_l j ≫ d_r i
-      by
-      ext i
-      rw [sum_comp]]
+      by ext i; rw [sum_comp]]
   rw [← Finset.sum_product']
   -- then, we decompose the index set P into a subet S and its complement Sᶜ
   let P := Fin (n + 2) × Fin (n + 3)
@@ -122,9 +120,7 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 :=
     simp only [term, d_l, d_r, φ, comp_zsmul, zsmul_comp, ← neg_smul, ← mul_smul, pow_add, neg_mul,
       mul_one, Fin.coe_castLT, Fin.val_succ, pow_one, mul_neg, neg_neg]
     let jj : Fin (n + 2) := (φ (i, j) hij).1
-    have ineq : jj ≤ i := by
-      rw [← Fin.val_fin_le]
-      simpa using hij
+    have ineq : jj ≤ i := by rw [← Fin.val_fin_le]; simpa using hij
     rw [CategoryTheory.SimplicialObject.δ_comp_δ X ineq, Fin.castSucc_castLT, mul_comm]
   · -- φ : S → Sᶜ is injective
     rintro ⟨i, j⟩ ⟨i', j'⟩ hij hij' h
@@ -301,9 +297,7 @@ def ε [Limits.HasZeroObject C] :
     simp only [alternating_face_map_complex_obj_d, obj_d, Fin.sum_univ_two, Fin.val_zero, pow_zero,
       one_zsmul, Fin.val_one, pow_one, neg_smul, add_comp, simplicial_object.δ_naturality, neg_comp]
     apply add_right_neg
-  naturality' X Y f := by
-    ext
-    exact congr_app f.w _
+  naturality' X Y f := by ext; exact congr_app f.w _
 #align algebraic_topology.alternating_face_map_complex.ε AlgebraicTopology.AlternatingFaceMapComplex.ε
 -/
 
@@ -335,9 +329,7 @@ def inclusionOfMooreComplexMap (X : SimplicialObject A) :
     have def_t :
       ∀ j : Fin (n + 2),
         t j = (normalized_Moore_complex.obj_X X (n + 1)).arrow ≫ ((-1 : ℤ) ^ (j : ℕ) • X.δ j) :=
-      by
-      intro j
-      rfl
+      by intro j; rfl
     rw [Fin.sum_univ_succ t]
     have null : ∀ j : Fin (n + 1), t j.succ = 0 :=
       by

86d1873c

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -83,10 +83,7 @@ def objD (n : ℕ) : X _[n + 1] ⟶ X _[n] :=
 #align algebraic_topology.alternating_face_map_complex.obj_d AlgebraicTopology.AlternatingFaceMapComplex.objD
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex.d_squared AlgebraicTopology.AlternatingFaceMapComplex.d_squaredₓ'. -/
 /-- ## The chain complex relation `d ≫ d`
 -/
@@ -173,10 +170,7 @@ theorem obj_X (X : SimplicialObject C) (n : ℕ) : (AlternatingFaceMapComplex.ob
 #align algebraic_topology.alternating_face_map_complex.obj_X AlgebraicTopology.AlternatingFaceMapComplex.obj_X
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex.obj_d_eq AlgebraicTopology.AlternatingFaceMapComplex.obj_d_eqₓ'. -/
 @[simp]
 theorem obj_d_eq (X : SimplicialObject C) (n : ℕ) :
@@ -236,10 +230,7 @@ theorem alternatingFaceMapComplex_obj_X (X : SimplicialObject C) (n : ℕ) :
 #align algebraic_topology.alternating_face_map_complex_obj_X AlgebraicTopology.alternatingFaceMapComplex_obj_X
 
 /- warning: algebraic_topology.alternating_face_map_complex_obj_d -> AlgebraicTopology.alternatingFaceMapComplex_obj_d is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex_obj_d AlgebraicTopology.alternatingFaceMapComplex_obj_dₓ'. -/
 @[simp]
 theorem alternatingFaceMapComplex_obj_d (X : SimplicialObject C) (n : ℕ) :
@@ -248,10 +239,7 @@ theorem alternatingFaceMapComplex_obj_d (X : SimplicialObject C) (n : ℕ) :
 #align algebraic_topology.alternating_face_map_complex_obj_d AlgebraicTopology.alternatingFaceMapComplex_obj_d
 
 /- warning: algebraic_topology.alternating_face_map_complex_map_f -> AlgebraicTopology.alternatingFaceMapComplex_map_f is a dubious translation:
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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.{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))))) Nat.hasOne) (CategoryTheory.Functor.obj.{u2, u2, max u2 u1, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1) (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.{u1, u2} C _inst_1 _inst_2) Y) 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))))) Nat.hasOne) (CategoryTheory.Functor.obj.{u2, u2, max u2 u1, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1) (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(CategoryTheory.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.{u1, u2} C _inst_1 _inst_2) Y) (CategoryTheory.Functor.map.{u2, u2, max u2 u1, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1) (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.{u1, u2} C _inst_1 _inst_2) X Y f) 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)))
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(AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, max u1 u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} 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))) (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))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, max u1 u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (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.{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)) (Prefunctor.obj.{succ u2, succ u2, max u1 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))) (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))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, max u1 u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (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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(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)) (Prefunctor.obj.{succ u2, succ u2, max u1 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))) (ChainComplex.{u2, u1, 0} C _inst_1 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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex_map_f AlgebraicTopology.alternatingFaceMapComplex_map_fₓ'. -/
 @[simp]
 theorem alternatingFaceMapComplex_map_f {X Y : SimplicialObject C} (f : X ⟶ Y) (n : ℕ) :
@@ -260,10 +248,7 @@ theorem alternatingFaceMapComplex_map_f {X Y : SimplicialObject C} (f : X ⟶ Y)
 #align algebraic_topology.alternating_face_map_complex_map_f AlgebraicTopology.alternatingFaceMapComplex_map_f
 
 /- warning: algebraic_topology.map_alternating_face_map_complex -> AlgebraicTopology.map_alternatingFaceMapComplex is a dubious translation:
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(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)) F) (AlgebraicTopology.alternatingFaceMapComplex.{u4, u3} D _inst_3 _inst_4))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.map_alternating_face_map_complex AlgebraicTopology.map_alternatingFaceMapComplexₓ'. -/
 theorem map_alternatingFaceMapComplex {D : Type _} [Category D] [Preadditive D] (F : C ⥤ D)
     [F.Additive] :
@@ -288,10 +273,7 @@ theorem map_alternatingFaceMapComplex {D : Type _} [Category D] [Preadditive D]
 #align algebraic_topology.map_alternating_face_map_complex AlgebraicTopology.map_alternatingFaceMapComplex
 
 /- warning: algebraic_topology.karoubi_alternating_face_map_complex_d -> AlgebraicTopology.karoubi_alternatingFaceMapComplex_d is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.karoubi_alternating_face_map_complex_d AlgebraicTopology.karoubi_alternatingFaceMapComplex_dₓ'. -/
 theorem karoubi_alternatingFaceMapComplex_d (P : Karoubi (SimplicialObject C)) (n : ℕ) :
     ((AlternatingFaceMapComplex.obj (KaroubiFunctorCategoryEmbedding.obj P)).d (n + 1) n).f =
@@ -335,10 +317,7 @@ end AlternatingFaceMapComplex
 variable {A : Type _} [Category A] [Abelian A]
 
 /- warning: algebraic_topology.inclusion_of_Moore_complex_map -> AlgebraicTopology.inclusionOfMooreComplexMap is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.inclusion_of_Moore_complex_map AlgebraicTopology.inclusionOfMooreComplexMapₓ'. -/
 /-- The inclusion map of the Moore complex in the alternating face map complex -/
 def inclusionOfMooreComplexMap (X : SimplicialObject A) :
@@ -382,10 +361,7 @@ def inclusionOfMooreComplexMap (X : SimplicialObject A) :
 #align algebraic_topology.inclusion_of_Moore_complex_map AlgebraicTopology.inclusionOfMooreComplexMap
 
 /- warning: algebraic_topology.inclusion_of_Moore_complex_map_f -> AlgebraicTopology.inclusionOfMooreComplexMap_f is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align algebraic_topology.inclusion_of_Moore_complex_map_f AlgebraicTopology.inclusionOfMooreComplexMap_fₓ'. -/
 @[simp]
 theorem inclusionOfMooreComplexMap_f (X : SimplicialObject A) (n : ℕ) :
@@ -422,10 +398,7 @@ def objD (n : ℕ) : X.obj [n] ⟶ X.obj [n + 1] :=
 #align algebraic_topology.alternating_coface_map_complex.obj_d AlgebraicTopology.AlternatingCofaceMapComplex.objD
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_coface_map_complex.d_eq_unop_d AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_dₓ'. -/
 theorem d_eq_unop_d (n : ℕ) :
     objD X n =
@@ -435,10 +408,7 @@ theorem d_eq_unop_d (n : ℕ) :
 #align algebraic_topology.alternating_coface_map_complex.d_eq_unop_d AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_d
 
 /- warning: algebraic_topology.alternating_coface_map_complex.d_squared -> AlgebraicTopology.AlternatingCofaceMapComplex.d_squared is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_coface_map_complex.d_squared AlgebraicTopology.AlternatingCofaceMapComplex.d_squaredₓ'. -/
 theorem d_squared (n : ℕ) : objD X n ≫ objD X (n + 1) = 0 := by
   simp only [d_eq_unop_d, ← unop_comp, alternating_face_map_complex.d_squared, unop_zero]

86d1873c

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, Adam Topaz, Johan Commelin
 
 ! This file was ported from Lean 3 source module algebraic_topology.alternating_face_map_complex
-! leanprover-community/mathlib commit 88bca0ce5d22ebfd9e73e682e51d60ea13b48347
+! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -19,6 +19,9 @@ import Mathbin.Tactic.EquivRw
 
 # The alternating face map complex of a simplicial object in a preadditive category
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We construct the alternating face map complex, as a
 functor `alternating_face_map_complex : simplicial_object C ⥤ chain_complex C ℕ`
 for any preadditive category `C`. For any simplicial object `X` in `C`,

88bca0ce

bump to nightly-2023-04-20-20

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

e863e061

Diff

@@ -284,20 +284,20 @@ theorem map_alternatingFaceMapComplex {D : Type _} [Category D] [Preadditive D]
       rfl
 #align algebraic_topology.map_alternating_face_map_complex AlgebraicTopology.map_alternatingFaceMapComplex
 
-/- warning: algebraic_topology.karoubi_alternating_face_map_complex_d -> AlgebraicTopology.karoubi_alternating_face_map_complex_d is a dubious translation:
+/- warning: algebraic_topology.karoubi_alternating_face_map_complex_d -> AlgebraicTopology.karoubi_alternatingFaceMapComplex_d 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] (P : CategoryTheory.Idempotents.Karoubi.{max u2 u1, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1)) (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.x.{u1, u2} C _inst_1 (HomologicalComplex.x.{u2, max u1 u2, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) C (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) _inst_1 P)) (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.Idempotents.Karoubi.x.{u1, u2} C _inst_1 (HomologicalComplex.x.{u2, max u1 u2, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) C (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) _inst_1 P)) n))) (CategoryTheory.Idempotents.Karoubi.Hom.f.{u1, u2} C _inst_1 (HomologicalComplex.x.{u2, max u1 u2, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) C (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) _inst_1 P)) (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, max u1 u2, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) C (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) _inst_1 P)) n) (HomologicalComplex.d.{u2, max u1 u2, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) C (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) _inst_1 P)) (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)) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.x.{u1, u2} C _inst_1 (HomologicalComplex.x.{u2, max u1 u2, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) C (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) _inst_1 P)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (CategoryTheory.Idempotents.Karoubi.x.{max u2 u1, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1) P) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Idempotents.Karoubi.x.{u1, u2} C _inst_1 (HomologicalComplex.x.{u2, max u1 u2, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{max u1 u2, u2} (CategoryTheory.Idempotents.Karoubi.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.category.{u1, u2} C _inst_1) (CategoryTheory.Idempotents.Karoubi.CategoryTheory.preadditive.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) C (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) _inst_1 P)) n)) (CategoryTheory.NatTrans.app.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (CategoryTheory.Idempotents.Karoubi.x.{max u2 u1, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1) P) (CategoryTheory.Idempotents.Karoubi.x.{max u2 u1, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1) P) (CategoryTheory.Idempotents.Karoubi.p.{max u2 u1, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1) P) (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.d.{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 (CategoryTheory.Idempotents.Karoubi.x.{max u2 u1, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1) P)) (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))
 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] (P : CategoryTheory.Idempotents.Karoubi.{max u2 u1, u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (n : Nat), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.X.{u2, u1} C _inst_1 (HomologicalComplex.X.{u1, max u2 u1, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) C (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) _inst_1 P)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.Idempotents.Karoubi.X.{u2, u1} C _inst_1 (HomologicalComplex.X.{u1, max u2 u1, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) C (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) _inst_1 P)) n))) (CategoryTheory.Idempotents.Karoubi.Hom.f.{u2, u1} C _inst_1 (HomologicalComplex.X.{u1, max u2 u1, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{max u1 u2, u1} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Idempotents.KaroubiFunctorCategoryEmbedding.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) C (CategoryTheory.Category.opposite.{0, 0} SimplexCategory 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-Case conversion may be inaccurate. Consider using '#align algebraic_topology.karoubi_alternating_face_map_complex_d AlgebraicTopology.karoubi_alternating_face_map_complex_dₓ'. -/
-theorem karoubi_alternating_face_map_complex_d (P : Karoubi (SimplicialObject C)) (n : ℕ) :
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.karoubi_alternating_face_map_complex_d AlgebraicTopology.karoubi_alternatingFaceMapComplex_dₓ'. -/
+theorem karoubi_alternatingFaceMapComplex_d (P : Karoubi (SimplicialObject C)) (n : ℕ) :
     ((AlternatingFaceMapComplex.obj (KaroubiFunctorCategoryEmbedding.obj P)).d (n + 1) n).f =
       P.p.app (op [n + 1]) ≫ (AlternatingFaceMapComplex.obj P.pt).d (n + 1) n :=
   by
   dsimp
   simpa only [alternating_face_map_complex.obj_d_eq, karoubi.sum_hom, preadditive.comp_sum,
     karoubi.zsmul_hom, preadditive.comp_zsmul]
-#align algebraic_topology.karoubi_alternating_face_map_complex_d AlgebraicTopology.karoubi_alternating_face_map_complex_d
+#align algebraic_topology.karoubi_alternating_face_map_complex_d AlgebraicTopology.karoubi_alternatingFaceMapComplex_d
 
 namespace AlternatingFaceMapComplex

88bca0ce

bump to nightly-2023-04-20-00

mathlib commit https://github.com/leanprover-community/mathlib/commit/cd8fafa2fac98e1a67097e8a91ad9901cfde48af

d6678ca6

Diff

@@ -66,6 +66,12 @@ variable (X : SimplicialObject C)
 
 variable (Y : SimplicialObject C)
 
+/- warning: algebraic_topology.alternating_face_map_complex.obj_d -> AlgebraicTopology.AlternatingFaceMapComplex.objD is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (n : Nat), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk 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) (n : Nat), Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n)))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex.obj_d AlgebraicTopology.AlternatingFaceMapComplex.objDₓ'. -/
 /-- The differential on the alternating face map complex is the alternate
 sum of the face maps -/
 @[simp]
@@ -73,6 +79,12 @@ def objD (n : ℕ) : X _[n + 1] ⟶ X _[n] :=
   ∑ i : Fin (n + 2), (-1 : ℤ) ^ (i : ℕ) • X.δ i
 #align algebraic_topology.alternating_face_map_complex.obj_d AlgebraicTopology.AlternatingFaceMapComplex.objD
 
+/- warning: algebraic_topology.alternating_face_map_complex.d_squared -> AlgebraicTopology.AlternatingFaceMapComplex.d_squared is a dubious translation:
+lean 3 declaration is
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex.d_squared AlgebraicTopology.AlternatingFaceMapComplex.d_squaredₓ'. -/
 /-- ## The chain complex relation `d ≫ d`
 -/
 theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 :=
@@ -139,16 +151,30 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 :=
 -/
 
 
+#print AlgebraicTopology.AlternatingFaceMapComplex.obj /-
 /-- The alternating face map complex, on objects -/
 def obj : ChainComplex C ℕ :=
   ChainComplex.of (fun n => X _[n]) (objD X) (d_squared X)
 #align algebraic_topology.alternating_face_map_complex.obj AlgebraicTopology.AlternatingFaceMapComplex.obj
+-/
 
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex.obj_X AlgebraicTopology.AlternatingFaceMapComplex.obj_Xₓ'. -/
 @[simp]
-theorem obj_x (X : SimplicialObject C) (n : ℕ) : (AlternatingFaceMapComplex.obj X).pt n = X _[n] :=
+theorem obj_X (X : SimplicialObject C) (n : ℕ) : (AlternatingFaceMapComplex.obj X).pt n = X _[n] :=
   rfl
-#align algebraic_topology.alternating_face_map_complex.obj_X AlgebraicTopology.AlternatingFaceMapComplex.obj_x
-
+#align algebraic_topology.alternating_face_map_complex.obj_X AlgebraicTopology.AlternatingFaceMapComplex.obj_X
+
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex.obj_d_eq AlgebraicTopology.AlternatingFaceMapComplex.obj_d_eqₓ'. -/
 @[simp]
 theorem obj_d_eq (X : SimplicialObject C) (n : ℕ) :
     (AlternatingFaceMapComplex.obj X).d (n + 1) n = ∑ i : Fin (n + 2), (-1 : ℤ) ^ (i : ℕ) • X.δ i :=
@@ -157,6 +183,7 @@ theorem obj_d_eq (X : SimplicialObject C) (n : ℕ) :
 
 variable {X} {Y}
 
+#print AlgebraicTopology.AlternatingFaceMapComplex.map /-
 /-- The alternating face map complex, on morphisms -/
 def map (f : X ⟶ Y) : obj X ⟶ obj Y :=
   ChainComplex.ofHom _ _ _ _ _ _ (fun n => f.app (op [n])) fun n =>
@@ -169,43 +196,72 @@ def map (f : X ⟶ Y) : obj X ⟶ obj Y :=
     symm
     apply f.naturality
 #align algebraic_topology.alternating_face_map_complex.map AlgebraicTopology.AlternatingFaceMapComplex.map
+-/
 
+#print AlgebraicTopology.AlternatingFaceMapComplex.map_f /-
 @[simp]
 theorem map_f (f : X ⟶ Y) (n : ℕ) : (map f).f n = f.app (op [n]) :=
   rfl
 #align algebraic_topology.alternating_face_map_complex.map_f AlgebraicTopology.AlternatingFaceMapComplex.map_f
+-/
 
 end AlternatingFaceMapComplex
 
 variable (C : Type _) [Category C] [Preadditive C]
 
+#print AlgebraicTopology.alternatingFaceMapComplex /-
 /-- The alternating face map complex, as a functor -/
 def alternatingFaceMapComplex : SimplicialObject C ⥤ ChainComplex C ℕ
     where
   obj := AlternatingFaceMapComplex.obj
   map X Y f := AlternatingFaceMapComplex.map f
 #align algebraic_topology.alternating_face_map_complex AlgebraicTopology.alternatingFaceMapComplex
+-/
 
 variable {C}
 
+/- warning: algebraic_topology.alternating_face_map_complex_obj_X -> AlgebraicTopology.alternatingFaceMapComplex_obj_X is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex_obj_X AlgebraicTopology.alternatingFaceMapComplex_obj_Xₓ'. -/
 @[simp]
-theorem alternatingFaceMapComplex_obj_x (X : SimplicialObject C) (n : ℕ) :
+theorem alternatingFaceMapComplex_obj_X (X : SimplicialObject C) (n : ℕ) :
     ((alternatingFaceMapComplex C).obj X).pt n = X _[n] :=
   rfl
-#align algebraic_topology.alternating_face_map_complex_obj_X AlgebraicTopology.alternatingFaceMapComplex_obj_x
-
+#align algebraic_topology.alternating_face_map_complex_obj_X AlgebraicTopology.alternatingFaceMapComplex_obj_X
+
+/- warning: algebraic_topology.alternating_face_map_complex_obj_d -> AlgebraicTopology.alternatingFaceMapComplex_obj_d is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] (X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (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) (CategoryTheory.Functor.obj.{u2, u2, max u2 u1, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1) (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.{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))))) (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) (CategoryTheory.Functor.obj.{u2, u2, max u2 u1, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1) (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.{u1, u2} C _inst_1 _inst_2) X) n)) (HomologicalComplex.d.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{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))))) Nat.hasOne)) (AlgebraicTopology.alternatingFaceMapComplex.{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) (AlgebraicTopology.AlternatingFaceMapComplex.objD.{u1, u2} C _inst_1 _inst_2 X n)
+but is expected to have type
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_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.{u1, u2} C _inst_1 _inst_2)) X) n)) (HomologicalComplex.d.{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)) (Prefunctor.obj.{succ u2, succ u2, max u1 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))) (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))))) 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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex_obj_d AlgebraicTopology.alternatingFaceMapComplex_obj_dₓ'. -/
 @[simp]
-theorem alternatingFaceMapComplex_objD (X : SimplicialObject C) (n : ℕ) :
+theorem alternatingFaceMapComplex_obj_d (X : SimplicialObject C) (n : ℕ) :
     ((alternatingFaceMapComplex C).obj X).d (n + 1) n = AlternatingFaceMapComplex.objD X n := by
   apply ChainComplex.of_d
-#align algebraic_topology.alternating_face_map_complex_obj_d AlgebraicTopology.alternatingFaceMapComplex_objD
-
+#align algebraic_topology.alternating_face_map_complex_obj_d AlgebraicTopology.alternatingFaceMapComplex_obj_d
+
+/- warning: algebraic_topology.alternating_face_map_complex_map_f -> AlgebraicTopology.alternatingFaceMapComplex_map_f 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 : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} (f : Quiver.Hom.{succ u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u2, max u2 u1} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1))) X Y) (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)) (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) (CategoryTheory.Functor.obj.{u2, u2, max u2 u1, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1) (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.{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))))) Nat.hasOne) (CategoryTheory.Functor.obj.{u2, u2, max u2 u1, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1) (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 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (AlgebraicTopology.alternatingFaceMapComplex.{u1, u2} C _inst_1 _inst_2) X Y f) 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)))
+but is expected to have type
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(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 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(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))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, max u1 u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u2, u1} C _inst_1) (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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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_face_map_complex_map_f AlgebraicTopology.alternatingFaceMapComplex_map_fₓ'. -/
 @[simp]
 theorem alternatingFaceMapComplex_map_f {X Y : SimplicialObject C} (f : X ⟶ Y) (n : ℕ) :
     ((alternatingFaceMapComplex C).map f).f n = f.app (op [n]) :=
   rfl
 #align algebraic_topology.alternating_face_map_complex_map_f AlgebraicTopology.alternatingFaceMapComplex_map_f
 
+/- warning: algebraic_topology.map_alternating_face_map_complex -> AlgebraicTopology.map_alternatingFaceMapComplex is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.map_alternating_face_map_complex AlgebraicTopology.map_alternatingFaceMapComplexₓ'. -/
 theorem map_alternatingFaceMapComplex {D : Type _} [Category D] [Preadditive D] (F : C ⥤ D)
     [F.Additive] :
     alternatingFaceMapComplex C ⋙ F.mapHomologicalComplex _ =
@@ -228,6 +284,12 @@ theorem map_alternatingFaceMapComplex {D : Type _} [Category D] [Preadditive D]
       rfl
 #align algebraic_topology.map_alternating_face_map_complex AlgebraicTopology.map_alternatingFaceMapComplex
 
+/- warning: algebraic_topology.karoubi_alternating_face_map_complex_d -> AlgebraicTopology.karoubi_alternating_face_map_complex_d is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.Idempotents.Karoubi.x.{max u2 u1, u2} (CategoryTheory.SimplicialObject.{u2, u1} C _inst_1) (CategoryTheory.SimplicialObject.category.{u2, u1} C _inst_1) P)) (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))
+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] (P : CategoryTheory.Idempotents.Karoubi.{max u2 u1, u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1)) (n : Nat), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Idempotents.Karoubi.X.{u2, u1} C _inst_1 (HomologicalComplex.X.{u1, max u2 u1, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _inst_1 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(OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (CategoryTheory.Idempotents.Karoubi.X.{u2, u1} C _inst_1 (HomologicalComplex.X.{u1, max u2 u1, 0} Nat (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, max u1 u2} (CategoryTheory.Idempotents.Karoubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.Karoubi.instCategoryKaroubi.{u2, u1} C _inst_1) (CategoryTheory.Idempotents.instPreadditiveKaroubiInstCategoryKaroubi.{u2, u1} C _inst_1 _inst_2)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) 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(CategoryTheory.NatTrans.app.{0, u1, 0, u2} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 (CategoryTheory.Idempotents.Karoubi.X.{max u2 u1, u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) P) (CategoryTheory.Idempotents.Karoubi.X.{max u2 u1, u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) P) (CategoryTheory.Idempotents.Karoubi.p.{max u2 u1, u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) P) (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.d.{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 (CategoryTheory.Idempotents.Karoubi.X.{max u2 u1, u1} (CategoryTheory.SimplicialObject.{u1, u2} C _inst_1) (CategoryTheory.instCategorySimplicialObject.{u1, u2} C _inst_1) P)) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) n))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.karoubi_alternating_face_map_complex_d AlgebraicTopology.karoubi_alternating_face_map_complex_dₓ'. -/
 theorem karoubi_alternating_face_map_complex_d (P : Karoubi (SimplicialObject C)) (n : ℕ) :
     ((AlternatingFaceMapComplex.obj (KaroubiFunctorCategoryEmbedding.obj P)).d (n + 1) n).f =
       P.p.app (op [n + 1]) ≫ (AlternatingFaceMapComplex.obj P.pt).d (n + 1) n :=
@@ -239,6 +301,7 @@ theorem karoubi_alternating_face_map_complex_d (P : Karoubi (SimplicialObject C)
 
 namespace AlternatingFaceMapComplex
 
+#print AlgebraicTopology.AlternatingFaceMapComplex.ε /-
 /-- The natural transformation which gives the augmentation of the alternating face map
 complex attached to an augmented simplicial object. -/
 @[simps]
@@ -256,7 +319,8 @@ def ε [Limits.HasZeroObject C] :
   naturality' X Y f := by
     ext
     exact congr_app f.w _
-#align algebraic_topology.alternating_face_map_complex.ε AlgebraicTopology.alternatingFaceMapComplex.ε
+#align algebraic_topology.alternating_face_map_complex.ε AlgebraicTopology.AlternatingFaceMapComplex.ε
+-/
 
 end AlternatingFaceMapComplex
 
@@ -267,6 +331,12 @@ end AlternatingFaceMapComplex
 
 variable {A : Type _} [Category A] [Abelian A]
 
+/- warning: algebraic_topology.inclusion_of_Moore_complex_map -> AlgebraicTopology.inclusionOfMooreComplexMap is a dubious translation:
+lean 3 declaration is
+  forall {A : Type.{u1}} [_inst_3 : CategoryTheory.Category.{u2, u1} A] [_inst_4 : CategoryTheory.Abelian.{u2, u1} A _inst_3] (X : CategoryTheory.SimplicialObject.{u2, u1} A _inst_3), Quiver.Hom.{succ u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} 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_inst_3 _inst_4)) X)
+but is expected to have type
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(AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (AlgebraicTopology.alternatingFaceMapComplex.{u1, u2} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4))) X)
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.inclusion_of_Moore_complex_map AlgebraicTopology.inclusionOfMooreComplexMapₓ'. -/
 /-- The inclusion map of the Moore complex in the alternating face map complex -/
 def inclusionOfMooreComplexMap (X : SimplicialObject A) :
     (normalizedMooreComplex A).obj X ⟶ (alternatingFaceMapComplex A).obj X :=
@@ -308,6 +378,12 @@ def inclusionOfMooreComplexMap (X : SimplicialObject A) :
     cases n <;> dsimp <;> simp
 #align algebraic_topology.inclusion_of_Moore_complex_map AlgebraicTopology.inclusionOfMooreComplexMap
 
+/- warning: algebraic_topology.inclusion_of_Moore_complex_map_f -> AlgebraicTopology.inclusionOfMooreComplexMap_f is a dubious translation:
+lean 3 declaration is
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Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (AlgebraicTopology.normalizedMooreComplex.{u1, u2} A _inst_3 _inst_4) X) n) (HomologicalComplex.x.{u2, u1, 0} Nat A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Functor.obj.{u2, u2, max u2 u1, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_3) (CategoryTheory.SimplicialObject.category.{u2, u1} A _inst_3) (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 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(CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) X) n)) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Functor.obj.{u2, u2, max u2 u1, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_3) (CategoryTheory.SimplicialObject.category.{u2, u1} A _inst_3) (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (AlgebraicTopology.normalizedMooreComplex.{u1, u2} A _inst_3 _inst_4) X) (CategoryTheory.Functor.obj.{u2, u2, max u2 u1, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_3) (CategoryTheory.SimplicialObject.category.{u2, u1} A _inst_3) (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (AlgebraicTopology.alternatingFaceMapComplex.{u1, u2} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) X) (AlgebraicTopology.inclusionOfMooreComplexMap.{u1, u2} A _inst_3 _inst_4 X) n) (CategoryTheory.Subobject.arrow.{u2, u1} A _inst_3 (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) A _inst_3 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (AlgebraicTopology.NormalizedMooreComplex.objX.{u1, u2} A _inst_3 _inst_4 X n))
+but is expected to have type
+  forall {A : Type.{u1}} [_inst_3 : CategoryTheory.Category.{u2, u1} A] [_inst_4 : CategoryTheory.Abelian.{u2, u1} A _inst_3] (X : CategoryTheory.SimplicialObject.{u2, u1} A _inst_3) (n : Nat), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} A (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} A (CategoryTheory.Category.toCategoryStruct.{u2, u1} A _inst_3)) (HomologicalComplex.X.{u2, u1, 0} Nat A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, max u1 u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_3) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_3) (CategoryTheory.instCategorySimplicialObject.{u2, u1} A _inst_3))) (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, max u1 u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_3) (CategoryTheory.instCategorySimplicialObject.{u2, u1} A _inst_3) (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (AlgebraicTopology.normalizedMooreComplex.{u1, u2} A _inst_3 _inst_4)) X) n) (HomologicalComplex.X.{u2, u1, 0} Nat A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, max u1 u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_3) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_3) (CategoryTheory.instCategorySimplicialObject.{u2, u1} A _inst_3))) (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, max u1 u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_3) (CategoryTheory.instCategorySimplicialObject.{u2, u1} A _inst_3) (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (AlgebraicTopology.alternatingFaceMapComplex.{u1, u2} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4))) X) n)) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, max u1 u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_3) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_3) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_3) (CategoryTheory.instCategorySimplicialObject.{u2, u1} A _inst_3))) (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, max u1 u2, max u1 u2} (CategoryTheory.SimplicialObject.{u2, u1} A _inst_3) (CategoryTheory.instCategorySimplicialObject.{u2, u1} A _inst_3) (ChainComplex.{u2, u1, 0} A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat A _inst_3 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} A _inst_3 (CategoryTheory.Abelian.toPreadditive.{u2, u1} A _inst_3 _inst_4)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.inclusion_of_Moore_complex_map_f AlgebraicTopology.inclusionOfMooreComplexMap_fₓ'. -/
 @[simp]
 theorem inclusionOfMooreComplexMap_f (X : SimplicialObject A) (n : ℕ) :
     (inclusionOfMooreComplexMap X).f n = (NormalizedMooreComplex.objX X n).arrow :=
@@ -316,17 +392,25 @@ theorem inclusionOfMooreComplexMap_f (X : SimplicialObject A) (n : ℕ) :
 
 variable (A)
 
+#print AlgebraicTopology.inclusionOfMooreComplex /-
 /-- The inclusion map of the Moore complex in the alternating face map complex,
 as a natural transformation -/
 @[simps]
 def inclusionOfMooreComplex : normalizedMooreComplex A ⟶ alternatingFaceMapComplex A
     where app := inclusionOfMooreComplexMap
 #align algebraic_topology.inclusion_of_Moore_complex AlgebraicTopology.inclusionOfMooreComplex
+-/
 
 namespace AlternatingCofaceMapComplex
 
 variable (X Y : CosimplicialObject C)
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_coface_map_complex.obj_d AlgebraicTopology.AlternatingCofaceMapComplex.objDₓ'. -/
 /-- The differential on the alternating coface map complex is the alternate
 sum of the coface maps -/
 @[simp]
@@ -334,6 +418,12 @@ def objD (n : ℕ) : X.obj [n] ⟶ X.obj [n + 1] :=
   ∑ i : Fin (n + 2), (-1 : ℤ) ^ (i : ℕ) • X.δ i
 #align algebraic_topology.alternating_coface_map_complex.obj_d AlgebraicTopology.AlternatingCofaceMapComplex.objD
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_coface_map_complex.d_eq_unop_d AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_dₓ'. -/
 theorem d_eq_unop_d (n : ℕ) :
     objD X n =
       (AlternatingFaceMapComplex.objD ((cosimplicialSimplicialEquiv C).Functor.obj (op X))
@@ -341,17 +431,26 @@ theorem d_eq_unop_d (n : ℕ) :
   by simpa only [obj_d, alternating_face_map_complex.obj_d, unop_sum, unop_zsmul]
 #align algebraic_topology.alternating_coface_map_complex.d_eq_unop_d AlgebraicTopology.AlternatingCofaceMapComplex.d_eq_unop_d
 
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(CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u2, 0, u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{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} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) 0 (Zero.toOfNat0.{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} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{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} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u2, 0, u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{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} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (CategoryTheory.Limits.HasZeroMorphisms.Zero.{u2, u1} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (Prefunctor.obj.{1, succ u2, 0, u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{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} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk n)) (Prefunctor.obj.{1, succ u2, 0, u1} SimplexCategory (CategoryTheory.CategoryStruct.toQuiver.{0, 0} SimplexCategory (CategoryTheory.Category.toCategoryStruct.{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} SimplexCategory SimplexCategory.smallCategory C _inst_1 X) (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.alternating_coface_map_complex.d_squared AlgebraicTopology.AlternatingCofaceMapComplex.d_squaredₓ'. -/
 theorem d_squared (n : ℕ) : objD X n ≫ objD X (n + 1) = 0 := by
   simp only [d_eq_unop_d, ← unop_comp, alternating_face_map_complex.d_squared, unop_zero]
 #align algebraic_topology.alternating_coface_map_complex.d_squared AlgebraicTopology.AlternatingCofaceMapComplex.d_squared
 
+#print AlgebraicTopology.AlternatingCofaceMapComplex.obj /-
 /-- The alternating coface map complex, on objects -/
 def obj : CochainComplex C ℕ :=
   CochainComplex.of (fun n => X.obj [n]) (objD X) (d_squared X)
 #align algebraic_topology.alternating_coface_map_complex.obj AlgebraicTopology.AlternatingCofaceMapComplex.obj
+-/
 
 variable {X} {Y}
 
+#print AlgebraicTopology.AlternatingCofaceMapComplex.map /-
 /-- The alternating face map complex, on morphisms -/
 @[simp]
 def map (f : X ⟶ Y) : obj X ⟶ obj Y :=
@@ -365,11 +464,13 @@ def map (f : X ⟶ Y) : obj X ⟶ obj Y :=
     symm
     apply f.naturality
 #align algebraic_topology.alternating_coface_map_complex.map AlgebraicTopology.AlternatingCofaceMapComplex.map
+-/
 
 end AlternatingCofaceMapComplex
 
 variable (C)
 
+#print AlgebraicTopology.alternatingCofaceMapComplex /-
 /-- The alternating coface map complex, as a functor -/
 @[simps]
 def alternatingCofaceMapComplex : CosimplicialObject C ⥤ CochainComplex C ℕ
@@ -377,6 +478,7 @@ def alternatingCofaceMapComplex : CosimplicialObject C ⥤ CochainComplex C ℕ
   obj := AlternatingCofaceMapComplex.obj
   map X Y f := AlternatingCofaceMapComplex.map f
 #align algebraic_topology.alternating_coface_map_complex AlgebraicTopology.alternatingCofaceMapComplex
+-/
 
 end AlgebraicTopology

88bca0ce

bump to nightly-2023-04-07-12

mathlib commit https://github.com/leanprover-community/mathlib/commit/5ec62c8106221a3f9160e4e4fcc3eed79fe213e9

77742840

Diff

@@ -98,28 +98,28 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 :=
     by constructing a bijection φ : S -> Sᶜ, which maps (i,j) to (j,i+1),
     and by comparing the terms -/
   let φ : ∀ ij : P, ij ∈ S → P := fun ij hij =>
-    (Fin.castLt ij.2 (lt_of_le_of_lt (finset.mem_filter.mp hij).right (Fin.is_lt ij.1)), ij.1.succ)
+    (Fin.castLT ij.2 (lt_of_le_of_lt (finset.mem_filter.mp hij).right (Fin.is_lt ij.1)), ij.1.succ)
   apply Finset.sum_bij φ
   · -- φ(S) is contained in Sᶜ
     intro ij hij
     simp only [Finset.mem_univ, Finset.compl_filter, Finset.mem_filter, true_and_iff, Fin.val_succ,
-      Fin.coe_castLt] at hij⊢
+      Fin.coe_castLT] at hij⊢
     linarith
   · -- identification of corresponding terms in both sums
     rintro ⟨i, j⟩ hij
     simp only [term, d_l, d_r, φ, comp_zsmul, zsmul_comp, ← neg_smul, ← mul_smul, pow_add, neg_mul,
-      mul_one, Fin.coe_castLt, Fin.val_succ, pow_one, mul_neg, neg_neg]
+      mul_one, Fin.coe_castLT, Fin.val_succ, pow_one, mul_neg, neg_neg]
     let jj : Fin (n + 2) := (φ (i, j) hij).1
     have ineq : jj ≤ i := by
       rw [← Fin.val_fin_le]
       simpa using hij
-    rw [CategoryTheory.SimplicialObject.δ_comp_δ X ineq, Fin.castSucc_cast_lt, mul_comm]
+    rw [CategoryTheory.SimplicialObject.δ_comp_δ X ineq, Fin.castSucc_castLT, mul_comm]
   · -- φ : S → Sᶜ is injective
     rintro ⟨i, j⟩ ⟨i', j'⟩ hij hij' h
     rw [Prod.mk.inj_iff]
     refine' ⟨by simpa using congr_arg Prod.snd h, _⟩
     have h1 := congr_arg Fin.castSucc (congr_arg Prod.fst h)
-    simpa [Fin.castSucc_cast_lt] using h1
+    simpa [Fin.castSucc_castLT] using h1
   · -- φ : S → Sᶜ is surjective
     rintro ⟨i', j'⟩ hij'
     simp only [true_and_iff, Finset.mem_univ, Finset.compl_filter, not_le, Finset.mem_filter] at
@@ -130,7 +130,7 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 :=
     ·
       simpa only [true_and_iff, Finset.mem_univ, Fin.coe_castSucc, Fin.coe_pred,
         Finset.mem_filter] using Nat.le_pred_of_lt hij'
-    · simp only [Prod.mk.inj_iff, Fin.succ_pred, Fin.cast_lt_castSucc]
+    · simp only [Prod.mk.inj_iff, Fin.succ_pred, Fin.castLT_castSucc]
       constructor <;> rfl
 #align algebraic_topology.alternating_face_map_complex.d_squared AlgebraicTopology.AlternatingFaceMapComplex.d_squared

88bca0ce

bump to nightly-2023-02-28-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

1fb1623f

Diff

@@ -145,7 +145,7 @@ def obj : ChainComplex C ℕ :=
 #align algebraic_topology.alternating_face_map_complex.obj AlgebraicTopology.AlternatingFaceMapComplex.obj
 
 @[simp]
-theorem obj_x (X : SimplicialObject C) (n : ℕ) : (AlternatingFaceMapComplex.obj X).x n = X _[n] :=
+theorem obj_x (X : SimplicialObject C) (n : ℕ) : (AlternatingFaceMapComplex.obj X).pt n = X _[n] :=
   rfl
 #align algebraic_topology.alternating_face_map_complex.obj_X AlgebraicTopology.AlternatingFaceMapComplex.obj_x
 
@@ -190,7 +190,7 @@ variable {C}
 
 @[simp]
 theorem alternatingFaceMapComplex_obj_x (X : SimplicialObject C) (n : ℕ) :
-    ((alternatingFaceMapComplex C).obj X).x n = X _[n] :=
+    ((alternatingFaceMapComplex C).obj X).pt n = X _[n] :=
   rfl
 #align algebraic_topology.alternating_face_map_complex_obj_X AlgebraicTopology.alternatingFaceMapComplex_obj_x
 
@@ -230,7 +230,7 @@ theorem map_alternatingFaceMapComplex {D : Type _} [Category D] [Preadditive D]
 
 theorem karoubi_alternating_face_map_complex_d (P : Karoubi (SimplicialObject C)) (n : ℕ) :
     ((AlternatingFaceMapComplex.obj (KaroubiFunctorCategoryEmbedding.obj P)).d (n + 1) n).f =
-      P.p.app (op [n + 1]) ≫ (AlternatingFaceMapComplex.obj P.x).d (n + 1) n :=
+      P.p.app (op [n + 1]) ≫ (AlternatingFaceMapComplex.obj P.pt).d (n + 1) n :=
   by
   dsimp
   simpa only [alternating_face_map_complex.obj_d_eq, karoubi.sum_hom, preadditive.comp_sum,

88bca0ce

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

88bca0ce

chore(*): remove empty lines between variable statements (#11418)

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

75c86f04

Diff

@@ -57,9 +57,7 @@ namespace AlternatingFaceMapComplex
 
 
 variable {C : Type*} [Category C] [Preadditive C]
-
 variable (X : SimplicialObject C)
-
 variable (Y : SimplicialObject C)
 
 /-- The differential on the alternating face map complex is the alternate

88bca0ce

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

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

38bce757

Diff

@@ -87,8 +87,8 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 := by
   apply Finset.sum_bij φ
   · -- φ(S) is contained in Sᶜ
     intro ij hij
-    simp only [Finset.mem_univ, Finset.compl_filter, Finset.mem_filter, true_and_iff, Fin.val_succ,
-      Fin.coe_castLT] at hij ⊢
+    simp only [S, Finset.mem_univ, Finset.compl_filter, Finset.mem_filter, true_and_iff,
+      Fin.val_succ, Fin.coe_castLT] at hij ⊢
     linarith
   · -- φ : S → Sᶜ is injective
     rintro ⟨i, j⟩ hij ⟨i', j'⟩ hij' h
@@ -97,14 +97,14 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 := by
       by simpa [Fin.castSucc_castLT] using congr_arg Fin.castSucc (congr_arg Prod.fst h)⟩
   · -- φ : S → Sᶜ is surjective
     rintro ⟨i', j'⟩ hij'
-    simp only [Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.compl_filter,
+    simp only [S, Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.compl_filter,
       not_le, Finset.mem_filter, true_and] at hij'
     refine' ⟨(j'.pred <| _, Fin.castSucc i'), _, _⟩
     · rintro rfl
       simp only [Fin.val_zero, not_lt_zero'] at hij'
-    · simpa only [Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.mem_filter,
+    · simpa only [S, Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.mem_filter,
         Fin.coe_castSucc, Fin.coe_pred, true_and] using Nat.le_sub_one_of_lt hij'
-    · simp only [Fin.castLT_castSucc, Fin.succ_pred]
+    · simp only [φ, Fin.castLT_castSucc, Fin.succ_pred]
   · -- identification of corresponding terms in both sums
     rintro ⟨i, j⟩ hij
     dsimp
@@ -113,7 +113,7 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 := by
     · simp only [Fin.val_succ, pow_add, pow_one, mul_neg, neg_neg, mul_one]
       apply mul_comm
     · rw [CategoryTheory.SimplicialObject.δ_comp_δ'']
-      simpa using hij
+      simpa [S] using hij
 #align algebraic_topology.alternating_face_map_complex.d_squared AlgebraicTopology.AlternatingFaceMapComplex.d_squared
 
 /-!

88bca0ce

feat: Better lemmas for transferring finite sums along equivalences (#9237)

Lemmas around this were a mess, throth in terms of names, statement and location. This PR standardises everything to be in Algebra.BigOperators.Basic and changes the lemmas to take in InjOn and SurjOn assumptions where possible (and where impossible make sure the hypotheses are taken in the correct order) and moves the equality of functions hypothesis last.

Also add a few lemmas that help fix downstream uses by golfing.

From LeanAPAP and LeanCamCombi

82c60323

Diff

@@ -90,17 +90,8 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 := by
     simp only [Finset.mem_univ, Finset.compl_filter, Finset.mem_filter, true_and_iff, Fin.val_succ,
       Fin.coe_castLT] at hij ⊢
     linarith
-  · -- identification of corresponding terms in both sums
-    rintro ⟨i, j⟩ hij
-    dsimp
-    simp only [zsmul_comp, comp_zsmul, smul_smul, ← neg_smul]
-    congr 1
-    · simp only [Fin.val_succ, pow_add, pow_one, mul_neg, neg_neg, mul_one]
-      apply mul_comm
-    · rw [CategoryTheory.SimplicialObject.δ_comp_δ'']
-      simpa using hij
   · -- φ : S → Sᶜ is injective
-    rintro ⟨i, j⟩ ⟨i', j'⟩ hij hij' h
+    rintro ⟨i, j⟩ hij ⟨i', j'⟩ hij' h
     rw [Prod.mk.inj_iff]
     exact ⟨by simpa using congr_arg Prod.snd h,
       by simpa [Fin.castSucc_castLT] using congr_arg Fin.castSucc (congr_arg Prod.fst h)⟩
@@ -114,6 +105,15 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 := by
     · simpa only [Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.mem_filter,
         Fin.coe_castSucc, Fin.coe_pred, true_and] using Nat.le_sub_one_of_lt hij'
     · simp only [Fin.castLT_castSucc, Fin.succ_pred]
+  · -- identification of corresponding terms in both sums
+    rintro ⟨i, j⟩ hij
+    dsimp
+    simp only [zsmul_comp, comp_zsmul, smul_smul, ← neg_smul]
+    congr 1
+    · simp only [Fin.val_succ, pow_add, pow_one, mul_neg, neg_neg, mul_one]
+      apply mul_comm
+    · rw [CategoryTheory.SimplicialObject.δ_comp_δ'']
+      simpa using hij
 #align algebraic_topology.alternating_face_map_complex.d_squared AlgebraicTopology.AlternatingFaceMapComplex.d_squared
 
 /-!

88bca0ce

refactor(Algebra/Homology): remove single₀ (#8208)

This PR removes the special definitions of single₀ for chain and cochain complexes, so as to avoid duplication of code with HomologicalComplex.single which is the functor constructing the complex that is supported by a single arbitrary degree. single₀ was supposed to have better definitional properties, but it turns out that in Lean4, it is no longer true (at least for the action of this functor on objects). The computation of the homology of these single complexes is generalized for HomologicalComplex.single using the new homology API: this result is moved to a separate file Algebra.Homology.SingleHomology.

ecdd87a3

Diff

@@ -224,7 +224,6 @@ namespace AlternatingFaceMapComplex
 
 /-- The natural transformation which gives the augmentation of the alternating face map
 complex attached to an augmented simplicial object. -/
---@[simps]
 def ε [Limits.HasZeroObject C] :
     SimplicialObject.Augmented.drop ⋙ AlgebraicTopology.alternatingFaceMapComplex C ⟶
       SimplicialObject.Augmented.point ⋙ ChainComplex.single₀ C where
@@ -236,9 +235,24 @@ def ε [Limits.HasZeroObject C] :
       pow_zero, one_smul, Fin.val_one, pow_one, neg_smul, one_smul, add_comp,
       neg_comp, SimplicialObject.δ_naturality, SimplicialObject.δ_naturality]
     apply add_right_neg
-  naturality _ _ f := ChainComplex.to_single₀_ext _ _ (by exact congr_app f.w _)
+  naturality X Y f := by
+    apply HomologicalComplex.to_single_hom_ext
+    dsimp
+    erw [ChainComplex.toSingle₀Equiv_symm_apply_f_zero,
+      ChainComplex.toSingle₀Equiv_symm_apply_f_zero]
+    simp only [ChainComplex.single₀_map_f_zero]
+    exact congr_app f.w _
 #align algebraic_topology.alternating_face_map_complex.ε AlgebraicTopology.AlternatingFaceMapComplex.ε
 
+@[simp]
+lemma ε_app_f_zero [Limits.HasZeroObject C] (X : SimplicialObject.Augmented C) :
+    (ε.app X).f 0 = X.hom.app (op [0]) :=
+  ChainComplex.toSingle₀Equiv_symm_apply_f_zero _ _
+
+@[simp]
+lemma ε_app_f_succ [Limits.HasZeroObject C] (X : SimplicialObject.Augmented C) (n : ℕ) :
+    (ε.app X).f (n + 1) = 0 := rfl
+
 end AlternatingFaceMapComplex
 
 /-!

88bca0ce

fix: patch for std4#195 (more succ/pred lemmas for Nat) (#6203)

cdcad962

Diff

@@ -112,7 +112,7 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 := by
     · rintro rfl
       simp only [Fin.val_zero, not_lt_zero'] at hij'
     · simpa only [Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.mem_filter,
-        Fin.coe_castSucc, Fin.coe_pred, true_and] using Nat.le_pred_of_lt hij'
+        Fin.coe_castSucc, Fin.coe_pred, true_and] using Nat.le_sub_one_of_lt hij'
     · simp only [Fin.castLT_castSucc, Fin.succ_pred]
 #align algebraic_topology.alternating_face_map_complex.d_squared AlgebraicTopology.AlternatingFaceMapComplex.d_squared

88bca0ce

style: fix wrapping of where (#7149)

084cfb35

Diff

@@ -285,8 +285,8 @@ variable (A)
 /-- The inclusion map of the Moore complex in the alternating face map complex,
 as a natural transformation -/
 @[simps]
-def inclusionOfMooreComplex : normalizedMooreComplex A ⟶ alternatingFaceMapComplex A
-    where app := inclusionOfMooreComplexMap
+def inclusionOfMooreComplex : normalizedMooreComplex A ⟶ alternatingFaceMapComplex A where
+  app := inclusionOfMooreComplexMap
 set_option linter.uppercaseLean3 false in
 #align algebraic_topology.inclusion_of_Moore_complex AlgebraicTopology.inclusionOfMooreComplex

88bca0ce

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

@@ -56,7 +56,7 @@ namespace AlternatingFaceMapComplex
 -/
 
 
-variable {C : Type _} [Category C] [Preadditive C]
+variable {C : Type*} [Category C] [Preadditive C]
 
 variable (X : SimplicialObject C)
 
@@ -159,7 +159,7 @@ theorem map_f (f : X ⟶ Y) (n : ℕ) : (map f).f n = f.app (op [n]) :=
 
 end AlternatingFaceMapComplex
 
-variable (C : Type _) [Category C] [Preadditive C]
+variable (C : Type*) [Category C] [Preadditive C]
 
 /-- The alternating face map complex, as a functor -/
 def alternatingFaceMapComplex : SimplicialObject C ⥤ ChainComplex C ℕ where
@@ -189,7 +189,7 @@ theorem alternatingFaceMapComplex_map_f {X Y : SimplicialObject C} (f : X ⟶ Y)
   rfl
 #align algebraic_topology.alternating_face_map_complex_map_f AlgebraicTopology.alternatingFaceMapComplex_map_f
 
-theorem map_alternatingFaceMapComplex {D : Type _} [Category D] [Preadditive D] (F : C ⥤ D)
+theorem map_alternatingFaceMapComplex {D : Type*} [Category D] [Preadditive D] (F : C ⥤ D)
     [F.Additive] :
     alternatingFaceMapComplex C ⋙ F.mapHomologicalComplex _ =
       (SimplicialObject.whiskering C D).obj F ⋙ alternatingFaceMapComplex D := by
@@ -245,7 +245,7 @@ end AlternatingFaceMapComplex
 ## Construction of the natural inclusion of the normalized Moore complex
 -/
 
-variable {A : Type _} [Category A] [Abelian A]
+variable {A : Type*} [Category A] [Abelian A]
 
 /-- The inclusion map of the Moore complex in the alternating face map complex -/
 def inclusionOfMooreComplexMap (X : SimplicialObject A) :

88bca0ce

chore: bump to nightly-2023-07-15 (#5992)

Various adaptations to changes when Fin API was moved to Std. One notable change is that many lemmas are now stated in terms of i ≠ 0 (for i : Fin n) rather then i.1 ≠ 0, and as a consequence many Fin.vne_of_ne applications have been added or removed, mostly removed.

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

24924f96

Diff

@@ -108,7 +108,7 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 := by
     rintro ⟨i', j'⟩ hij'
     simp only [Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.compl_filter,
       not_le, Finset.mem_filter, true_and] at hij'
-    refine' ⟨(j'.pred <| Fin.vne_of_ne (j := 0) _, Fin.castSucc i'), _, _⟩
+    refine' ⟨(j'.pred <| _, Fin.castSucc i'), _, _⟩
     · rintro rfl
       simp only [Fin.val_zero, not_lt_zero'] at hij'
     · simpa only [Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.mem_filter,

88bca0ce

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

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou, Adam Topaz, Johan Commelin
-
-! This file was ported from Lean 3 source module algebraic_topology.alternating_face_map_complex
-! leanprover-community/mathlib commit 88bca0ce5d22ebfd9e73e682e51d60ea13b48347
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Homology.Additive
 import Mathlib.AlgebraicTopology.MooreComplex
@@ -14,6 +9,8 @@ import Mathlib.Algebra.BigOperators.Fin
 import Mathlib.CategoryTheory.Preadditive.Opposite
 import Mathlib.CategoryTheory.Idempotents.FunctorCategories
 
+#align_import algebraic_topology.alternating_face_map_complex from "leanprover-community/mathlib"@"88bca0ce5d22ebfd9e73e682e51d60ea13b48347"
+
 /-!
 
 # The alternating face map complex of a simplicial object in a preadditive category

88bca0ce

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

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

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

906f7221

Diff

@@ -106,17 +106,17 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 := by
     rintro ⟨i, j⟩ ⟨i', j'⟩ hij hij' h
     rw [Prod.mk.inj_iff]
     exact ⟨by simpa using congr_arg Prod.snd h,
-      by simpa [Fin.castSuccEmb_castLT] using congr_arg Fin.castSuccEmb (congr_arg Prod.fst h)⟩
+      by simpa [Fin.castSucc_castLT] using congr_arg Fin.castSucc (congr_arg Prod.fst h)⟩
   · -- φ : S → Sᶜ is surjective
     rintro ⟨i', j'⟩ hij'
     simp only [Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.compl_filter,
       not_le, Finset.mem_filter, true_and] at hij'
-    refine' ⟨(j'.pred _, Fin.castSuccEmb i'), _, _⟩
+    refine' ⟨(j'.pred <| Fin.vne_of_ne (j := 0) _, Fin.castSucc i'), _, _⟩
     · rintro rfl
       simp only [Fin.val_zero, not_lt_zero'] at hij'
     · simpa only [Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.mem_filter,
-        Fin.coe_castSuccEmb, Fin.coe_pred, true_and] using Nat.le_pred_of_lt hij'
-    · simp only [Fin.castLT_castSuccEmb, Fin.succ_pred]
+        Fin.coe_castSucc, Fin.coe_pred, true_and] using Nat.le_pred_of_lt hij'
+    · simp only [Fin.castLT_castSucc, Fin.succ_pred]
 #align algebraic_topology.alternating_face_map_complex.d_squared AlgebraicTopology.AlternatingFaceMapComplex.d_squared
 
 /-!

88bca0ce

chore: rename Fin.castSucc to Fin.castSuccEmb (#5729)

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

f4e42872

Diff

@@ -106,17 +106,17 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 := by
     rintro ⟨i, j⟩ ⟨i', j'⟩ hij hij' h
     rw [Prod.mk.inj_iff]
     exact ⟨by simpa using congr_arg Prod.snd h,
-      by simpa [Fin.castSucc_castLT] using congr_arg Fin.castSucc (congr_arg Prod.fst h)⟩
+      by simpa [Fin.castSuccEmb_castLT] using congr_arg Fin.castSuccEmb (congr_arg Prod.fst h)⟩
   · -- φ : S → Sᶜ is surjective
     rintro ⟨i', j'⟩ hij'
     simp only [Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.compl_filter,
       not_le, Finset.mem_filter, true_and] at hij'
-    refine' ⟨(j'.pred _, Fin.castSucc i'), _, _⟩
+    refine' ⟨(j'.pred _, Fin.castSuccEmb i'), _, _⟩
     · rintro rfl
       simp only [Fin.val_zero, not_lt_zero'] at hij'
     · simpa only [Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.mem_filter,
-        Fin.coe_castSucc, Fin.coe_pred, true_and] using Nat.le_pred_of_lt hij'
-    · simp only [Fin.castLT_castSucc, Fin.succ_pred]
+        Fin.coe_castSuccEmb, Fin.coe_pred, true_and] using Nat.le_pred_of_lt hij'
+    · simp only [Fin.castLT_castSuccEmb, Fin.succ_pred]
 #align algebraic_topology.alternating_face_map_complex.d_squared AlgebraicTopology.AlternatingFaceMapComplex.d_squared
 
 /-!

88bca0ce

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

@@ -98,9 +98,9 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 := by
     dsimp
     simp only [zsmul_comp, comp_zsmul, smul_smul, ← neg_smul]
     congr 1
-    . simp only [Fin.val_succ, pow_add, pow_one, mul_neg, neg_neg, mul_one]
+    · simp only [Fin.val_succ, pow_add, pow_one, mul_neg, neg_neg, mul_one]
       apply mul_comm
-    . rw [CategoryTheory.SimplicialObject.δ_comp_δ'']
+    · rw [CategoryTheory.SimplicialObject.δ_comp_δ'']
       simpa using hij
   · -- φ : S → Sᶜ is injective
     rintro ⟨i, j⟩ ⟨i', j'⟩ hij hij' h
@@ -112,11 +112,11 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 := by
     simp only [Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.compl_filter,
       not_le, Finset.mem_filter, true_and] at hij'
     refine' ⟨(j'.pred _, Fin.castSucc i'), _, _⟩
-    . rintro rfl
+    · rintro rfl
       simp only [Fin.val_zero, not_lt_zero'] at hij'
-    . simpa only [Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.mem_filter,
+    · simpa only [Finset.mem_univ, forall_true_left, Prod.forall, ge_iff_le, Finset.mem_filter,
         Fin.coe_castSucc, Fin.coe_pred, true_and] using Nat.le_pred_of_lt hij'
-    . simp only [Fin.castLT_castSucc, Fin.succ_pred]
+    · simp only [Fin.castLT_castSucc, Fin.succ_pred]
 #align algebraic_topology.alternating_face_map_complex.d_squared AlgebraicTopology.AlternatingFaceMapComplex.d_squared
 
 /-!
@@ -264,7 +264,7 @@ def inclusionOfMooreComplexMap (X : SimplicialObject A) :
   simp only [AlternatingFaceMapComplex.objD, comp_sum]
   rw [Fin.sum_univ_succ, Fintype.sum_eq_zero]
   swap
-  . intro j
+  · intro j
     rw [NormalizedMooreComplex.objX, comp_zsmul,
       ← factorThru_arrow _ _ (finset_inf_arrow_factors Finset.univ _ _ (Finset.mem_univ j)),
       Category.assoc, kernelSubobject_arrow_comp, comp_zero, smul_zero]

88bca0ce

chore: fix many typos (#4967)

These are all doc fixes

6f9e51c3

Diff

@@ -78,7 +78,7 @@ theorem d_squared (n : ℕ) : objD X (n + 1) ≫ objD X n = 0 := by
   -- we start by expanding d ≫ d as a double sum
   dsimp
   simp only [comp_sum, sum_comp, ← Finset.sum_product']
-  -- then, we decompose the index set P into a subet S and its complement Sᶜ
+  -- then, we decompose the index set P into a subset S and its complement Sᶜ
   let P := Fin (n + 2) × Fin (n + 3)
   let S := Finset.univ.filter fun ij : P => (ij.2 : ℕ) ≤ (ij.1 : ℕ)
   erw [← Finset.sum_add_sum_compl S, ← eq_neg_iff_add_eq_zero, ← Finset.sum_neg_distrib]

88bca0ce

feat: port AlgebraicTopology.DoldKan.PInfty (#3539)

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

1d9fdc01

Diff

@@ -214,14 +214,14 @@ theorem map_alternatingFaceMapComplex {D : Type _} [Category D] [Preadditive D]
       rfl
 #align algebraic_topology.map_alternating_face_map_complex AlgebraicTopology.map_alternatingFaceMapComplex
 
-theorem karoubi_alternating_face_map_complex_d (P : Karoubi (SimplicialObject C)) (n : ℕ) :
+theorem karoubi_alternatingFaceMapComplex_d (P : Karoubi (SimplicialObject C)) (n : ℕ) :
     ((AlternatingFaceMapComplex.obj (KaroubiFunctorCategoryEmbedding.obj P)).d (n + 1) n).f =
       P.p.app (op [n + 1]) ≫ (AlternatingFaceMapComplex.obj P.X).d (n + 1) n := by
   dsimp
   simp only [AlternatingFaceMapComplex.obj_d_eq, Karoubi.sum_hom, Preadditive.comp_sum,
     Karoubi.zsmul_hom, Preadditive.comp_zsmul]
   rfl
-#align algebraic_topology.karoubi_alternating_face_map_complex_d AlgebraicTopology.karoubi_alternating_face_map_complex_d
+#align algebraic_topology.karoubi_alternating_face_map_complex_d AlgebraicTopology.karoubi_alternatingFaceMapComplex_d
 
 namespace AlternatingFaceMapComplex

88bca0ce

feat: port AlgebraicTopology.AlternatingFaceMapComplex (#3519)

Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>

bb39bf93

`algebraic_topology.alternating_face_map_complex` ⟷ `Mathlib.AlgebraicTopology.AlternatingFaceMapComplex`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 515

algebraic_topology.alternating_face_map_complex ⟷ Mathlib.AlgebraicTopology.AlternatingFaceMapComplex

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 515

`algebraic_topology.alternating_face_map_complex` ⟷ `Mathlib.AlgebraicTopology.AlternatingFaceMapComplex`