algebraic_topology.dold_kan.homotopies

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

b12099d3

(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

@@ -110,7 +110,7 @@ theorem c_mk (i j : ℕ) (h : j + 1 = i) : c.Rel i j :=
 theorem cs_down_0_not_rel_left (j : ℕ) : ¬c.Rel 0 j :=
   by
   intro hj
-  dsimp at hj 
+  dsimp at hj
   apply Nat.not_succ_le_zero j
   rw [Nat.succ_eq_add_one, hj]
 #align algebraic_topology.dold_kan.cs_down_0_not_rel_left AlgebraicTopology.DoldKan.cs_down_0_not_rel_left
@@ -245,7 +245,7 @@ theorem map_Hσ {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Addit
   by
   unfold Hσ
   have eq := HomologicalComplex.congr_hom (map_null_homotopic_map' G (hσ' q)) n
-  simp only [functor.map_homological_complex_map_f, ← map_hσ'] at eq 
+  simp only [functor.map_homological_complex_map_f, ← map_hσ'] at eq
   rw [Eq]
   let h := (functor.congr_obj (map_alternating_face_map_complex G) X).symm
   congr

86d1873c

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 -/
-import Mathbin.Algebra.Homology.Homotopy
-import Mathbin.AlgebraicTopology.DoldKan.Notations
+import Algebra.Homology.Homotopy
+import AlgebraicTopology.DoldKan.Notations
 
 #align_import algebraic_topology.dold_kan.homotopies 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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
-
-! This file was ported from Lean 3 source module algebraic_topology.dold_kan.homotopies
-! 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.Homotopy
 import Mathbin.AlgebraicTopology.DoldKan.Notations
 
+#align_import algebraic_topology.dold_kan.homotopies from "leanprover-community/mathlib"@"86d1873c01a723aba6788f0b9051ae3d23b4c1c3"
+
 /-!
 
 # Construction of homotopies for the Dold-Kan correspondence

86d1873c

bump to nightly-2023-06-20-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

9b351f8c

Diff

@@ -221,7 +221,7 @@ def natTransHσ (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapCo
     unfold Hσ
     rw [null_homotopic_map'_comp, comp_null_homotopic_map']
     congr
-    ext (n m hnm)
+    ext n m hnm
     simp only [alternating_face_map_complex_map_f, hσ'_naturality]
 #align algebraic_topology.dold_kan.nat_trans_Hσ AlgebraicTopology.DoldKan.natTransHσ
 -/

86d1873c

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -119,11 +119,13 @@ theorem cs_down_0_not_rel_left (j : ℕ) : ¬c.Rel 0 j :=
 #align algebraic_topology.dold_kan.cs_down_0_not_rel_left AlgebraicTopology.DoldKan.cs_down_0_not_rel_left
 -/
 
+#print AlgebraicTopology.DoldKan.hσ /-
 /-- The sequence of maps which gives the null homotopic maps `Hσ` that shall be in
 the inductive construction of the projections `P q : K[X] ⟶ K[X]` -/
 def hσ (q : ℕ) (n : ℕ) : X _[n] ⟶ X _[n + 1] :=
   if n < q then 0 else (-1 : ℤ) ^ (n - q) • X.σ ⟨n - q, Nat.sub_lt_succ n q⟩
 #align algebraic_topology.dold_kan.hσ AlgebraicTopology.DoldKan.hσ
+-/
 
 #print AlgebraicTopology.DoldKan.hσ' /-
 /-- We can turn `hσ` into a datum that can be passed to `null_homotopic_map'`. -/
@@ -138,6 +140,7 @@ theorem hσ'_eq_zero {q n m : ℕ} (hnq : n < q) (hnm : c.Rel m n) :
 #align algebraic_topology.dold_kan.hσ'_eq_zero AlgebraicTopology.DoldKan.hσ'_eq_zero
 -/
 
+#print AlgebraicTopology.DoldKan.hσ'_eq /-
 theorem hσ'_eq {q n a m : ℕ} (ha : n = a + q) (hnm : c.Rel m n) :
     (hσ' q n m hnm : X _[n] ⟶ X _[m]) =
       ((-1 : ℤ) ^ a • X.σ ⟨a, Nat.lt_succ_iff.mpr (Nat.le.intro (Eq.symm ha))⟩) ≫
@@ -149,24 +152,31 @@ theorem hσ'_eq {q n a m : ℕ} (ha : n = a + q) (hnm : c.Rel m n) :
   · have h' := tsub_eq_of_eq_add ha
     congr
 #align algebraic_topology.dold_kan.hσ'_eq AlgebraicTopology.DoldKan.hσ'_eq
+-/
 
+#print AlgebraicTopology.DoldKan.hσ'_eq' /-
 theorem hσ'_eq' {q n a : ℕ} (ha : n = a + q) :
     (hσ' q n (n + 1) rfl : X _[n] ⟶ X _[n + 1]) =
       (-1 : ℤ) ^ a • X.σ ⟨a, Nat.lt_succ_iff.mpr (Nat.le.intro (Eq.symm ha))⟩ :=
   by rw [hσ'_eq ha rfl, eq_to_hom_refl, comp_id]
 #align algebraic_topology.dold_kan.hσ'_eq' AlgebraicTopology.DoldKan.hσ'_eq'
+-/
 
 /- warning: algebraic_topology.dold_kan.Hσ clashes with algebraic_topology.dold_kan.hσ -> AlgebraicTopology.DoldKan.hσ
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Hσ AlgebraicTopology.DoldKan.hσₓ'. -/
+#print AlgebraicTopology.DoldKan.hσ /-
 /-- The null homotopic map $(hσ q) ∘ d + d ∘ (hσ q)$ -/
 def hσ (q : ℕ) : K[X] ⟶ K[X] :=
   nullHomotopicMap' (hσ' q)
 #align algebraic_topology.dold_kan.Hσ AlgebraicTopology.DoldKan.hσ
+-/
 
+#print AlgebraicTopology.DoldKan.homotopyHσToZero /-
 /-- `Hσ` is null homotopic -/
 def homotopyHσToZero (q : ℕ) : Homotopy (hσ q : K[X] ⟶ K[X]) 0 :=
   nullHomotopy' (hσ' q)
 #align algebraic_topology.dold_kan.homotopy_Hσ_to_zero AlgebraicTopology.DoldKan.homotopyHσToZero
+-/
 
 #print AlgebraicTopology.DoldKan.Hσ_eq_zero /-
 /-- In degree `0`, the null homotopic map `Hσ` is zero. -/
@@ -185,6 +195,7 @@ theorem Hσ_eq_zero (q : ℕ) : (hσ q : K[X] ⟶ K[X]).f 0 = 0 :=
 #align algebraic_topology.dold_kan.Hσ_eq_zero AlgebraicTopology.DoldKan.Hσ_eq_zero
 -/
 
+#print AlgebraicTopology.DoldKan.hσ'_naturality /-
 /-- The maps `hσ' q n m hnm` are natural on the simplicial object -/
 theorem hσ'_naturality (q : ℕ) (n m : ℕ) (hnm : c.Rel m n) {X Y : SimplicialObject C} (f : X ⟶ Y) :
     f.app (op [n]) ≫ hσ' q n m hnm = hσ' q n m hnm ≫ f.app (op [m]) :=
@@ -199,6 +210,7 @@ theorem hσ'_naturality (q : ℕ) (n m : ℕ) (hnm : c.Rel m n) {X Y : Simplicia
     erw [f.naturality]
     rfl
 #align algebraic_topology.dold_kan.hσ'_naturality AlgebraicTopology.DoldKan.hσ'_naturality
+-/
 
 #print AlgebraicTopology.DoldKan.natTransHσ /-
 /-- For each q, `Hσ q` is a natural transformation. -/
@@ -214,6 +226,7 @@ def natTransHσ (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapCo
 #align algebraic_topology.dold_kan.nat_trans_Hσ AlgebraicTopology.DoldKan.natTransHσ
 -/
 
+#print AlgebraicTopology.DoldKan.map_hσ' /-
 /-- The maps `hσ' q n m hnm` are compatible with the application of additive functors. -/
 theorem map_hσ' {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n m : ℕ) (hnm : c.Rel m n) :
@@ -225,7 +238,9 @@ theorem map_hσ' {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Addi
   · simp only [functor.map_zero, zero_comp]
   · simpa only [eq_to_hom_map, functor.map_comp, functor.map_zsmul]
 #align algebraic_topology.dold_kan.map_hσ' AlgebraicTopology.DoldKan.map_hσ'
+-/
 
+#print AlgebraicTopology.DoldKan.map_Hσ /-
 /-- The null homotopic maps `Hσ` are compatible with the application of additive functors. -/
 theorem map_Hσ {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n : ℕ) :
@@ -238,6 +253,7 @@ theorem map_Hσ {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Addit
   let h := (functor.congr_obj (map_alternating_face_map_complex G) X).symm
   congr
 #align algebraic_topology.dold_kan.map_Hσ AlgebraicTopology.DoldKan.map_Hσ
+-/
 
 end DoldKan

86d1873c

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -113,7 +113,7 @@ theorem c_mk (i j : ℕ) (h : j + 1 = i) : c.Rel i j :=
 theorem cs_down_0_not_rel_left (j : ℕ) : ¬c.Rel 0 j :=
   by
   intro hj
-  dsimp at hj
+  dsimp at hj 
   apply Nat.not_succ_le_zero j
   rw [Nat.succ_eq_add_one, hj]
 #align algebraic_topology.dold_kan.cs_down_0_not_rel_left AlgebraicTopology.DoldKan.cs_down_0_not_rel_left
@@ -128,7 +128,7 @@ def hσ (q : ℕ) (n : ℕ) : X _[n] ⟶ X _[n + 1] :=
 #print AlgebraicTopology.DoldKan.hσ' /-
 /-- We can turn `hσ` into a datum that can be passed to `null_homotopic_map'`. -/
 def hσ' (q : ℕ) : ∀ n m, c.Rel m n → (K[X].pt n ⟶ K[X].pt m) := fun n m hnm =>
-  hσ q n ≫ eqToHom (by congr )
+  hσ q n ≫ eqToHom (by congr)
 #align algebraic_topology.dold_kan.hσ' AlgebraicTopology.DoldKan.hσ'
 -/
 
@@ -141,7 +141,7 @@ theorem hσ'_eq_zero {q n m : ℕ} (hnq : n < q) (hnm : c.Rel m n) :
 theorem hσ'_eq {q n a m : ℕ} (ha : n = a + q) (hnm : c.Rel m n) :
     (hσ' q n m hnm : X _[n] ⟶ X _[m]) =
       ((-1 : ℤ) ^ a • X.σ ⟨a, Nat.lt_succ_iff.mpr (Nat.le.intro (Eq.symm ha))⟩) ≫
-        eqToHom (by congr ) :=
+        eqToHom (by congr) :=
   by
   simp only [hσ', hσ]
   split_ifs
@@ -233,7 +233,7 @@ theorem map_Hσ {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Addit
   by
   unfold Hσ
   have eq := HomologicalComplex.congr_hom (map_null_homotopic_map' G (hσ' q)) n
-  simp only [functor.map_homological_complex_map_f, ← map_hσ'] at eq
+  simp only [functor.map_homological_complex_map_f, ← map_hσ'] at eq 
   rw [Eq]
   let h := (functor.congr_obj (map_alternating_face_map_complex G) X).symm
   congr

86d1873c

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -80,7 +80,7 @@ open Homotopy
 
 open Opposite
 
-open Simplicial DoldKan
+open scoped Simplicial DoldKan
 
 noncomputable section

86d1873c

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -119,12 +119,6 @@ theorem cs_down_0_not_rel_left (j : ℕ) : ¬c.Rel 0 j :=
 #align algebraic_topology.dold_kan.cs_down_0_not_rel_left AlgebraicTopology.DoldKan.cs_down_0_not_rel_left
 -/
 
-/- warning: algebraic_topology.dold_kan.hσ -> AlgebraicTopology.DoldKan.hσ 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}, Nat -> (forall (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 n))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
-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}, Nat -> (forall (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 n))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.hσ AlgebraicTopology.DoldKan.hσₓ'. -/
 /-- The sequence of maps which gives the null homotopic maps `Hσ` that shall be in
 the inductive construction of the projections `P q : K[X] ⟶ K[X]` -/
 def hσ (q : ℕ) (n : ℕ) : X _[n] ⟶ X _[n + 1] :=
@@ -144,9 +138,6 @@ theorem hσ'_eq_zero {q n m : ℕ} (hnq : n < q) (hnm : c.Rel m n) :
 #align algebraic_topology.dold_kan.hσ'_eq_zero AlgebraicTopology.DoldKan.hσ'_eq_zero
 -/
 
-/- warning: algebraic_topology.dold_kan.hσ'_eq -> AlgebraicTopology.DoldKan.hσ'_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.hσ'_eq AlgebraicTopology.DoldKan.hσ'_eqₓ'. -/
 theorem hσ'_eq {q n a m : ℕ} (ha : n = a + q) (hnm : c.Rel m n) :
     (hσ' q n m hnm : X _[n] ⟶ X _[m]) =
       ((-1 : ℤ) ^ a • X.σ ⟨a, Nat.lt_succ_iff.mpr (Nat.le.intro (Eq.symm ha))⟩) ≫
@@ -159,9 +150,6 @@ theorem hσ'_eq {q n a m : ℕ} (ha : n = a + q) (hnm : c.Rel m n) :
     congr
 #align algebraic_topology.dold_kan.hσ'_eq AlgebraicTopology.DoldKan.hσ'_eq
 
-/- warning: algebraic_topology.dold_kan.hσ'_eq' -> AlgebraicTopology.DoldKan.hσ'_eq' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.hσ'_eq' AlgebraicTopology.DoldKan.hσ'_eq'ₓ'. -/
 theorem hσ'_eq' {q n a : ℕ} (ha : n = a + q) :
     (hσ' q n (n + 1) rfl : X _[n] ⟶ X _[n + 1]) =
       (-1 : ℤ) ^ a • X.σ ⟨a, Nat.lt_succ_iff.mpr (Nat.le.intro (Eq.symm ha))⟩ :=
@@ -169,20 +157,12 @@ theorem hσ'_eq' {q n a : ℕ} (ha : n = a + q) :
 #align algebraic_topology.dold_kan.hσ'_eq' AlgebraicTopology.DoldKan.hσ'_eq'
 
 /- warning: algebraic_topology.dold_kan.Hσ clashes with algebraic_topology.dold_kan.hσ -> AlgebraicTopology.DoldKan.hσ
-warning: algebraic_topology.dold_kan.Hσ -> AlgebraicTopology.DoldKan.hσ is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Hσ AlgebraicTopology.DoldKan.hσₓ'. -/
 /-- The null homotopic map $(hσ q) ∘ d + d ∘ (hσ q)$ -/
 def hσ (q : ℕ) : K[X] ⟶ K[X] :=
   nullHomotopicMap' (hσ' q)
 #align algebraic_topology.dold_kan.Hσ AlgebraicTopology.DoldKan.hσ
 
-/- warning: algebraic_topology.dold_kan.homotopy_Hσ_to_zero -> AlgebraicTopology.DoldKan.homotopyHσToZero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.homotopy_Hσ_to_zero AlgebraicTopology.DoldKan.homotopyHσToZeroₓ'. -/
 /-- `Hσ` is null homotopic -/
 def homotopyHσToZero (q : ℕ) : Homotopy (hσ q : K[X] ⟶ K[X]) 0 :=
   nullHomotopy' (hσ' q)
@@ -205,9 +185,6 @@ theorem Hσ_eq_zero (q : ℕ) : (hσ q : K[X] ⟶ K[X]).f 0 = 0 :=
 #align algebraic_topology.dold_kan.Hσ_eq_zero AlgebraicTopology.DoldKan.Hσ_eq_zero
 -/
 
-/- warning: algebraic_topology.dold_kan.hσ'_naturality -> AlgebraicTopology.DoldKan.hσ'_naturality is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.hσ'_naturality AlgebraicTopology.DoldKan.hσ'_naturalityₓ'. -/
 /-- The maps `hσ' q n m hnm` are natural on the simplicial object -/
 theorem hσ'_naturality (q : ℕ) (n m : ℕ) (hnm : c.Rel m n) {X Y : SimplicialObject C} (f : X ⟶ Y) :
     f.app (op [n]) ≫ hσ' q n m hnm = hσ' q n m hnm ≫ f.app (op [m]) :=
@@ -237,9 +214,6 @@ def natTransHσ (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapCo
 #align algebraic_topology.dold_kan.nat_trans_Hσ AlgebraicTopology.DoldKan.natTransHσ
 -/
 
-/- warning: algebraic_topology.dold_kan.map_hσ' -> AlgebraicTopology.DoldKan.map_hσ' is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.map_hσ' AlgebraicTopology.DoldKan.map_hσ'ₓ'. -/
 /-- The maps `hσ' q n m hnm` are compatible with the application of additive functors. -/
 theorem map_hσ' {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n m : ℕ) (hnm : c.Rel m n) :
@@ -252,9 +226,6 @@ theorem map_hσ' {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Addi
   · simpa only [eq_to_hom_map, functor.map_comp, functor.map_zsmul]
 #align algebraic_topology.dold_kan.map_hσ' AlgebraicTopology.DoldKan.map_hσ'
 
-/- warning: algebraic_topology.dold_kan.map_Hσ -> AlgebraicTopology.DoldKan.map_Hσ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.map_Hσ AlgebraicTopology.DoldKan.map_Hσₓ'. -/
 /-- The null homotopic maps `Hσ` are compatible with the application of additive functors. -/
 theorem map_Hσ {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n : ℕ) :

86d1873c

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -140,11 +140,7 @@ def hσ' (q : ℕ) : ∀ n m, c.Rel m n → (K[X].pt n ⟶ K[X].pt m) := fun n m
 
 #print AlgebraicTopology.DoldKan.hσ'_eq_zero /-
 theorem hσ'_eq_zero {q n m : ℕ} (hnq : n < q) (hnm : c.Rel m n) :
-    (hσ' q n m hnm : X _[n] ⟶ X _[m]) = 0 :=
-  by
-  simp only [hσ', hσ]
-  split_ifs
-  exact zero_comp
+    (hσ' q n m hnm : X _[n] ⟶ X _[m]) = 0 := by simp only [hσ', hσ]; split_ifs; exact zero_comp
 #align algebraic_topology.dold_kan.hσ'_eq_zero AlgebraicTopology.DoldKan.hσ'_eq_zero
 -/
 
@@ -158,8 +154,7 @@ theorem hσ'_eq {q n a m : ℕ} (ha : n = a + q) (hnm : c.Rel m n) :
   by
   simp only [hσ', hσ]
   split_ifs
-  · exfalso
-    linarith
+  · exfalso; linarith
   · have h' := tsub_eq_of_eq_add ha
     congr
 #align algebraic_topology.dold_kan.hσ'_eq AlgebraicTopology.DoldKan.hσ'_eq

86d1873c

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -149,10 +149,7 @@ theorem hσ'_eq_zero {q n m : ℕ} (hnq : n < q) (hnm : c.Rel m n) :
 -/
 
 /- warning: algebraic_topology.dold_kan.hσ'_eq -> AlgebraicTopology.DoldKan.hσ'_eq is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.hσ'_eq AlgebraicTopology.DoldKan.hσ'_eqₓ'. -/
 theorem hσ'_eq {q n a m : ℕ} (ha : n = a + q) (hnm : c.Rel m n) :
     (hσ' q n m hnm : X _[n] ⟶ X _[m]) =
@@ -168,10 +165,7 @@ theorem hσ'_eq {q n a m : ℕ} (ha : n = a + q) (hnm : c.Rel m n) :
 #align algebraic_topology.dold_kan.hσ'_eq AlgebraicTopology.DoldKan.hσ'_eq
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.hσ'_eq' AlgebraicTopology.DoldKan.hσ'_eq'ₓ'. -/
 theorem hσ'_eq' {q n a : ℕ} (ha : n = a + q) :
     (hσ' q n (n + 1) rfl : X _[n] ⟶ X _[n + 1]) =
@@ -192,10 +186,7 @@ def hσ (q : ℕ) : K[X] ⟶ K[X] :=
 #align algebraic_topology.dold_kan.Hσ AlgebraicTopology.DoldKan.hσ
 
 /- warning: algebraic_topology.dold_kan.homotopy_Hσ_to_zero -> AlgebraicTopology.DoldKan.homotopyHσToZero is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.homotopy_Hσ_to_zero AlgebraicTopology.DoldKan.homotopyHσToZeroₓ'. -/
 /-- `Hσ` is null homotopic -/
 def homotopyHσToZero (q : ℕ) : Homotopy (hσ q : K[X] ⟶ K[X]) 0 :=
@@ -220,10 +211,7 @@ theorem Hσ_eq_zero (q : ℕ) : (hσ q : K[X] ⟶ K[X]).f 0 = 0 :=
 -/
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.hσ'_naturality AlgebraicTopology.DoldKan.hσ'_naturalityₓ'. -/
 /-- The maps `hσ' q n m hnm` are natural on the simplicial object -/
 theorem hσ'_naturality (q : ℕ) (n m : ℕ) (hnm : c.Rel m n) {X Y : SimplicialObject C} (f : X ⟶ Y) :
@@ -255,10 +243,7 @@ def natTransHσ (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapCo
 -/
 
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 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.map_hσ' AlgebraicTopology.DoldKan.map_hσ'ₓ'. -/
 /-- The maps `hσ' q n m hnm` are compatible with the application of additive functors. -/
 theorem map_hσ' {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
@@ -273,10 +258,7 @@ theorem map_hσ' {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Addi
 #align algebraic_topology.dold_kan.map_hσ' AlgebraicTopology.DoldKan.map_hσ'
 
 /- warning: algebraic_topology.dold_kan.map_Hσ -> AlgebraicTopology.DoldKan.map_Hσ is a dubious translation:
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Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.DoldKan.Hσ.{u1, u2} C _inst_1 _inst_2 X q) n))
+<too large>
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.map_Hσ AlgebraicTopology.DoldKan.map_Hσₓ'. -/
 /-- The null homotopic maps `Hσ` are compatible with the application of additive functors. -/
 theorem map_Hσ {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]

86d1873c

bump to nightly-2023-05-19-16

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

a31df521

Diff

@@ -152,7 +152,7 @@ theorem hσ'_eq_zero {q n m : ℕ} (hnq : n < q) (hnm : c.Rel m n) :
 lean 3 declaration is
   forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {q : Nat} {n : Nat} {a : Nat} {m : Nat} (ha : Eq.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) a q)) (hnm : ComplexShape.Rel.{0} Nat AlgebraicTopology.DoldKan.c m n), 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) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) m)) (AlgebraicTopology.DoldKan.hσ'.{u1, u2} C _inst_1 _inst_2 X q n m hnm) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) m) (SMul.smul.{0, u2} Int (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) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (SubNegMonoid.SMulInt.{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) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (AddGroup.toSubNegMonoid.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(CategoryTheory.SimplicialObject.σ.{u2, u1} C _inst_1 X n (Fin.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)))) a (Iff.mpr (LT.lt.{0} Nat Nat.hasLt a (Nat.succ n)) (LE.le.{0} Nat Nat.hasLe a n) (Nat.lt_succ_iff a n) (Nat.le.intro a n q (Eq.symm.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) a q) ha)))))) (CategoryTheory.eqToHom.{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))))))) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) m) ((fun (self : CategoryTheory.Functor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) (self_1 : CategoryTheory.Functor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) (e_1 : Eq.{succ (max u2 u1)} (CategoryTheory.Functor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) self self_1) (ᾰ : Opposite.{1} SimplexCategory) (ᾰ_1 : Opposite.{1} SimplexCategory) (e_2 : Eq.{1} (Opposite.{1} SimplexCategory) ᾰ ᾰ_1) => congr.{1, succ u1} (Opposite.{1} SimplexCategory) C (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 self) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 self_1) ᾰ ᾰ_1 (congr_arg.{succ (max u2 u1), succ u1} (CategoryTheory.Functor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) ((Opposite.{1} SimplexCategory) -> C) self self_1 (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1) e_1) e_2) X X (rfl.{succ (max u2 u1)} (CategoryTheory.Functor.{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)))))) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk m)) ((fun (ᾰ : SimplexCategory) (ᾰ_1 : SimplexCategory) (e_1 : Eq.{1} SimplexCategory ᾰ ᾰ_1) => congr_arg.{1, 1} SimplexCategory (Opposite.{1} SimplexCategory) ᾰ ᾰ_1 (Opposite.op.{1} SimplexCategory) e_1) (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))))) (SimplexCategory.mk m) ((fun (n : Nat) (n_1 : Nat) (e_1 : Eq.{1} Nat n n_1) => congr_arg.{1, 1} Nat SimplexCategory n n_1 SimplexCategory.mk e_1) (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)))) m hnm)))))
 but is expected to have type
-  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {q : Nat} {n : Nat} {a : Nat} {m : Nat} (ha : Eq.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) a q)) (hnm : ComplexShape.Rel.{0} Nat AlgebraicTopology.DoldKan.c m n), 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))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) m)) (AlgebraicTopology.DoldKan.hσ'.{u1, u2} C _inst_1 _inst_2 X q n m hnm) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) m) (HSMul.hSMul.{0, u2, u2} Int (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u2, 0, u1} 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(Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (instHSMul.{0, u2} Int (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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))))))) (SubNegMonoid.SMulInt.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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))))))) (AddGroup.toSubNegMonoid.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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))))))) (AddCommGroup.toAddGroup.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (CategoryTheory.Preadditive.homGroup.{u2, u1} C _inst_1 _inst_2 (Prefunctor.obj.{1, succ u2, 0, u1} 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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))))))))))) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat (Neg.neg.{0} Int Int.instNegInt (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) a) (CategoryTheory.SimplicialObject.σ.{u2, u1} C _inst_1 X n (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) a (Iff.mpr (LT.lt.{0} Nat instLTNat a (Nat.succ n)) (LE.le.{0} Nat instLENat a n) (Nat.lt_succ_iff a n) (Nat.le.intro a n q (Eq.symm.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) a q) ha)))))) (CategoryTheory.eqToHom.{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)))))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) m) ((fun {V : Type} [inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.586 : Quiver.{1, 0} V] {W : Type.{u1}} [inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.590 : Quiver.{succ u2, u1} W] (self : Prefunctor.{1, succ u2, 0, u1} V inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.586 W inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.590) (self_1 : Prefunctor.{1, succ u2, 0, u1} V inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.586 W inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.590) (e_self : Eq.{max (succ u1) (succ u2)} (Prefunctor.{1, succ u2, 0, u1} V inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.586 W inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.590) self self_1) => Eq.rec.{0, max (succ u1) (succ u2)} (Prefunctor.{1, succ u2, 0, u1} V inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.586 W inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.590) self (fun (self_1 : Prefunctor.{1, succ u2, 0, u1} V inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.586 W inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.590) (e_self : Eq.{max (succ u1) (succ u2)} (Prefunctor.{1, succ u2, 0, u1} V inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.586 W inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.590) self self_1) => forall (a._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594 : V) (a_1._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594 : V), (Eq.{1} V a._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594 a_1._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594) -> (Eq.{succ u1} W (Prefunctor.obj.{1, succ u2, 0, u1} V inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.586 W inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.590 self a._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594) (Prefunctor.obj.{1, succ u2, 0, u1} V inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.586 W inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.590 self_1 a_1._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594))) (fun (a._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594 : V) (a_1._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594 : V) (e_a._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594 : Eq.{1} V a._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594 a_1._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594) => Eq.rec.{0, 1} V a._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594 (fun (a_1._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594 : V) (e_a._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594 : Eq.{1} V a._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594 a_1._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594) => Eq.{succ u1} W (Prefunctor.obj.{1, succ u2, 0, u1} V inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.586 W inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.590 self a._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594) (Prefunctor.obj.{1, succ u2, 0, u1} V inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.586 W inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.590 self a_1._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594)) (Eq.refl.{succ u1} W (Prefunctor.obj.{1, succ u2, 0, u1} V inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.586 W inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.590 self a._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594)) a_1._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594 e_a._@.Mathlib.Combinatorics.Quiver.Basic._hyg.594) self_1 e_self) (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) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Eq.refl.{max (succ u1) (succ u2)} (Prefunctor.{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))))) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk m)) ((fun {α : Type} (x : α) (x_1 : α) (e_x : Eq.{1} α x x_1) => Eq.rec.{0, 1} α x (fun (x_1 : α) (e_x : Eq.{1} α x x_1) => Eq.{1} (Opposite.{1} α) (Opposite.op.{1} α x) (Opposite.op.{1} α x_1)) (Eq.refl.{1} (Opposite.{1} α) (Opposite.op.{1} α x)) x_1 e_x) SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk m) ((fun (n : Nat) (n_1 : Nat) (e_1 : Eq.{1} Nat n n_1) => Eq.rec.{0, 1} Nat n (fun (n_1 : Nat) (e_n : Eq.{1} Nat n n_1) => Eq.{1} SimplexCategory (SimplexCategory.mk n) (SimplexCategory.mk n_1)) (Eq.refl.{1} SimplexCategory (SimplexCategory.mk n)) n_1 e_1) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) m hnm)))))
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {q : Nat} {n : Nat} {a : Nat} {m : Nat} (ha : Eq.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) a q)) (hnm : ComplexShape.Rel.{0} Nat AlgebraicTopology.DoldKan.c m n), 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))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) m)) (AlgebraicTopology.DoldKan.hσ'.{u1, u2} C _inst_1 _inst_2 X q n m hnm) (CategoryTheory.CategoryStruct.comp.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) m) (HSMul.hSMul.{0, u2, u2} Int (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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))))))) (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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))))))) (instHSMul.{0, u2} Int (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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))))))) (SubNegMonoid.SMulInt.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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))))))) (AddGroup.toSubNegMonoid.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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) 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inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.588 W inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.592) self self_1) => Eq.rec.{0, max (succ u1) (succ u2)} (Prefunctor.{1, succ u2, 0, u1} V inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.588 W inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.592) self (fun (self_1 : Prefunctor.{1, succ u2, 0, u1} V inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.588 W inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.592) (e_self : Eq.{max (succ u1) (succ u2)} (Prefunctor.{1, succ u2, 0, u1} V inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.588 W inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.592) self self_1) => forall (a._@.Mathlib.Combinatorics.Quiver.Basic._hyg.596 : V) (a_1._@.Mathlib.Combinatorics.Quiver.Basic._hyg.596 : V), (Eq.{1} V a._@.Mathlib.Combinatorics.Quiver.Basic._hyg.596 a_1._@.Mathlib.Combinatorics.Quiver.Basic._hyg.596) -> (Eq.{succ u1} W (Prefunctor.obj.{1, succ u2, 0, u1} V inst._@.Mathlib.Combinatorics.Quiver.Basic._hyg.588 W 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(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))))) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk m)) ((fun {α : Type} (x : α) (x_1 : α) (e_x : Eq.{1} α x x_1) => Eq.rec.{0, 1} α x (fun (x_1 : α) (e_x : Eq.{1} α x x_1) => Eq.{1} (Opposite.{1} α) (Opposite.op.{1} α x) (Opposite.op.{1} α x_1)) (Eq.refl.{1} (Opposite.{1} α) (Opposite.op.{1} α x)) x_1 e_x) SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (SimplexCategory.mk m) ((fun (n : Nat) (n_1 : Nat) (e_1 : Eq.{1} Nat n n_1) => Eq.rec.{0, 1} Nat n (fun (n_1 : Nat) (e_n : Eq.{1} Nat n n_1) => Eq.{1} SimplexCategory (SimplexCategory.mk n) (SimplexCategory.mk n_1)) (Eq.refl.{1} SimplexCategory (SimplexCategory.mk n)) n_1 e_1) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) m hnm)))))
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.hσ'_eq AlgebraicTopology.DoldKan.hσ'_eqₓ'. -/
 theorem hσ'_eq {q n a m : ℕ} (ha : n = a + q) (hnm : c.Rel m n) :
     (hσ' q n m hnm : X _[n] ⟶ X _[m]) =

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
 
 ! This file was ported from Lean 3 source module algebraic_topology.dold_kan.homotopies
-! leanprover-community/mathlib commit b12099d3b7febf4209824444dd836ef5ad96db55
+! leanprover-community/mathlib commit 86d1873c01a723aba6788f0b9051ae3d23b4c1c3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.AlgebraicTopology.DoldKan.Notations
 
 # Construction of homotopies for the Dold-Kan correspondence
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 TODO (@joelriou) continue adding the various files referenced below
 
 (The general strategy of proof of the Dold-Kan correspondence is explained

b12099d3

bump to nightly-2023-04-20-08

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

8f3c244e

Diff

@@ -89,18 +89,23 @@ variable {C : Type _} [Category C] [Preadditive C]
 
 variable {X : SimplicialObject C}
 
+#print AlgebraicTopology.DoldKan.c /-
 /-- As we are using chain complexes indexed by `ℕ`, we shall need the relation
 `c` such `c m n` if and only if `n+1=m`. -/
 abbrev c :=
   ComplexShape.down ℕ
 #align algebraic_topology.dold_kan.c AlgebraicTopology.DoldKan.c
+-/
 
+#print AlgebraicTopology.DoldKan.c_mk /-
 /-- Helper when we need some `c.rel i j` (i.e. `complex_shape.down ℕ`),
 e.g. `c_mk n (n+1) rfl` -/
 theorem c_mk (i j : ℕ) (h : j + 1 = i) : c.Rel i j :=
   ComplexShape.down_mk i j h
 #align algebraic_topology.dold_kan.c_mk AlgebraicTopology.DoldKan.c_mk
+-/
 
+#print AlgebraicTopology.DoldKan.cs_down_0_not_rel_left /-
 /-- This lemma is meant to be used with `null_homotopic_map'_f_of_not_rel_left` -/
 theorem cs_down_0_not_rel_left (j : ℕ) : ¬c.Rel 0 j :=
   by
@@ -109,18 +114,28 @@ theorem cs_down_0_not_rel_left (j : ℕ) : ¬c.Rel 0 j :=
   apply Nat.not_succ_le_zero j
   rw [Nat.succ_eq_add_one, hj]
 #align algebraic_topology.dold_kan.cs_down_0_not_rel_left AlgebraicTopology.DoldKan.cs_down_0_not_rel_left
+-/
 
+/- warning: algebraic_topology.dold_kan.hσ -> AlgebraicTopology.DoldKan.hσ 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}, Nat -> (forall (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 n))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
+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}, Nat -> (forall (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 n))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.hσ AlgebraicTopology.DoldKan.hσₓ'. -/
 /-- The sequence of maps which gives the null homotopic maps `Hσ` that shall be in
 the inductive construction of the projections `P q : K[X] ⟶ K[X]` -/
 def hσ (q : ℕ) (n : ℕ) : X _[n] ⟶ X _[n + 1] :=
   if n < q then 0 else (-1 : ℤ) ^ (n - q) • X.σ ⟨n - q, Nat.sub_lt_succ n q⟩
 #align algebraic_topology.dold_kan.hσ AlgebraicTopology.DoldKan.hσ
 
+#print AlgebraicTopology.DoldKan.hσ' /-
 /-- We can turn `hσ` into a datum that can be passed to `null_homotopic_map'`. -/
 def hσ' (q : ℕ) : ∀ n m, c.Rel m n → (K[X].pt n ⟶ K[X].pt m) := fun n m hnm =>
   hσ q n ≫ eqToHom (by congr )
 #align algebraic_topology.dold_kan.hσ' AlgebraicTopology.DoldKan.hσ'
+-/
 
+#print AlgebraicTopology.DoldKan.hσ'_eq_zero /-
 theorem hσ'_eq_zero {q n m : ℕ} (hnq : n < q) (hnm : c.Rel m n) :
     (hσ' q n m hnm : X _[n] ⟶ X _[m]) = 0 :=
   by
@@ -128,7 +143,14 @@ theorem hσ'_eq_zero {q n m : ℕ} (hnq : n < q) (hnm : c.Rel m n) :
   split_ifs
   exact zero_comp
 #align algebraic_topology.dold_kan.hσ'_eq_zero AlgebraicTopology.DoldKan.hσ'_eq_zero
+-/
 
+/- warning: algebraic_topology.dold_kan.hσ'_eq -> AlgebraicTopology.DoldKan.hσ'_eq is a dubious translation:
+lean 3 declaration is
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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))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))) (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 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))) (AddGroup.toSubNegMonoid.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) m hnm)))))
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {q : Nat} {n : Nat} {a : Nat} {m : Nat} (ha : Eq.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) a q)) (hnm : ComplexShape.Rel.{0} Nat AlgebraicTopology.DoldKan.c m n), 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))))) 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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} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat 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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.hσ'_eq AlgebraicTopology.DoldKan.hσ'_eqₓ'. -/
 theorem hσ'_eq {q n a m : ℕ} (ha : n = a + q) (hnm : c.Rel m n) :
     (hσ' q n m hnm : X _[n] ⟶ X _[m]) =
       ((-1 : ℤ) ^ a • X.σ ⟨a, Nat.lt_succ_iff.mpr (Nat.le.intro (Eq.symm ha))⟩) ≫
@@ -142,6 +164,12 @@ theorem hσ'_eq {q n a m : ℕ} (ha : n = a + q) (hnm : c.Rel m n) :
     congr
 #align algebraic_topology.dold_kan.hσ'_eq AlgebraicTopology.DoldKan.hσ'_eq
 
+/- warning: algebraic_topology.dold_kan.hσ'_eq' -> AlgebraicTopology.DoldKan.hσ'_eq' is a dubious translation:
+lean 3 declaration is
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_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) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (AlgebraicTopology.DoldKan.hσ'.{u1, u2} C _inst_1 _inst_2 X q n (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)))) (rfl.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toHasAdd.{0} Nat (AddRightCancelSemigroup.toAddSemigroup.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))))) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (SMul.smul.{0, u2} Int (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) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (SubNegMonoid.SMulInt.{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) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (AddGroup.toSubNegMonoid.{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) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (AddCommGroup.toAddGroup.{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) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (CategoryTheory.Preadditive.homGroup.{u2, u1} C _inst_1 _inst_2 (HomologicalComplex.x.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) 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) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))) (HPow.hPow.{0, 0, 0} Int Nat Int (instHPow.{0, 0} Int Nat (Monoid.Pow.{0} Int Int.monoid)) (Neg.neg.{0} Int Int.hasNeg (OfNat.ofNat.{0} Int 1 (OfNat.mk.{0} Int 1 (One.one.{0} Int Int.hasOne)))) a) (CategoryTheory.SimplicialObject.σ.{u2, u1} C _inst_1 X n (Fin.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)))) a (Iff.mpr (LT.lt.{0} Nat Nat.hasLt a (Nat.succ n)) (LE.le.{0} Nat Nat.hasLe a n) (Nat.lt_succ_iff a n) (Nat.le.intro a n q (Eq.symm.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) a q) ha))))))
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Preadditive.{u2, u1} C _inst_1] {X : CategoryTheory.SimplicialObject.{u2, u1} C _inst_1} {q : Nat} {n : Nat} {a : Nat} (ha : Eq.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) a q)), 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))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (AlgebraicTopology.DoldKan.hσ'.{u1, u2} C _inst_1 _inst_2 X q n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (rfl.{1} Nat (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat (AddSemigroup.toAdd.{0} Nat (AddRightCancelSemigroup.toAddSemigroup.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))))) n (OfNat.ofNat.{0} Nat 1 (One.toOfNat1.{0} Nat (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))))) (HSMul.hSMul.{0, u2, u2} Int (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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, 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SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (instHSMul.{0, u2} Int (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) 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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} (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))))))) (SubNegMonoid.SMulInt.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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))))))) (AddGroup.toSubNegMonoid.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (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))))))) (AddCommGroup.toAddGroup.{u2} (Quiver.Hom.{succ u2, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))) (CategoryTheory.Preadditive.homGroup.{u2, u1} C _inst_1 _inst_2 (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk n))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))))))) (HPow.hPow.{0, 0, 0} Int Nat Int Int.instHPowIntNat (Neg.neg.{0} Int Int.instNegInt (OfNat.ofNat.{0} Int 1 (instOfNatInt 1))) a) (CategoryTheory.SimplicialObject.σ.{u2, u1} C _inst_1 X n (Fin.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) a (Iff.mpr (LT.lt.{0} Nat instLTNat a (Nat.succ n)) (LE.le.{0} Nat instLENat a n) (Nat.lt_succ_iff a n) (Nat.le.intro a n q (Eq.symm.{1} Nat n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) a q) ha))))))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.hσ'_eq' AlgebraicTopology.DoldKan.hσ'_eq'ₓ'. -/
 theorem hσ'_eq' {q n a : ℕ} (ha : n = a + q) :
     (hσ' q n (n + 1) rfl : X _[n] ⟶ X _[n + 1]) =
       (-1 : ℤ) ^ a • X.σ ⟨a, Nat.lt_succ_iff.mpr (Nat.le.intro (Eq.symm ha))⟩ :=
@@ -153,20 +181,27 @@ warning: algebraic_topology.dold_kan.Hσ -> AlgebraicTopology.DoldKan.hσ is a d
 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}, Nat -> (Quiver.Hom.{succ u2, max u1 u2} (ChainComplex.{u2, u1, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (HomologicalComplex.{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.Category.toCategoryStruct.{u2, max u1 u2} (HomologicalComplex.{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)) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X))
 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}, Nat -> (forall (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 n))) (CategoryTheory.Functor.obj.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
+  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}, Nat -> (forall (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 n))) (Prefunctor.obj.{1, succ u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.CategoryStruct.toQuiver.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.toCategoryStruct.{0, 0} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory))) C (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} C (CategoryTheory.Category.toCategoryStruct.{u2, u1} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u2, 0, u1} (Opposite.{1} SimplexCategory) (CategoryTheory.Category.opposite.{0, 0} SimplexCategory SimplexCategory.smallCategory) C _inst_1 X) (Opposite.op.{1} SimplexCategory (SimplexCategory.mk (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
 Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.Hσ AlgebraicTopology.DoldKan.hσₓ'. -/
 /-- The null homotopic map $(hσ q) ∘ d + d ∘ (hσ q)$ -/
 def hσ (q : ℕ) : K[X] ⟶ K[X] :=
   nullHomotopicMap' (hσ' q)
 #align algebraic_topology.dold_kan.Hσ AlgebraicTopology.DoldKan.hσ
 
+/- warning: algebraic_topology.dold_kan.homotopy_Hσ_to_zero -> AlgebraicTopology.DoldKan.homotopyHσToZero is a dubious translation:
+lean 3 declaration is
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(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.CategoryStruct.toQuiver.{u2, max u1 u2} (HomologicalComplex.{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.Category.toCategoryStruct.{u2, max u1 u2} (HomologicalComplex.{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)) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) 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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.homotopy_Hσ_to_zero AlgebraicTopology.DoldKan.homotopyHσToZeroₓ'. -/
 /-- `Hσ` is null homotopic -/
 def homotopyHσToZero (q : ℕ) : Homotopy (hσ q : K[X] ⟶ K[X]) 0 :=
   nullHomotopy' (hσ' q)
 #align algebraic_topology.dold_kan.homotopy_Hσ_to_zero AlgebraicTopology.DoldKan.homotopyHσToZero
 
+#print AlgebraicTopology.DoldKan.Hσ_eq_zero /-
 /-- In degree `0`, the null homotopic map `Hσ` is zero. -/
-theorem hσ_eq_zero (q : ℕ) : (hσ q : K[X] ⟶ K[X]).f 0 = 0 :=
+theorem Hσ_eq_zero (q : ℕ) : (hσ q : K[X] ⟶ K[X]).f 0 = 0 :=
   by
   unfold Hσ
   rw [null_homotopic_map'_f_of_not_rel_left (c_mk 1 0 rfl) cs_down_0_not_rel_left]
@@ -178,8 +213,15 @@ theorem hσ_eq_zero (q : ℕ) : (hσ q : K[X] ⟶ K[X]).f 0 = 0 :=
       one_zsmul, Fin.val_one, pow_one, comp_add, neg_smul, one_zsmul, comp_neg, add_neg_eq_zero]
     erw [δ_comp_σ_self, δ_comp_σ_succ]
   · rw [hσ'_eq_zero (Nat.succ_pos q) (c_mk 1 0 rfl), zero_comp]
-#align algebraic_topology.dold_kan.Hσ_eq_zero AlgebraicTopology.DoldKan.hσ_eq_zero
+#align algebraic_topology.dold_kan.Hσ_eq_zero AlgebraicTopology.DoldKan.Hσ_eq_zero
+-/
 
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.hσ'_naturality AlgebraicTopology.DoldKan.hσ'_naturalityₓ'. -/
 /-- The maps `hσ' q n m hnm` are natural on the simplicial object -/
 theorem hσ'_naturality (q : ℕ) (n m : ℕ) (hnm : c.Rel m n) {X Y : SimplicialObject C} (f : X ⟶ Y) :
     f.app (op [n]) ≫ hσ' q n m hnm = hσ' q n m hnm ≫ f.app (op [m]) :=
@@ -195,6 +237,7 @@ theorem hσ'_naturality (q : ℕ) (n m : ℕ) (hnm : c.Rel m n) {X Y : Simplicia
     rfl
 #align algebraic_topology.dold_kan.hσ'_naturality AlgebraicTopology.DoldKan.hσ'_naturality
 
+#print AlgebraicTopology.DoldKan.natTransHσ /-
 /-- For each q, `Hσ q` is a natural transformation. -/
 def natTransHσ (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapComplex C
     where
@@ -206,7 +249,14 @@ def natTransHσ (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapCo
     ext (n m hnm)
     simp only [alternating_face_map_complex_map_f, hσ'_naturality]
 #align algebraic_topology.dold_kan.nat_trans_Hσ AlgebraicTopology.DoldKan.natTransHσ
+-/
 
+/- warning: algebraic_topology.dold_kan.map_hσ' -> AlgebraicTopology.DoldKan.map_hσ' is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.map_hσ' AlgebraicTopology.DoldKan.map_hσ'ₓ'. -/
 /-- The maps `hσ' q n m hnm` are compatible with the application of additive functors. -/
 theorem map_hσ' {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n m : ℕ) (hnm : c.Rel m n) :
@@ -219,8 +269,14 @@ theorem map_hσ' {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Addi
   · simpa only [eq_to_hom_map, functor.map_comp, functor.map_zsmul]
 #align algebraic_topology.dold_kan.map_hσ' AlgebraicTopology.DoldKan.map_hσ'
 
+/- warning: algebraic_topology.dold_kan.map_Hσ -> AlgebraicTopology.DoldKan.map_Hσ is a dubious translation:
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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (HomologicalComplex.X.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) n) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 _inst_2) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.AlternatingFaceMapComplex.obj.{u1, u2} C _inst_1 _inst_2 X) (AlgebraicTopology.DoldKan.Hσ.{u1, u2} C _inst_1 _inst_2 X q) n))
+Case conversion may be inaccurate. Consider using '#align algebraic_topology.dold_kan.map_Hσ AlgebraicTopology.DoldKan.map_Hσₓ'. -/
 /-- The null homotopic maps `Hσ` are compatible with the application of additive functors. -/
-theorem map_hσ {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
+theorem map_Hσ {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n : ℕ) :
     (hσ q : K[((whiskering C D).obj G).obj X] ⟶ _).f n = G.map ((hσ q : K[X] ⟶ _).f n) :=
   by
@@ -230,7 +286,7 @@ theorem map_hσ {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Addit
   rw [Eq]
   let h := (functor.congr_obj (map_alternating_face_map_complex G) X).symm
   congr
-#align algebraic_topology.dold_kan.map_Hσ AlgebraicTopology.DoldKan.map_hσ
+#align algebraic_topology.dold_kan.map_Hσ AlgebraicTopology.DoldKan.map_Hσ
 
 end DoldKan

b12099d3

bump to nightly-2023-02-28-22

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

1fb1623f

Diff

@@ -117,7 +117,7 @@ def hσ (q : ℕ) (n : ℕ) : X _[n] ⟶ X _[n + 1] :=
 #align algebraic_topology.dold_kan.hσ AlgebraicTopology.DoldKan.hσ
 
 /-- We can turn `hσ` into a datum that can be passed to `null_homotopic_map'`. -/
-def hσ' (q : ℕ) : ∀ n m, c.Rel m n → (K[X].x n ⟶ K[X].x m) := fun n m hnm =>
+def hσ' (q : ℕ) : ∀ n m, c.Rel m n → (K[X].pt n ⟶ K[X].pt m) := fun n m hnm =>
   hσ q n ≫ eqToHom (by congr )
 #align algebraic_topology.dold_kan.hσ' AlgebraicTopology.DoldKan.hσ'
 
@@ -210,8 +210,8 @@ def natTransHσ (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapCo
 /-- The maps `hσ' q n m hnm` are compatible with the application of additive functors. -/
 theorem map_hσ' {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n m : ℕ) (hnm : c.Rel m n) :
-    (hσ' q n m hnm : K[((whiskering _ _).obj G).obj X].x n ⟶ _) =
-      G.map (hσ' q n m hnm : K[X].x n ⟶ _) :=
+    (hσ' q n m hnm : K[((whiskering _ _).obj G).obj X].pt n ⟶ _) =
+      G.map (hσ' q n m hnm : K[X].pt n ⟶ _) :=
   by
   unfold hσ' hσ
   split_ifs

b12099d3

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

b12099d3

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

@@ -68,7 +68,6 @@ namespace AlgebraicTopology
 namespace DoldKan
 
 variable {C : Type*} [Category C] [Preadditive C]
-
 variable {X : SimplicialObject C}
 
 /-- As we are using chain complexes indexed by `ℕ`, we shall need the relation

b12099d3

refactor: optimize proofs with omega (#11093)

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

37bc4aba

Diff

@@ -115,8 +115,7 @@ theorem hσ'_eq {q n a m : ℕ} (ha : n = a + q) (hnm : c.Rel m n) :
         eqToHom (by congr) := by
   simp only [hσ', hσ]
   split_ifs
-  · exfalso
-    linarith
+  · omega
   · have h' := tsub_eq_of_eq_add ha
     congr
 #align algebraic_topology.dold_kan.hσ'_eq AlgebraicTopology.DoldKan.hσ'_eq

Diff

@@ -53,7 +53,7 @@ compatible the application of additive functors (see `map_Hσ`).
 
 ## References
 * [Albrecht Dold, *Homology of Symmetric Products and Other Functors of Complexes*][dold1958]
-* [Paul G. Goerss, John F. Jardine, *Simplical Homotopy Theory*][goerss-jardine-2009]
+* [Paul G. Goerss, John F. Jardine, *Simplicial Homotopy Theory*][goerss-jardine-2009]
 
 -/

b12099d3

fix: patch for std4#203 (more sub lemmas for Nat) (#6216)

c159834a

Diff

@@ -94,7 +94,7 @@ theorem cs_down_0_not_rel_left (j : ℕ) : ¬c.Rel 0 j := by
 /-- The sequence of maps which gives the null homotopic maps `Hσ` that shall be in
 the inductive construction of the projections `P q : K[X] ⟶ K[X]` -/
 def hσ (q : ℕ) (n : ℕ) : X _[n] ⟶ X _[n + 1] :=
-  if n < q then 0 else (-1 : ℤ) ^ (n - q) • X.σ ⟨n - q, Nat.sub_lt_succ n q⟩
+  if n < q then 0 else (-1 : ℤ) ^ (n - q) • X.σ ⟨n - q, Nat.lt_succ_of_le (Nat.sub_le _ _)⟩
 #align algebraic_topology.dold_kan.hσ AlgebraicTopology.DoldKan.hσ
 
 /-- We can turn `hσ` into a datum that can be passed to `nullHomotopicMap'`. -/

b12099d3

chore: cleanup some spaces (#7484)

Purely cosmetic PR.

c93575a3

Diff

@@ -112,7 +112,7 @@ theorem hσ'_eq_zero {q n m : ℕ} (hnq : n < q) (hnm : c.Rel m n) :
 theorem hσ'_eq {q n a m : ℕ} (ha : n = a + q) (hnm : c.Rel m n) :
     (hσ' q n m hnm : X _[n] ⟶ X _[m]) =
       ((-1 : ℤ) ^ a • X.σ ⟨a, Nat.lt_succ_iff.mpr (Nat.le.intro (Eq.symm ha))⟩) ≫
-        eqToHom (by congr ) := by
+        eqToHom (by congr) := by
   simp only [hσ', hσ]
   split_ifs
   · exfalso

b12099d3

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

@@ -67,7 +67,7 @@ namespace AlgebraicTopology
 
 namespace DoldKan
 
-variable {C : Type _} [Category C] [Preadditive C]
+variable {C : Type*} [Category C] [Preadditive C]
 
 variable {X : SimplicialObject C}
 
@@ -181,7 +181,7 @@ set_option linter.uppercaseLean3 false in
 #align algebraic_topology.dold_kan.nat_trans_Hσ AlgebraicTopology.DoldKan.natTransHσ
 
 /-- The maps `hσ' q n m hnm` are compatible with the application of additive functors. -/
-theorem map_hσ' {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
+theorem map_hσ' {D : Type*} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n m : ℕ) (hnm : c.Rel m n) :
     (hσ' q n m hnm : K[((whiskering _ _).obj G).obj X].X n ⟶ _) =
       G.map (hσ' q n m hnm : K[X].X n ⟶ _) := by
@@ -193,7 +193,7 @@ theorem map_hσ' {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Addi
 #align algebraic_topology.dold_kan.map_hσ' AlgebraicTopology.DoldKan.map_hσ'
 
 /-- The null homotopic maps `Hσ` are compatible with the application of additive functors. -/
-theorem map_Hσ {D : Type _} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
+theorem map_Hσ {D : Type*} [Category D] [Preadditive D] (G : C ⥤ D) [G.Additive]
     (X : SimplicialObject C) (q n : ℕ) :
     (Hσ q : K[((whiskering C D).obj G).obj X] ⟶ _).f n = G.map ((Hσ q : K[X] ⟶ _).f n) := by
   unfold Hσ

b12099d3

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
-
-! This file was ported from Lean 3 source module algebraic_topology.dold_kan.homotopies
-! leanprover-community/mathlib commit b12099d3b7febf4209824444dd836ef5ad96db55
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Homology.Homotopy
 import Mathlib.AlgebraicTopology.DoldKan.Notations
 
+#align_import algebraic_topology.dold_kan.homotopies from "leanprover-community/mathlib"@"b12099d3b7febf4209824444dd836ef5ad96db55"
+
 /-!
 
 # Construction of homotopies for the Dold-Kan correspondence

b12099d3

chore: remove superfluous parentheses in calls to ext (#5258)

Co-authored-by: Xavier Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Riccardo Brasca <riccardo.brasca@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Pol'tta / Miyahara Kō <pol_tta@outlook.jp> Co-authored-by: Jason Yuen <jason_yuen2007@hotmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Jireh Loreaux <loreaujy@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com> Co-authored-by: Jujian Zhang <jujian.zhang1998@outlook.com> Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

3d6731dc

Diff

@@ -178,7 +178,7 @@ def natTransHσ (q : ℕ) : alternatingFaceMapComplex C ⟶ alternatingFaceMapCo
     unfold Hσ
     rw [nullHomotopicMap'_comp, comp_nullHomotopicMap']
     congr
-    ext (n m hnm)
+    ext n m hnm
     simp only [alternatingFaceMapComplex_map_f, hσ'_naturality]
 set_option linter.uppercaseLean3 false in
 #align algebraic_topology.dold_kan.nat_trans_Hσ AlgebraicTopology.DoldKan.natTransHσ

b12099d3

feat: port AlgebraicTopology.DoldKan.Homotopies (#3523)

Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

66fc2fe4

`algebraic_topology.dold_kan.homotopies` ⟷ `Mathlib.AlgebraicTopology.DoldKan.Homotopies`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 518

algebraic_topology.dold_kan.homotopies ⟷ Mathlib.AlgebraicTopology.DoldKan.Homotopies

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 518

`algebraic_topology.dold_kan.homotopies` ⟷ `Mathlib.AlgebraicTopology.DoldKan.Homotopies`