category_theory.abelian.injective_resolution ⟷ Mathlib.CategoryTheory.Abelian.InjectiveResolution

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

@@ -152,7 +152,7 @@ def descHomotopyZeroSucc {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveRes
     (by
       simp [preadditive.comp_sub, ← category.assoc, preadditive.sub_comp,
         show I.cocomplex.d (n + 1) (n + 2) ≫ g' = f.f (n + 1) - g ≫ J.cocomplex.d n (n + 1) by
-          rw [w]; simp only [add_sub_cancel]])
+          rw [w]; simp only [add_sub_cancel_right]])
 #align category_theory.InjectiveResolution.desc_homotopy_zero_succ CategoryTheory.InjectiveResolution.descHomotopyZeroSucc
 -/
 

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

@@ -236,23 +236,19 @@ abbrev injectiveResolution (Z : C) [HasInjectiveResolution Z] : CochainComplex C
 #align category_theory.injective_resolution CategoryTheory.injectiveResolution
 -/
 
-#print CategoryTheory.injectiveResolution.ι /-
 /-- The cochain map from cochain complex consisting of `Z` supported in degree `0`
 back to the arbitrarily chosen injective resolution `injective_resolution Z`. -/
 abbrev injectiveResolution.ι (Z : C) [HasInjectiveResolution Z] :
     (CochainComplex.single₀ C).obj Z ⟶ injectiveResolution Z :=
   (HasInjectiveResolution.out Z).some.ι
 #align category_theory.injective_resolution.ι CategoryTheory.injectiveResolution.ι
--/
 
-#print CategoryTheory.injectiveResolution.desc /-
 /-- The descent of a morphism to a cochain map between the arbitrarily chosen injective resolutions.
 -/
 abbrev injectiveResolution.desc {X Y : C} (f : X ⟶ Y) [HasInjectiveResolution X]
     [HasInjectiveResolution Y] : injectiveResolution X ⟶ injectiveResolution Y :=
   InjectiveResolution.desc f _ _
 #align category_theory.injective_resolution.desc CategoryTheory.injectiveResolution.desc
--/
 
 variable (C) [HasInjectiveResolutions C]
 
@@ -347,7 +343,6 @@ namespace HomologicalComplex.Hom
 
 variable {C : Type u} [Category.{v} C] [Abelian C]
 
-#print HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution /-
 /-- If `X` is a cochain complex of injective objects and we have a quasi-isomorphism
 `f : Y[0] ⟶ X`, then `X` is an injective resolution of `Y.` -/
 def HomologicalComplex.Hom.fromSingle₀InjectiveResolution (X : CochainComplex C ℕ) (Y : C)
@@ -360,7 +355,6 @@ def HomologicalComplex.Hom.fromSingle₀InjectiveResolution (X : CochainComplex
   exact := f.from_single₀_exact_at_succ
   Mono := f.from_single₀_mono_at_zero
 #align homological_complex.hom.homological_complex.hom.from_single₀_InjectiveResolution HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution
--/
 
 end HomologicalComplex.Hom
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/3365b20c2ffa7c35e47e5209b89ba9abdddf3ffe

@@ -351,7 +351,7 @@ variable {C : Type u} [Category.{v} C] [Abelian C]
 /-- If `X` is a cochain complex of injective objects and we have a quasi-isomorphism
 `f : Y[0] ⟶ X`, then `X` is an injective resolution of `Y.` -/
 def HomologicalComplex.Hom.fromSingle₀InjectiveResolution (X : CochainComplex C ℕ) (Y : C)
-    (f : (CochainComplex.single₀ C).obj Y ⟶ X) [QuasiIso f] (H : ∀ n, Injective (X.pt n)) :
+    (f : (CochainComplex.single₀ C).obj Y ⟶ X) [QuasiIso' f] (H : ∀ n, Injective (X.pt n)) :
     InjectiveResolution Y where
   cocomplex := X
   ι := f

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

@@ -3,9 +3,9 @@ Copyright (c) 2022 Jujian Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jujian Zhang, Scott Morrison
 -/
-import Mathbin.Algebra.Homology.QuasiIso
-import Mathbin.CategoryTheory.Preadditive.InjectiveResolution
-import Mathbin.Algebra.Homology.HomotopyCategory
+import Algebra.Homology.QuasiIso
+import CategoryTheory.Preadditive.InjectiveResolution
+import Algebra.Homology.HomotopyCategory
 
 #align_import category_theory.abelian.injective_resolution from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Jujian Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jujian Zhang, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.abelian.injective_resolution
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Homology.QuasiIso
 import Mathbin.CategoryTheory.Preadditive.InjectiveResolution
 import Mathbin.Algebra.Homology.HomotopyCategory
 
+#align_import category_theory.abelian.injective_resolution from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
 /-!
 # Main result
 

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

@@ -110,6 +110,7 @@ def desc {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y) (J : InjectiveResol
 #align category_theory.InjectiveResolution.desc CategoryTheory.InjectiveResolution.desc
 -/
 
+#print CategoryTheory.InjectiveResolution.desc_commutes /-
 /-- The resolution maps intertwine the descent of a morphism and that morphism. -/
 @[simp, reassoc]
 theorem desc_commutes {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y)
@@ -118,7 +119,9 @@ theorem desc_commutes {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y)
   ext n
   rcases n with (_ | _ | n) <;> · dsimp [desc, desc_f_one, desc_f_zero]; simp
 #align category_theory.InjectiveResolution.desc_commutes CategoryTheory.InjectiveResolution.desc_commutes
+-/
 
+#print CategoryTheory.InjectiveResolution.descHomotopyZeroZero /-
 -- Now that we've checked this property of the descent,
 -- we can seal away the actual definition.
 /-- An auxiliary definition for `desc_homotopy_zero`. -/
@@ -127,7 +130,9 @@ def descHomotopyZeroZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveRes
   Exact.desc (f.f 0) (I.ι.f 0) (I.cocomplex.d 0 1) (Abelian.Exact.op _ _ I.exact₀)
     (congr_fun (congr_arg HomologicalComplex.Hom.f comm) 0)
 #align category_theory.InjectiveResolution.desc_homotopy_zero_zero CategoryTheory.InjectiveResolution.descHomotopyZeroZero
+-/
 
+#print CategoryTheory.InjectiveResolution.descHomotopyZeroOne /-
 /-- An auxiliary definition for `desc_homotopy_zero`. -/
 def descHomotopyZeroOne {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (f : I.cocomplex ⟶ J.cocomplex) (comm : I.ι ≫ f = (0 : _ ⟶ J.cocomplex)) :
@@ -136,7 +141,9 @@ def descHomotopyZeroOne {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveReso
     (I.cocomplex.d 1 2) (Abelian.Exact.op _ _ (I.exact _))
     (by simp [desc_homotopy_zero_zero, ← category.assoc])
 #align category_theory.InjectiveResolution.desc_homotopy_zero_one CategoryTheory.InjectiveResolution.descHomotopyZeroOne
+-/
 
+#print CategoryTheory.InjectiveResolution.descHomotopyZeroSucc /-
 /-- An auxiliary definition for `desc_homotopy_zero`. -/
 def descHomotopyZeroSucc {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (f : I.cocomplex ⟶ J.cocomplex) (n : ℕ) (g : I.cocomplex.pt (n + 1) ⟶ J.cocomplex.pt n)
@@ -150,7 +157,9 @@ def descHomotopyZeroSucc {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveRes
         show I.cocomplex.d (n + 1) (n + 2) ≫ g' = f.f (n + 1) - g ≫ J.cocomplex.d n (n + 1) by
           rw [w]; simp only [add_sub_cancel]])
 #align category_theory.InjectiveResolution.desc_homotopy_zero_succ CategoryTheory.InjectiveResolution.descHomotopyZeroSucc
+-/
 
+#print CategoryTheory.InjectiveResolution.descHomotopyZero /-
 /-- Any descent of the zero morphism is homotopic to zero. -/
 def descHomotopyZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (f : I.cocomplex ⟶ J.cocomplex) (comm : I.ι ≫ f = 0) : Homotopy f 0 :=
@@ -159,13 +168,16 @@ def descHomotopyZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolut
     ⟨descHomotopyZeroSucc f n g g' (by simp only [w, add_comm]), by
       simp [desc_homotopy_zero_succ, w]⟩
 #align category_theory.InjectiveResolution.desc_homotopy_zero CategoryTheory.InjectiveResolution.descHomotopyZero
+-/
 
+#print CategoryTheory.InjectiveResolution.descHomotopy /-
 /-- Two descents of the same morphism are homotopic. -/
 def descHomotopy {Y Z : C} (f : Y ⟶ Z) {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (g h : I.cocomplex ⟶ J.cocomplex) (g_comm : I.ι ≫ g = (CochainComplex.single₀ C).map f ≫ J.ι)
     (h_comm : I.ι ≫ h = (CochainComplex.single₀ C).map f ≫ J.ι) : Homotopy g h :=
   Homotopy.equivSubZero.invFun (descHomotopyZero _ (by simp [g_comm, h_comm]))
 #align category_theory.InjectiveResolution.desc_homotopy CategoryTheory.InjectiveResolution.descHomotopy
+-/
 
 #print CategoryTheory.InjectiveResolution.descIdHomotopy /-
 /-- The descent of the identity morphism is homotopic to the identity cochain map. -/
@@ -198,15 +210,19 @@ def homotopyEquiv {X : C} (I J : InjectiveResolution X) : HomotopyEquiv I.cocomp
 #align category_theory.InjectiveResolution.homotopy_equiv CategoryTheory.InjectiveResolution.homotopyEquiv
 -/
 
+#print CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι /-
 @[simp, reassoc]
 theorem homotopyEquiv_hom_ι {X : C} (I J : InjectiveResolution X) :
     I.ι ≫ (homotopyEquiv I J).Hom = J.ι := by simp [HomotopyEquiv]
 #align category_theory.InjectiveResolution.homotopy_equiv_hom_ι CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι
+-/
 
+#print CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ι /-
 @[simp, reassoc]
 theorem homotopyEquiv_inv_ι {X : C} (I J : InjectiveResolution X) :
     J.ι ≫ (homotopyEquiv I J).inv = I.ι := by simp [HomotopyEquiv]
 #align category_theory.InjectiveResolution.homotopy_equiv_inv_ι CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ι
+-/
 
 end Abelian
 
@@ -223,12 +239,14 @@ abbrev injectiveResolution (Z : C) [HasInjectiveResolution Z] : CochainComplex C
 #align category_theory.injective_resolution CategoryTheory.injectiveResolution
 -/
 
+#print CategoryTheory.injectiveResolution.ι /-
 /-- The cochain map from cochain complex consisting of `Z` supported in degree `0`
 back to the arbitrarily chosen injective resolution `injective_resolution Z`. -/
 abbrev injectiveResolution.ι (Z : C) [HasInjectiveResolution Z] :
     (CochainComplex.single₀ C).obj Z ⟶ injectiveResolution Z :=
   (HasInjectiveResolution.out Z).some.ι
 #align category_theory.injective_resolution.ι CategoryTheory.injectiveResolution.ι
+-/
 
 #print CategoryTheory.injectiveResolution.desc /-
 /-- The descent of a morphism to a cochain map between the arbitrarily chosen injective resolutions.
@@ -300,6 +318,7 @@ def ofCocomplex (Z : C) : CochainComplex C ℕ :=
 #align category_theory.InjectiveResolution.of_cocomplex CategoryTheory.InjectiveResolution.ofCocomplex
 -/
 
+#print CategoryTheory.InjectiveResolution.of /-
 /-- In any abelian category with enough injectives,
 `InjectiveResolution.of Z` constructs an injective resolution of the object `Z`.
 -/
@@ -317,6 +336,7 @@ irreducible_def of (Z : C) : InjectiveResolution Z :=
     exact := by rintro (_ | n) <;> · simp; apply exact_f_d
     Mono := Injective.ι_mono Z }
 #align category_theory.InjectiveResolution.of CategoryTheory.InjectiveResolution.of
+-/
 
 instance (priority := 100) (Z : C) : HasInjectiveResolution Z where out := ⟨of Z⟩
 
@@ -330,6 +350,7 @@ namespace HomologicalComplex.Hom
 
 variable {C : Type u} [Category.{v} C] [Abelian C]
 
+#print HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution /-
 /-- If `X` is a cochain complex of injective objects and we have a quasi-isomorphism
 `f : Y[0] ⟶ X`, then `X` is an injective resolution of `Y.` -/
 def HomologicalComplex.Hom.fromSingle₀InjectiveResolution (X : CochainComplex C ℕ) (Y : C)
@@ -342,6 +363,7 @@ def HomologicalComplex.Hom.fromSingle₀InjectiveResolution (X : CochainComplex
   exact := f.from_single₀_exact_at_succ
   Mono := f.from_single₀_mono_at_zero
 #align homological_complex.hom.homological_complex.hom.from_single₀_InjectiveResolution HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution
+-/
 
 end HomologicalComplex.Hom
 

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

@@ -92,7 +92,7 @@ theorem descFOne_zero_comm {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y)
 def descFSucc {Y Z : C} (I : InjectiveResolution Y) (J : InjectiveResolution Z) (n : ℕ)
     (g : J.cocomplex.pt n ⟶ I.cocomplex.pt n) (g' : J.cocomplex.pt (n + 1) ⟶ I.cocomplex.pt (n + 1))
     (w : J.cocomplex.d n (n + 1) ≫ g' = g ≫ I.cocomplex.d n (n + 1)) :
-    Σ'g'' : J.cocomplex.pt (n + 2) ⟶ I.cocomplex.pt (n + 2),
+    Σ' g'' : J.cocomplex.pt (n + 2) ⟶ I.cocomplex.pt (n + 2),
       J.cocomplex.d (n + 1) (n + 2) ≫ g'' = g' ≫ I.cocomplex.d (n + 1) (n + 2) :=
   ⟨@Exact.desc C _ _ _ _ _ _ _ _ _ (g' ≫ I.cocomplex.d (n + 1) (n + 2)) (J.cocomplex.d n (n + 1))
       (J.cocomplex.d (n + 1) (n + 2)) (Abelian.Exact.op _ _ (J.exact _))

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

@@ -110,9 +110,6 @@ def desc {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y) (J : InjectiveResol
 #align category_theory.InjectiveResolution.desc CategoryTheory.InjectiveResolution.desc
 -/
 
-/- warning: category_theory.InjectiveResolution.desc_commutes -> CategoryTheory.InjectiveResolution.desc_commutes is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_commutes CategoryTheory.InjectiveResolution.desc_commutesₓ'. -/
 /-- The resolution maps intertwine the descent of a morphism and that morphism. -/
 @[simp, reassoc]
 theorem desc_commutes {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y)
@@ -122,9 +119,6 @@ theorem desc_commutes {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y)
   rcases n with (_ | _ | n) <;> · dsimp [desc, desc_f_one, desc_f_zero]; simp
 #align category_theory.InjectiveResolution.desc_commutes CategoryTheory.InjectiveResolution.desc_commutes
 
-/- warning: category_theory.InjectiveResolution.desc_homotopy_zero_zero -> CategoryTheory.InjectiveResolution.descHomotopyZeroZero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_homotopy_zero_zero CategoryTheory.InjectiveResolution.descHomotopyZeroZeroₓ'. -/
 -- Now that we've checked this property of the descent,
 -- we can seal away the actual definition.
 /-- An auxiliary definition for `desc_homotopy_zero`. -/
@@ -134,9 +128,6 @@ def descHomotopyZeroZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveRes
     (congr_fun (congr_arg HomologicalComplex.Hom.f comm) 0)
 #align category_theory.InjectiveResolution.desc_homotopy_zero_zero CategoryTheory.InjectiveResolution.descHomotopyZeroZero
 
-/- warning: category_theory.InjectiveResolution.desc_homotopy_zero_one -> CategoryTheory.InjectiveResolution.descHomotopyZeroOne is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_homotopy_zero_one CategoryTheory.InjectiveResolution.descHomotopyZeroOneₓ'. -/
 /-- An auxiliary definition for `desc_homotopy_zero`. -/
 def descHomotopyZeroOne {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (f : I.cocomplex ⟶ J.cocomplex) (comm : I.ι ≫ f = (0 : _ ⟶ J.cocomplex)) :
@@ -146,9 +137,6 @@ def descHomotopyZeroOne {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveReso
     (by simp [desc_homotopy_zero_zero, ← category.assoc])
 #align category_theory.InjectiveResolution.desc_homotopy_zero_one CategoryTheory.InjectiveResolution.descHomotopyZeroOne
 
-/- warning: category_theory.InjectiveResolution.desc_homotopy_zero_succ -> CategoryTheory.InjectiveResolution.descHomotopyZeroSucc is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_homotopy_zero_succ CategoryTheory.InjectiveResolution.descHomotopyZeroSuccₓ'. -/
 /-- An auxiliary definition for `desc_homotopy_zero`. -/
 def descHomotopyZeroSucc {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (f : I.cocomplex ⟶ J.cocomplex) (n : ℕ) (g : I.cocomplex.pt (n + 1) ⟶ J.cocomplex.pt n)
@@ -163,9 +151,6 @@ def descHomotopyZeroSucc {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveRes
           rw [w]; simp only [add_sub_cancel]])
 #align category_theory.InjectiveResolution.desc_homotopy_zero_succ CategoryTheory.InjectiveResolution.descHomotopyZeroSucc
 
-/- warning: category_theory.InjectiveResolution.desc_homotopy_zero -> CategoryTheory.InjectiveResolution.descHomotopyZero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_homotopy_zero CategoryTheory.InjectiveResolution.descHomotopyZeroₓ'. -/
 /-- Any descent of the zero morphism is homotopic to zero. -/
 def descHomotopyZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (f : I.cocomplex ⟶ J.cocomplex) (comm : I.ι ≫ f = 0) : Homotopy f 0 :=
@@ -175,9 +160,6 @@ def descHomotopyZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolut
       simp [desc_homotopy_zero_succ, w]⟩
 #align category_theory.InjectiveResolution.desc_homotopy_zero CategoryTheory.InjectiveResolution.descHomotopyZero
 
-/- warning: category_theory.InjectiveResolution.desc_homotopy -> CategoryTheory.InjectiveResolution.descHomotopy is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_homotopy CategoryTheory.InjectiveResolution.descHomotopyₓ'. -/
 /-- Two descents of the same morphism are homotopic. -/
 def descHomotopy {Y Z : C} (f : Y ⟶ Z) {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (g h : I.cocomplex ⟶ J.cocomplex) (g_comm : I.ι ≫ g = (CochainComplex.single₀ C).map f ≫ J.ι)
@@ -216,17 +198,11 @@ def homotopyEquiv {X : C} (I J : InjectiveResolution X) : HomotopyEquiv I.cocomp
 #align category_theory.InjectiveResolution.homotopy_equiv CategoryTheory.InjectiveResolution.homotopyEquiv
 -/
 
-/- warning: category_theory.InjectiveResolution.homotopy_equiv_hom_ι -> CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.homotopy_equiv_hom_ι CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ιₓ'. -/
 @[simp, reassoc]
 theorem homotopyEquiv_hom_ι {X : C} (I J : InjectiveResolution X) :
     I.ι ≫ (homotopyEquiv I J).Hom = J.ι := by simp [HomotopyEquiv]
 #align category_theory.InjectiveResolution.homotopy_equiv_hom_ι CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι
 
-/- warning: category_theory.InjectiveResolution.homotopy_equiv_inv_ι -> CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ι is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.homotopy_equiv_inv_ι CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ιₓ'. -/
 @[simp, reassoc]
 theorem homotopyEquiv_inv_ι {X : C} (I J : InjectiveResolution X) :
     J.ι ≫ (homotopyEquiv I J).inv = I.ι := by simp [HomotopyEquiv]
@@ -247,9 +223,6 @@ abbrev injectiveResolution (Z : C) [HasInjectiveResolution Z] : CochainComplex C
 #align category_theory.injective_resolution CategoryTheory.injectiveResolution
 -/
 
-/- warning: category_theory.injective_resolution.ι -> CategoryTheory.injectiveResolution.ι is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.injective_resolution.ι CategoryTheory.injectiveResolution.ιₓ'. -/
 /-- The cochain map from cochain complex consisting of `Z` supported in degree `0`
 back to the arbitrarily chosen injective resolution `injective_resolution Z`. -/
 abbrev injectiveResolution.ι (Z : C) [HasInjectiveResolution Z] :
@@ -327,12 +300,6 @@ def ofCocomplex (Z : C) : CochainComplex C ℕ :=
 #align category_theory.InjectiveResolution.of_cocomplex CategoryTheory.InjectiveResolution.ofCocomplex
 -/
 
-/- warning: category_theory.InjectiveResolution.of -> CategoryTheory.InjectiveResolution.of is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.EnoughInjectives.{u1, u2} C _inst_1] (Z : C), CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.of._proof_1.{u2, u1} C _inst_1 _inst_2) Z
-but is expected to have type
-  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Abelian.{u2, u1} C _inst_1] [_inst_3 : CategoryTheory.EnoughInjectives.{u2, u1} C _inst_1] (Z : C), CategoryTheory.InjectiveResolution.{u2, u1} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} C _inst_1 _inst_2)) Z
-Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.of CategoryTheory.InjectiveResolution.ofₓ'. -/
 /-- In any abelian category with enough injectives,
 `InjectiveResolution.of Z` constructs an injective resolution of the object `Z`.
 -/
@@ -363,9 +330,6 @@ namespace HomologicalComplex.Hom
 
 variable {C : Type u} [Category.{v} C] [Abelian C]
 
-/- warning: homological_complex.hom.homological_complex.hom.from_single₀_InjectiveResolution -> HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homological_complex.hom.homological_complex.hom.from_single₀_InjectiveResolution HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolutionₓ'. -/
 /-- If `X` is a cochain complex of injective objects and we have a quasi-isomorphism
 `f : Y[0] ⟶ X`, then `X` is an injective resolution of `Y.` -/
 def HomologicalComplex.Hom.fromSingle₀InjectiveResolution (X : CochainComplex C ℕ) (Y : C)

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

@@ -119,9 +119,7 @@ theorem desc_commutes {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y)
     (J : InjectiveResolution Z) : J.ι ≫ desc f I J = (CochainComplex.single₀ C).map f ≫ I.ι :=
   by
   ext n
-  rcases n with (_ | _ | n) <;>
-    · dsimp [desc, desc_f_one, desc_f_zero]
-      simp
+  rcases n with (_ | _ | n) <;> · dsimp [desc, desc_f_one, desc_f_zero]; simp
 #align category_theory.InjectiveResolution.desc_commutes CategoryTheory.InjectiveResolution.desc_commutes
 
 /- warning: category_theory.InjectiveResolution.desc_homotopy_zero_zero -> CategoryTheory.InjectiveResolution.descHomotopyZeroZero is a dubious translation:
@@ -161,10 +159,8 @@ def descHomotopyZeroSucc {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveRes
     (I.cocomplex.d (n + 2) (n + 3)) (Abelian.Exact.op _ _ (I.exact _))
     (by
       simp [preadditive.comp_sub, ← category.assoc, preadditive.sub_comp,
-        show I.cocomplex.d (n + 1) (n + 2) ≫ g' = f.f (n + 1) - g ≫ J.cocomplex.d n (n + 1)
-          by
-          rw [w]
-          simp only [add_sub_cancel]])
+        show I.cocomplex.d (n + 1) (n + 2) ≫ g' = f.f (n + 1) - g ≫ J.cocomplex.d n (n + 1) by
+          rw [w]; simp only [add_sub_cancel]])
 #align category_theory.InjectiveResolution.desc_homotopy_zero_succ CategoryTheory.InjectiveResolution.descHomotopyZeroSucc
 
 /- warning: category_theory.InjectiveResolution.desc_homotopy_zero -> CategoryTheory.InjectiveResolution.descHomotopyZero is a dubious translation:
@@ -351,10 +347,7 @@ irreducible_def of (Z : C) : InjectiveResolution Z :=
         fun n _ => ⟨0, by ext⟩
     Injective := by rintro (_ | _ | _ | n) <;> · apply injective.injective_under
     exact₀ := by simpa using exact_f_d (injective.ι Z)
-    exact := by
-      rintro (_ | n) <;>
-        · simp
-          apply exact_f_d
+    exact := by rintro (_ | n) <;> · simp; apply exact_f_d
     Mono := Injective.ι_mono Z }
 #align category_theory.InjectiveResolution.of CategoryTheory.InjectiveResolution.of
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jujian Zhang, Scott Morrison
 
 ! This file was ported from Lean 3 source module category_theory.abelian.injective_resolution
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Algebra.Homology.HomotopyCategory
 /-!
 # Main result
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 When the underlying category is abelian:
 * `category_theory.InjectiveResolution.desc`: Given `I : InjectiveResolution X` and
   `J : InjectiveResolution Y`, any morphism `X ⟶ Y` admits a descent to a chain map
@@ -108,10 +111,7 @@ def desc {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y) (J : InjectiveResol
 -/
 
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_inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} 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(CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y I))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_commutes CategoryTheory.InjectiveResolution.desc_commutesₓ'. -/
 /-- The resolution maps intertwine the descent of a morphism and that morphism. -/
 @[simp, reassoc]
@@ -125,10 +125,7 @@ theorem desc_commutes {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y)
 #align category_theory.InjectiveResolution.desc_commutes CategoryTheory.InjectiveResolution.desc_commutes
 
 /- warning: category_theory.InjectiveResolution.desc_homotopy_zero_zero -> CategoryTheory.InjectiveResolution.descHomotopyZeroZero is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_homotopy_zero_zero CategoryTheory.InjectiveResolution.descHomotopyZeroZeroₓ'. -/
 -- Now that we've checked this property of the descent,
 -- we can seal away the actual definition.
@@ -140,10 +137,7 @@ def descHomotopyZeroZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveRes
 #align category_theory.InjectiveResolution.desc_homotopy_zero_zero CategoryTheory.InjectiveResolution.descHomotopyZeroZero
 
 /- warning: category_theory.InjectiveResolution.desc_homotopy_zero_one -> CategoryTheory.InjectiveResolution.descHomotopyZeroOne is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_homotopy_zero_one CategoryTheory.InjectiveResolution.descHomotopyZeroOneₓ'. -/
 /-- An auxiliary definition for `desc_homotopy_zero`. -/
 def descHomotopyZeroOne {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
@@ -155,10 +149,7 @@ def descHomotopyZeroOne {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveReso
 #align category_theory.InjectiveResolution.desc_homotopy_zero_one CategoryTheory.InjectiveResolution.descHomotopyZeroOne
 
 /- warning: category_theory.InjectiveResolution.desc_homotopy_zero_succ -> CategoryTheory.InjectiveResolution.descHomotopyZeroSucc is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_homotopy_zero_succ CategoryTheory.InjectiveResolution.descHomotopyZeroSuccₓ'. -/
 /-- An auxiliary definition for `desc_homotopy_zero`. -/
 def descHomotopyZeroSucc {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
@@ -177,10 +168,7 @@ def descHomotopyZeroSucc {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveRes
 #align category_theory.InjectiveResolution.desc_homotopy_zero_succ CategoryTheory.InjectiveResolution.descHomotopyZeroSucc
 
 /- warning: category_theory.InjectiveResolution.desc_homotopy_zero -> CategoryTheory.InjectiveResolution.descHomotopyZero is a dubious translation:
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_inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_homotopy_zero CategoryTheory.InjectiveResolution.descHomotopyZeroₓ'. -/
 /-- Any descent of the zero morphism is homotopic to zero. -/
 def descHomotopyZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
@@ -192,10 +180,7 @@ def descHomotopyZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolut
 #align category_theory.InjectiveResolution.desc_homotopy_zero CategoryTheory.InjectiveResolution.descHomotopyZero
 
 /- warning: category_theory.InjectiveResolution.desc_homotopy -> CategoryTheory.InjectiveResolution.descHomotopy is a dubious translation:
-lean 3 declaration is
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(CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopy._proof_2.{u2, u1} C _inst_1 _inst_2) Z} (g : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat 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u2} C _inst_1 _inst_2)) (ComplexShape.up.{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.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopy._proof_3.{u2, u1} C _inst_1 _inst_2) Y I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopy._proof_4.{u2, u1} C _inst_1 _inst_2) Z J)), (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopy._proof_4.{u2, u1} C _inst_1 _inst_2) Z J) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopy._proof_5.{u2, u1} C _inst_1 _inst_2) Y I) g) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Z) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, 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(CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J))) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Y) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Y) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y I) h) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 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_inst_2)) Z J) (Prefunctor.map.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Y Z f) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J))) -> (Homotopy.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J) g h)
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_homotopy CategoryTheory.InjectiveResolution.descHomotopyₓ'. -/
 /-- Two descents of the same morphism are homotopic. -/
 def descHomotopy {Y Z : C} (f : Y ⟶ Z) {I : InjectiveResolution Y} {J : InjectiveResolution Z}
@@ -236,10 +221,7 @@ def homotopyEquiv {X : C} (I J : InjectiveResolution X) : HomotopyEquiv I.cocomp
 -/
 
 /- warning: category_theory.InjectiveResolution.homotopy_equiv_hom_ι -> CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι is a dubious translation:
-lean 3 declaration is
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(CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X J)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) 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Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) X) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X J) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X I) (HomotopyEquiv.hom.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X J) (CategoryTheory.InjectiveResolution.homotopyEquiv.{u1, u2} C _inst_1 _inst_2 X I J))) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X J)
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.homotopy_equiv_hom_ι CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ιₓ'. -/
 @[simp, reassoc]
 theorem homotopyEquiv_hom_ι {X : C} (I J : InjectiveResolution X) :
@@ -247,10 +229,7 @@ theorem homotopyEquiv_hom_ι {X : C} (I J : InjectiveResolution X) :
 #align category_theory.InjectiveResolution.homotopy_equiv_hom_ι CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι
 
 /- warning: category_theory.InjectiveResolution.homotopy_equiv_inv_ι -> CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ι is a dubious translation:
-lean 3 declaration is
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(CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat 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u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne))) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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)) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2)) X) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X J) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.homotopyEquiv._proof_3.{u2, u1} C _inst_1 _inst_2) X I) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X J) (HomotopyEquiv.inv.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) (ComplexShape.up.{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.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.homotopyEquiv._proof_3.{u2, u1} C _inst_1 _inst_2) X I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.homotopyEquiv._proof_4.{u2, u1} C _inst_1 _inst_2) X J) (CategoryTheory.InjectiveResolution.homotopyEquiv.{u1, u2} C _inst_1 _inst_2 X I J))) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X I)
-but is expected to have type
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(CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) 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(AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) X) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X I)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) 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_inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X J) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X I) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X I)
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.homotopy_equiv_inv_ι CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ιₓ'. -/
 @[simp, reassoc]
 theorem homotopyEquiv_inv_ι {X : C} (I J : InjectiveResolution X) :
@@ -273,10 +252,7 @@ abbrev injectiveResolution (Z : C) [HasInjectiveResolution Z] : CochainComplex C
 -/
 
 /- warning: category_theory.injective_resolution.ι -> CategoryTheory.injectiveResolution.ι is a dubious translation:
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(AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 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(CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Z) (CategoryTheory.injectiveResolution.{u1, u2} C _inst_1 _inst_2 Z _inst_3)
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.injective_resolution.ι CategoryTheory.injectiveResolution.ιₓ'. -/
 /-- The cochain map from cochain complex consisting of `Z` supported in degree `0`
 back to the arbitrarily chosen injective resolution `injective_resolution Z`. -/
@@ -395,10 +371,7 @@ namespace HomologicalComplex.Hom
 variable {C : Type u} [Category.{v} C] [Abelian C]
 
 /- warning: homological_complex.hom.homological_complex.hom.from_single₀_InjectiveResolution -> HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution is a dubious translation:
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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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)) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2)) Y) X) [_inst_3 : QuasiIso.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution._proof_1.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u1, u2} C _inst_1 (HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution._proof_2.{u2, u1} C _inst_1 _inst_2) (HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution._proof_3.{u2, u1} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasCokernels.{u1, u2} C _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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)) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2)) Y) X f], (forall (n : Nat), CategoryTheory.Injective.{u1, u2} C _inst_1 (HomologicalComplex.x.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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) X n)) -> (CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution._proof_4.{u2, u1} C _inst_1 _inst_2) Y)
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(AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Y) X) [_inst_3 : QuasiIso.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u1, u2} C _inst_1 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers.{u1, u2} C _inst_1 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasPullbacks.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2))) (CategoryTheory.Limits.hasCokernels_of_hasCoequalizers.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasCoequalizers.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat 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(AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Y) X f], (forall (n : Nat), CategoryTheory.Injective.{u1, u2} C _inst_1 (HomologicalComplex.X.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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)) X n)) -> (CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y)
+<too large>
 Case conversion may be inaccurate. Consider using '#align homological_complex.hom.homological_complex.hom.from_single₀_InjectiveResolution HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolutionₓ'. -/
 /-- If `X` is a cochain complex of injective objects and we have a quasi-isomorphism
 `f : Y[0] ⟶ X`, then `X` is an injective resolution of `Y.` -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -52,11 +52,13 @@ section
 
 variable [HasZeroMorphisms C] [HasZeroObject C] [HasEqualizers C] [HasImages C]
 
+#print CategoryTheory.InjectiveResolution.descFZero /-
 /-- Auxiliary construction for `desc`. -/
 def descFZero {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y) (J : InjectiveResolution Z) :
     J.cocomplex.pt 0 ⟶ I.cocomplex.pt 0 :=
   factorThru (f ≫ I.ι.f 0) (J.ι.f 0)
 #align category_theory.InjectiveResolution.desc_f_zero CategoryTheory.InjectiveResolution.descFZero
+-/
 
 end
 
@@ -64,20 +66,25 @@ section Abelian
 
 variable [Abelian C]
 
+#print CategoryTheory.InjectiveResolution.descFOne /-
 /-- Auxiliary construction for `desc`. -/
 def descFOne {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y) (J : InjectiveResolution Z) :
     J.cocomplex.pt 1 ⟶ I.cocomplex.pt 1 :=
   Exact.desc (descFZero f I J ≫ I.cocomplex.d 0 1) (J.ι.f 0) (J.cocomplex.d 0 1)
     (Abelian.Exact.op _ _ J.exact₀) (by simp [← category.assoc, desc_f_zero])
 #align category_theory.InjectiveResolution.desc_f_one CategoryTheory.InjectiveResolution.descFOne
+-/
 
+#print CategoryTheory.InjectiveResolution.descFOne_zero_comm /-
 @[simp]
 theorem descFOne_zero_comm {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y)
     (J : InjectiveResolution Z) :
     J.cocomplex.d 0 1 ≫ descFOne f I J = descFZero f I J ≫ I.cocomplex.d 0 1 := by
   simp [desc_f_zero, desc_f_one]
 #align category_theory.InjectiveResolution.desc_f_one_zero_comm CategoryTheory.InjectiveResolution.descFOne_zero_comm
+-/
 
+#print CategoryTheory.InjectiveResolution.descFSucc /-
 /-- Auxiliary construction for `desc`. -/
 def descFSucc {Y Z : C} (I : InjectiveResolution Y) (J : InjectiveResolution Z) (n : ℕ)
     (g : J.cocomplex.pt n ⟶ I.cocomplex.pt n) (g' : J.cocomplex.pt (n + 1) ⟶ I.cocomplex.pt (n + 1))
@@ -89,14 +96,23 @@ def descFSucc {Y Z : C} (I : InjectiveResolution Y) (J : InjectiveResolution Z)
       (by simp [← category.assoc, w]),
     by simp⟩
 #align category_theory.InjectiveResolution.desc_f_succ CategoryTheory.InjectiveResolution.descFSucc
+-/
 
+#print CategoryTheory.InjectiveResolution.desc /-
 /-- A morphism in `C` descends to a chain map between injective resolutions. -/
 def desc {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y) (J : InjectiveResolution Z) :
     J.cocomplex ⟶ I.cocomplex :=
   CochainComplex.mkHom _ _ (descFZero f _ _) (descFOne f _ _) (descFOne_zero_comm f I J).symm
     fun n ⟨g, g', w⟩ => ⟨(descFSucc I J n g g' w.symm).1, (descFSucc I J n g g' w.symm).2.symm⟩
 #align category_theory.InjectiveResolution.desc CategoryTheory.InjectiveResolution.desc
+-/
 
+/- warning: category_theory.InjectiveResolution.desc_commutes -> CategoryTheory.InjectiveResolution.desc_commutes is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] {Y : C} {Z : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Z Y) (I : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y) (J : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) 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+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] {Y : C} {Z : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Z Y) (I : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y) (J : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Z) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y I)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Z) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y I) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J) (CategoryTheory.InjectiveResolution.desc.{u1, u2} C _inst_1 _inst_2 Y Z f I J)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat 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(CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y I))
+Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_commutes CategoryTheory.InjectiveResolution.desc_commutesₓ'. -/
 /-- The resolution maps intertwine the descent of a morphism and that morphism. -/
 @[simp, reassoc]
 theorem desc_commutes {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y)
@@ -108,6 +124,12 @@ theorem desc_commutes {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y)
       simp
 #align category_theory.InjectiveResolution.desc_commutes CategoryTheory.InjectiveResolution.desc_commutes
 
+/- warning: category_theory.InjectiveResolution.desc_homotopy_zero_zero -> CategoryTheory.InjectiveResolution.descHomotopyZeroZero is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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)) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2)) Y) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopyZeroZero._proof_4.{u2, u1} C _inst_1 _inst_2) Z J)))))) -> (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopyZeroZero._proof_3.{u2, u1} C _inst_1 _inst_2) Y I) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) (HomologicalComplex.x.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopyZeroZero._proof_4.{u2, u1} C _inst_1 _inst_2) Z J) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] {Y : C} {Z : C} {I : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y} {J : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z} (f : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J)), (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Y) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 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(CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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+Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_homotopy_zero_zero CategoryTheory.InjectiveResolution.descHomotopyZeroZeroₓ'. -/
 -- Now that we've checked this property of the descent,
 -- we can seal away the actual definition.
 /-- An auxiliary definition for `desc_homotopy_zero`. -/
@@ -117,6 +139,12 @@ def descHomotopyZeroZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveRes
     (congr_fun (congr_arg HomologicalComplex.Hom.f comm) 0)
 #align category_theory.InjectiveResolution.desc_homotopy_zero_zero CategoryTheory.InjectiveResolution.descHomotopyZeroZero
 
+/- warning: category_theory.InjectiveResolution.desc_homotopy_zero_one -> CategoryTheory.InjectiveResolution.descHomotopyZeroOne is a dubious translation:
+lean 3 declaration is
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_inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopyZeroOne._proof_4.{u2, u1} C _inst_1 _inst_2) Z J)))))) -> (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopyZeroOne._proof_3.{u2, u1} C _inst_1 _inst_2) Y I) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HomologicalComplex.x.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopyZeroOne._proof_4.{u2, u1} C _inst_1 _inst_2) Z J) (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] {Y : C} {Z : C} {I : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y} {J : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z} (f : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J)), (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Y) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
+Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_homotopy_zero_one CategoryTheory.InjectiveResolution.descHomotopyZeroOneₓ'. -/
 /-- An auxiliary definition for `desc_homotopy_zero`. -/
 def descHomotopyZeroOne {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (f : I.cocomplex ⟶ J.cocomplex) (comm : I.ι ≫ f = (0 : _ ⟶ J.cocomplex)) :
@@ -126,6 +154,12 @@ def descHomotopyZeroOne {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveReso
     (by simp [desc_homotopy_zero_zero, ← category.assoc])
 #align category_theory.InjectiveResolution.desc_homotopy_zero_one CategoryTheory.InjectiveResolution.descHomotopyZeroOne
 
+/- warning: category_theory.InjectiveResolution.desc_homotopy_zero_succ -> CategoryTheory.InjectiveResolution.descHomotopyZeroSucc is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopyZeroSucc._proof_3.{u2, u1} C _inst_1 _inst_2) Y I) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 3 (OfNat.mk.{0} Nat 3 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HomologicalComplex.x.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopyZeroSucc._proof_4.{u2, u1} C _inst_1 _inst_2) Z J) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] {Y : C} {Z : C} {I : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y} {J : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z} (f : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J)) (n : Nat) (g : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 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(HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.X.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) 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+Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_homotopy_zero_succ CategoryTheory.InjectiveResolution.descHomotopyZeroSuccₓ'. -/
 /-- An auxiliary definition for `desc_homotopy_zero`. -/
 def descHomotopyZeroSucc {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (f : I.cocomplex ⟶ J.cocomplex) (n : ℕ) (g : I.cocomplex.pt (n + 1) ⟶ J.cocomplex.pt n)
@@ -142,6 +176,12 @@ def descHomotopyZeroSucc {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveRes
           simp only [add_sub_cancel]])
 #align category_theory.InjectiveResolution.desc_homotopy_zero_succ CategoryTheory.InjectiveResolution.descHomotopyZeroSucc
 
+/- warning: category_theory.InjectiveResolution.desc_homotopy_zero -> CategoryTheory.InjectiveResolution.descHomotopyZero is a dubious translation:
+lean 3 declaration is
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Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopyZero._proof_3.{u2, u1} C _inst_1 _inst_2) Y I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopyZero._proof_4.{u2, u1} C _inst_1 _inst_2) Z J)) (HomologicalComplex.Quiver.Hom.hasZero.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) (ComplexShape.up.{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.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopyZero._proof_3.{u2, u1} C _inst_1 _inst_2) Y I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopyZero._proof_4.{u2, u1} C _inst_1 _inst_2) Z J))))))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] {Y : C} {Z : C} {I : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y} {J : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z} (f : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J)), (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Y) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 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_inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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+Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_homotopy_zero CategoryTheory.InjectiveResolution.descHomotopyZeroₓ'. -/
 /-- Any descent of the zero morphism is homotopic to zero. -/
 def descHomotopyZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (f : I.cocomplex ⟶ J.cocomplex) (comm : I.ι ≫ f = 0) : Homotopy f 0 :=
@@ -151,6 +191,12 @@ def descHomotopyZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolut
       simp [desc_homotopy_zero_succ, w]⟩
 #align category_theory.InjectiveResolution.desc_homotopy_zero CategoryTheory.InjectiveResolution.descHomotopyZero
 
+/- warning: category_theory.InjectiveResolution.desc_homotopy -> CategoryTheory.InjectiveResolution.descHomotopy is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] {Y : C} {Z : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y Z) {I : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopy._proof_1.{u2, u1} C _inst_1 _inst_2) Y} {J : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopy._proof_2.{u2, u1} C _inst_1 _inst_2) Z} (g : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat 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u2} C _inst_1 _inst_2)) (ComplexShape.up.{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.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopy._proof_3.{u2, u1} C _inst_1 _inst_2) Y I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopy._proof_4.{u2, u1} C _inst_1 _inst_2) Z J)) (h : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopy._proof_3.{u2, u1} C _inst_1 _inst_2) Y I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopy._proof_4.{u2, u1} C _inst_1 _inst_2) Z J)), (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopy._proof_4.{u2, u1} C _inst_1 _inst_2) Z J) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopy._proof_5.{u2, u1} C _inst_1 _inst_2) Y I) g) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat 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(CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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)) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2)) Y Z f) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopy._proof_6.{u2, u1} C _inst_1 _inst_2) Z J))) -> (Homotopy.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) (ComplexShape.up.{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.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopy._proof_3.{u2, u1} C _inst_1 _inst_2) Y I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.descHomotopy._proof_4.{u2, u1} C _inst_1 _inst_2) Z J) g h)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] {Y : C} {Z : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y Z) {I : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y} {J : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z} (g : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J)) (h : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J)), (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Y) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Z) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, 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(CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J))) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Y) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Y) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y I) h) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 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u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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_inst_2)) Z J) (Prefunctor.map.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Y Z f) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J))) -> (Homotopy.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z J) g h)
+Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.desc_homotopy CategoryTheory.InjectiveResolution.descHomotopyₓ'. -/
 /-- Two descents of the same morphism are homotopic. -/
 def descHomotopy {Y Z : C} (f : Y ⟶ Z) {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (g h : I.cocomplex ⟶ J.cocomplex) (g_comm : I.ι ≫ g = (CochainComplex.single₀ C).map f ≫ J.ι)
@@ -158,17 +204,22 @@ def descHomotopy {Y Z : C} (f : Y ⟶ Z) {I : InjectiveResolution Y} {J : Inject
   Homotopy.equivSubZero.invFun (descHomotopyZero _ (by simp [g_comm, h_comm]))
 #align category_theory.InjectiveResolution.desc_homotopy CategoryTheory.InjectiveResolution.descHomotopy
 
+#print CategoryTheory.InjectiveResolution.descIdHomotopy /-
 /-- The descent of the identity morphism is homotopic to the identity cochain map. -/
 def descIdHomotopy (X : C) (I : InjectiveResolution X) :
     Homotopy (desc (𝟙 X) I I) (𝟙 I.cocomplex) := by apply desc_homotopy (𝟙 X) <;> simp
 #align category_theory.InjectiveResolution.desc_id_homotopy CategoryTheory.InjectiveResolution.descIdHomotopy
+-/
 
+#print CategoryTheory.InjectiveResolution.descCompHomotopy /-
 /-- The descent of a composition is homotopic to the composition of the descents. -/
 def descCompHomotopy {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z) (I : InjectiveResolution X)
     (J : InjectiveResolution Y) (K : InjectiveResolution Z) :
     Homotopy (desc (f ≫ g) K I) (desc f J I ≫ desc g K J) := by apply desc_homotopy (f ≫ g) <;> simp
 #align category_theory.InjectiveResolution.desc_comp_homotopy CategoryTheory.InjectiveResolution.descCompHomotopy
+-/
 
+#print CategoryTheory.InjectiveResolution.homotopyEquiv /-
 -- We don't care about the actual definitions of these homotopies.
 /-- Any two injective resolutions are homotopy equivalent. -/
 def homotopyEquiv {X : C} (I J : InjectiveResolution X) : HomotopyEquiv I.cocomplex J.cocomplex
@@ -182,12 +233,25 @@ def homotopyEquiv {X : C} (I J : InjectiveResolution X) : HomotopyEquiv I.cocomp
     (descCompHomotopy (𝟙 X) (𝟙 X) J I J).symm.trans <| by
       simpa [category.id_comp] using desc_id_homotopy _ _
 #align category_theory.InjectiveResolution.homotopy_equiv CategoryTheory.InjectiveResolution.homotopyEquiv
+-/
 
+/- warning: category_theory.InjectiveResolution.homotopy_equiv_hom_ι -> CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] {X : C} (I : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X) (J : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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)) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2)) X) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.homotopyEquiv._proof_4.{u2, u1} C _inst_1 _inst_2) X J)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne))) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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)) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2)) X) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.homotopyEquiv._proof_4.{u2, u1} C _inst_1 _inst_2) X J) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X I) (HomotopyEquiv.hom.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) (ComplexShape.up.{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.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.homotopyEquiv._proof_3.{u2, u1} C _inst_1 _inst_2) X I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.homotopyEquiv._proof_4.{u2, u1} C _inst_1 _inst_2) X J) (CategoryTheory.InjectiveResolution.homotopyEquiv.{u1, u2} C _inst_1 _inst_2 X I J))) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X J)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] {X : C} (I : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X) (J : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat 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(CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X J)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X J)
+Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.homotopy_equiv_hom_ι CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ιₓ'. -/
 @[simp, reassoc]
 theorem homotopyEquiv_hom_ι {X : C} (I J : InjectiveResolution X) :
     I.ι ≫ (homotopyEquiv I J).Hom = J.ι := by simp [HomotopyEquiv]
 #align category_theory.InjectiveResolution.homotopy_equiv_hom_ι CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι
 
+/- warning: category_theory.InjectiveResolution.homotopy_equiv_inv_ι -> CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ι is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] {X : C} (I : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X) (J : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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)) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2)) X) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X J) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.homotopyEquiv._proof_3.{u2, u1} C _inst_1 _inst_2) X I) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X J) (HomotopyEquiv.inv.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) (ComplexShape.up.{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.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.homotopyEquiv._proof_3.{u2, u1} C _inst_1 _inst_2) X I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.homotopyEquiv._proof_4.{u2, u1} C _inst_1 _inst_2) X J) (CategoryTheory.InjectiveResolution.homotopyEquiv.{u1, u2} C _inst_1 _inst_2 X I J))) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X I)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] {X : C} (I : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X) (J : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) X) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X I)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) X) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X J) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X I) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X J) (HomotopyEquiv.inv.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X I) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X J) (CategoryTheory.InjectiveResolution.homotopyEquiv.{u1, u2} C _inst_1 _inst_2 X I J))) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) X I)
+Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.homotopy_equiv_inv_ι CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ιₓ'. -/
 @[simp, reassoc]
 theorem homotopyEquiv_inv_ι {X : C} (I J : InjectiveResolution X) :
     J.ι ≫ (homotopyEquiv I J).inv = I.ι := by simp [HomotopyEquiv]
@@ -201,11 +265,19 @@ section
 
 variable [Abelian C]
 
+#print CategoryTheory.injectiveResolution /-
 /-- An arbitrarily chosen injective resolution of an object. -/
 abbrev injectiveResolution (Z : C) [HasInjectiveResolution Z] : CochainComplex C ℕ :=
   (HasInjectiveResolution.out Z).some.cocomplex
 #align category_theory.injective_resolution CategoryTheory.injectiveResolution
+-/
 
+/- warning: category_theory.injective_resolution.ι -> CategoryTheory.injectiveResolution.ι is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] (Z : C) [_inst_3 : CategoryTheory.HasInjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.injectiveResolution.ι._proof_1.{u2, u1} C _inst_1 _inst_2) Z], Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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)) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2)) Z) (CategoryTheory.injectiveResolution.{u1, u2} C _inst_1 _inst_2 Z _inst_3)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] (Z : C) [_inst_3 : CategoryTheory.HasInjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Z], Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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(CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Z) (CategoryTheory.injectiveResolution.{u1, u2} C _inst_1 _inst_2 Z _inst_3)
+Case conversion may be inaccurate. Consider using '#align category_theory.injective_resolution.ι CategoryTheory.injectiveResolution.ιₓ'. -/
 /-- The cochain map from cochain complex consisting of `Z` supported in degree `0`
 back to the arbitrarily chosen injective resolution `injective_resolution Z`. -/
 abbrev injectiveResolution.ι (Z : C) [HasInjectiveResolution Z] :
@@ -213,15 +285,18 @@ abbrev injectiveResolution.ι (Z : C) [HasInjectiveResolution Z] :
   (HasInjectiveResolution.out Z).some.ι
 #align category_theory.injective_resolution.ι CategoryTheory.injectiveResolution.ι
 
+#print CategoryTheory.injectiveResolution.desc /-
 /-- The descent of a morphism to a cochain map between the arbitrarily chosen injective resolutions.
 -/
 abbrev injectiveResolution.desc {X Y : C} (f : X ⟶ Y) [HasInjectiveResolution X]
     [HasInjectiveResolution Y] : injectiveResolution X ⟶ injectiveResolution Y :=
   InjectiveResolution.desc f _ _
 #align category_theory.injective_resolution.desc CategoryTheory.injectiveResolution.desc
+-/
 
 variable (C) [HasInjectiveResolutions C]
 
+#print CategoryTheory.injectiveResolutions /-
 /-- Taking injective resolutions is functorial,
 if considered with target the homotopy category
 (`ℕ`-indexed cochain complexes and chain maps up to homotopy).
@@ -239,6 +314,7 @@ def injectiveResolutions : C ⥤ HomotopyCategory C (ComplexShape.up ℕ)
     apply HomotopyCategory.eq_of_homotopy
     apply InjectiveResolution.desc_comp_homotopy
 #align category_theory.injective_resolutions CategoryTheory.injectiveResolutions
+-/
 
 end
 
@@ -246,10 +322,12 @@ section
 
 variable [Abelian C] [EnoughInjectives C]
 
+#print CategoryTheory.exact_f_d /-
 theorem exact_f_d {X Y : C} (f : X ⟶ Y) : Exact f (d f) :=
   (Abelian.exact_iff _ _).2 <|
     ⟨by simp, zero_of_comp_mono (ι _) <| by rw [category.assoc, kernel.condition]⟩
 #align category_theory.exact_f_d CategoryTheory.exact_f_d
+-/
 
 end
 
@@ -267,6 +345,7 @@ and the map from the `n`-th object as `injective.d`.
 
 variable [Abelian C] [EnoughInjectives C]
 
+#print CategoryTheory.InjectiveResolution.ofCocomplex /-
 /-- Auxiliary definition for `InjectiveResolution.of`. -/
 @[simps]
 def ofCocomplex (Z : C) : CochainComplex C ℕ :=
@@ -274,7 +353,14 @@ def ofCocomplex (Z : C) : CochainComplex C ℕ :=
     (Injective.d (Injective.ι Z)) fun ⟨X, Y, f⟩ =>
     ⟨Injective.syzygies f, Injective.d f, (exact_f_d f).w⟩
 #align category_theory.InjectiveResolution.of_cocomplex CategoryTheory.InjectiveResolution.ofCocomplex
+-/
 
+/- warning: category_theory.InjectiveResolution.of -> CategoryTheory.InjectiveResolution.of is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.EnoughInjectives.{u1, u2} C _inst_1] (Z : C), CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.InjectiveResolution.of._proof_1.{u2, u1} C _inst_1 _inst_2) Z
+but is expected to have type
+  forall {C : Type.{u1}} [_inst_1 : CategoryTheory.Category.{u2, u1} C] [_inst_2 : CategoryTheory.Abelian.{u2, u1} C _inst_1] [_inst_3 : CategoryTheory.EnoughInjectives.{u2, u1} C _inst_1] (Z : C), CategoryTheory.InjectiveResolution.{u2, u1} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u2, u1} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} C _inst_1 _inst_2)) Z
+Case conversion may be inaccurate. Consider using '#align category_theory.InjectiveResolution.of CategoryTheory.InjectiveResolution.ofₓ'. -/
 /-- In any abelian category with enough injectives,
 `InjectiveResolution.of Z` constructs an injective resolution of the object `Z`.
 -/
@@ -308,6 +394,12 @@ namespace HomologicalComplex.Hom
 
 variable {C : Type u} [Category.{v} C] [Abelian C]
 
+/- warning: homological_complex.hom.homological_complex.hom.from_single₀_InjectiveResolution -> HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] (X : CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (Y : C) (f : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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)) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2)) Y) X) [_inst_3 : QuasiIso.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution._proof_1.{u2, u1} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u1, u2} C _inst_1 (HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution._proof_2.{u2, u1} C _inst_1 _inst_2) (HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution._proof_3.{u2, u1} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasCokernels.{u1, u2} C _inst_1 _inst_2) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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)) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2)) Y) X f], (forall (n : Nat), CategoryTheory.Injective.{u1, u2} C _inst_1 (HomologicalComplex.x.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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) X n)) -> (CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution._proof_4.{u2, u1} C _inst_1 _inst_2) Y)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] (X : CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Y : C) (f : Quiver.Hom.{succ u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Y) X) [_inst_3 : QuasiIso.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u1, u2} C _inst_1 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers.{u1, u2} C _inst_1 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasPullbacks.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2))) (CategoryTheory.Limits.hasCokernels_of_hasCoequalizers.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasCoequalizers.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2))) Y) X f], (forall (n : Nat), CategoryTheory.Injective.{u1, u2} C _inst_1 (HomologicalComplex.X.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (ComplexShape.up.{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)) X n)) -> (CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_2) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_2)) Y)
+Case conversion may be inaccurate. Consider using '#align homological_complex.hom.homological_complex.hom.from_single₀_InjectiveResolution HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolutionₓ'. -/
 /-- If `X` is a cochain complex of injective objects and we have a quasi-isomorphism
 `f : Y[0] ⟶ X`, then `X` is an injective resolution of `Y.` -/
 def HomologicalComplex.Hom.fromSingle₀InjectiveResolution (X : CochainComplex C ℕ) (Y : C)

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

@@ -98,7 +98,7 @@ def desc {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y) (J : InjectiveResol
 #align category_theory.InjectiveResolution.desc CategoryTheory.InjectiveResolution.desc
 
 /-- The resolution maps intertwine the descent of a morphism and that morphism. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem desc_commutes {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y)
     (J : InjectiveResolution Z) : J.ι ≫ desc f I J = (CochainComplex.single₀ C).map f ≫ I.ι :=
   by
@@ -183,12 +183,12 @@ def homotopyEquiv {X : C} (I J : InjectiveResolution X) : HomotopyEquiv I.cocomp
       simpa [category.id_comp] using desc_id_homotopy _ _
 #align category_theory.InjectiveResolution.homotopy_equiv CategoryTheory.InjectiveResolution.homotopyEquiv
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem homotopyEquiv_hom_ι {X : C} (I J : InjectiveResolution X) :
     I.ι ≫ (homotopyEquiv I J).Hom = J.ι := by simp [HomotopyEquiv]
 #align category_theory.InjectiveResolution.homotopy_equiv_hom_ι CategoryTheory.InjectiveResolution.homotopyEquiv_hom_ι
 
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem homotopyEquiv_inv_ι {X : C} (I J : InjectiveResolution X) :
     J.ι ≫ (homotopyEquiv I J).inv = I.ι := by simp [HomotopyEquiv]
 #align category_theory.InjectiveResolution.homotopy_equiv_inv_ι CategoryTheory.InjectiveResolution.homotopyEquiv_inv_ι

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

@@ -4,13 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jujian Zhang, Scott Morrison
 
 ! This file was ported from Lean 3 source module category_theory.abelian.injective_resolution
-! leanprover-community/mathlib commit 956af7c76589f444f2e1313911bad16366ea476d
+! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Homology.QuasiIso
 import Mathbin.CategoryTheory.Preadditive.InjectiveResolution
-import Mathbin.CategoryTheory.Abelian.Homology
 import Mathbin.Algebra.Homology.HomotopyCategory
 
 /-!

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

@@ -247,10 +247,10 @@ section
 
 variable [Abelian C] [EnoughInjectives C]
 
-theorem exactFD {X Y : C} (f : X ⟶ Y) : Exact f (d f) :=
+theorem exact_f_d {X Y : C} (f : X ⟶ Y) : Exact f (d f) :=
   (Abelian.exact_iff _ _).2 <|
     ⟨by simp, zero_of_comp_mono (ι _) <| by rw [category.assoc, kernel.condition]⟩
-#align category_theory.exact_f_d CategoryTheory.exactFD
+#align category_theory.exact_f_d CategoryTheory.exact_f_d
 
 end
 
@@ -273,7 +273,7 @@ variable [Abelian C] [EnoughInjectives C]
 def ofCocomplex (Z : C) : CochainComplex C ℕ :=
   CochainComplex.mk' (Injective.under Z) (Injective.syzygies (Injective.ι Z))
     (Injective.d (Injective.ι Z)) fun ⟨X, Y, f⟩ =>
-    ⟨Injective.syzygies f, Injective.d f, (exactFD f).w⟩
+    ⟨Injective.syzygies f, Injective.d f, (exact_f_d f).w⟩
 #align category_theory.InjectiveResolution.of_cocomplex CategoryTheory.InjectiveResolution.ofCocomplex
 
 /-- In any abelian category with enough injectives,
@@ -317,8 +317,8 @@ def HomologicalComplex.Hom.fromSingle₀InjectiveResolution (X : CochainComplex
   cocomplex := X
   ι := f
   Injective := H
-  exact₀ := f.fromSingle₀ExactFDAtZero
-  exact := f.fromSingle₀ExactAtSucc
+  exact₀ := f.from_single₀_exact_f_d_at_zero
+  exact := f.from_single₀_exact_at_succ
   Mono := f.from_single₀_mono_at_zero
 #align homological_complex.hom.homological_complex.hom.from_single₀_InjectiveResolution HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/17ad94b4953419f3e3ce3e77da3239c62d1d09f0

@@ -247,10 +247,10 @@ section
 
 variable [Abelian C] [EnoughInjectives C]
 
-theorem exact_f_d {X Y : C} (f : X ⟶ Y) : Exact f (d f) :=
+theorem exactFD {X Y : C} (f : X ⟶ Y) : Exact f (d f) :=
   (Abelian.exact_iff _ _).2 <|
     ⟨by simp, zero_of_comp_mono (ι _) <| by rw [category.assoc, kernel.condition]⟩
-#align category_theory.exact_f_d CategoryTheory.exact_f_d
+#align category_theory.exact_f_d CategoryTheory.exactFD
 
 end
 
@@ -273,7 +273,7 @@ variable [Abelian C] [EnoughInjectives C]
 def ofCocomplex (Z : C) : CochainComplex C ℕ :=
   CochainComplex.mk' (Injective.under Z) (Injective.syzygies (Injective.ι Z))
     (Injective.d (Injective.ι Z)) fun ⟨X, Y, f⟩ =>
-    ⟨Injective.syzygies f, Injective.d f, (exact_f_d f).w⟩
+    ⟨Injective.syzygies f, Injective.d f, (exactFD f).w⟩
 #align category_theory.InjectiveResolution.of_cocomplex CategoryTheory.InjectiveResolution.ofCocomplex
 
 /-- In any abelian category with enough injectives,
@@ -317,8 +317,8 @@ def HomologicalComplex.Hom.fromSingle₀InjectiveResolution (X : CochainComplex
   cocomplex := X
   ι := f
   Injective := H
-  exact₀ := f.from_single₀_exact_f_d_at_zero
-  exact := f.from_single₀_exact_at_succ
+  exact₀ := f.fromSingle₀ExactFDAtZero
+  exact := f.fromSingle₀ExactAtSucc
   Mono := f.from_single₀_mono_at_zero
 #align homological_complex.hom.homological_complex.hom.from_single₀_InjectiveResolution HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution
 

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

@@ -55,7 +55,7 @@ variable [HasZeroMorphisms C] [HasZeroObject C] [HasEqualizers C] [HasImages C]
 
 /-- Auxiliary construction for `desc`. -/
 def descFZero {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y) (J : InjectiveResolution Z) :
-    J.cocomplex.x 0 ⟶ I.cocomplex.x 0 :=
+    J.cocomplex.pt 0 ⟶ I.cocomplex.pt 0 :=
   factorThru (f ≫ I.ι.f 0) (J.ι.f 0)
 #align category_theory.InjectiveResolution.desc_f_zero CategoryTheory.InjectiveResolution.descFZero
 
@@ -67,7 +67,7 @@ variable [Abelian C]
 
 /-- Auxiliary construction for `desc`. -/
 def descFOne {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y) (J : InjectiveResolution Z) :
-    J.cocomplex.x 1 ⟶ I.cocomplex.x 1 :=
+    J.cocomplex.pt 1 ⟶ I.cocomplex.pt 1 :=
   Exact.desc (descFZero f I J ≫ I.cocomplex.d 0 1) (J.ι.f 0) (J.cocomplex.d 0 1)
     (Abelian.Exact.op _ _ J.exact₀) (by simp [← category.assoc, desc_f_zero])
 #align category_theory.InjectiveResolution.desc_f_one CategoryTheory.InjectiveResolution.descFOne
@@ -81,9 +81,9 @@ theorem descFOne_zero_comm {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y)
 
 /-- Auxiliary construction for `desc`. -/
 def descFSucc {Y Z : C} (I : InjectiveResolution Y) (J : InjectiveResolution Z) (n : ℕ)
-    (g : J.cocomplex.x n ⟶ I.cocomplex.x n) (g' : J.cocomplex.x (n + 1) ⟶ I.cocomplex.x (n + 1))
+    (g : J.cocomplex.pt n ⟶ I.cocomplex.pt n) (g' : J.cocomplex.pt (n + 1) ⟶ I.cocomplex.pt (n + 1))
     (w : J.cocomplex.d n (n + 1) ≫ g' = g ≫ I.cocomplex.d n (n + 1)) :
-    Σ'g'' : J.cocomplex.x (n + 2) ⟶ I.cocomplex.x (n + 2),
+    Σ'g'' : J.cocomplex.pt (n + 2) ⟶ I.cocomplex.pt (n + 2),
       J.cocomplex.d (n + 1) (n + 2) ≫ g'' = g' ≫ I.cocomplex.d (n + 1) (n + 2) :=
   ⟨@Exact.desc C _ _ _ _ _ _ _ _ _ (g' ≫ I.cocomplex.d (n + 1) (n + 2)) (J.cocomplex.d n (n + 1))
       (J.cocomplex.d (n + 1) (n + 2)) (Abelian.Exact.op _ _ (J.exact _))
@@ -113,7 +113,7 @@ theorem desc_commutes {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y)
 -- we can seal away the actual definition.
 /-- An auxiliary definition for `desc_homotopy_zero`. -/
 def descHomotopyZeroZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
-    (f : I.cocomplex ⟶ J.cocomplex) (comm : I.ι ≫ f = 0) : I.cocomplex.x 1 ⟶ J.cocomplex.x 0 :=
+    (f : I.cocomplex ⟶ J.cocomplex) (comm : I.ι ≫ f = 0) : I.cocomplex.pt 1 ⟶ J.cocomplex.pt 0 :=
   Exact.desc (f.f 0) (I.ι.f 0) (I.cocomplex.d 0 1) (Abelian.Exact.op _ _ I.exact₀)
     (congr_fun (congr_arg HomologicalComplex.Hom.f comm) 0)
 #align category_theory.InjectiveResolution.desc_homotopy_zero_zero CategoryTheory.InjectiveResolution.descHomotopyZeroZero
@@ -121,7 +121,7 @@ def descHomotopyZeroZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveRes
 /-- An auxiliary definition for `desc_homotopy_zero`. -/
 def descHomotopyZeroOne {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (f : I.cocomplex ⟶ J.cocomplex) (comm : I.ι ≫ f = (0 : _ ⟶ J.cocomplex)) :
-    I.cocomplex.x 2 ⟶ J.cocomplex.x 1 :=
+    I.cocomplex.pt 2 ⟶ J.cocomplex.pt 1 :=
   Exact.desc (f.f 1 - descHomotopyZeroZero f comm ≫ J.cocomplex.d 0 1) (I.cocomplex.d 0 1)
     (I.cocomplex.d 1 2) (Abelian.Exact.op _ _ (I.exact _))
     (by simp [desc_homotopy_zero_zero, ← category.assoc])
@@ -129,10 +129,10 @@ def descHomotopyZeroOne {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveReso
 
 /-- An auxiliary definition for `desc_homotopy_zero`. -/
 def descHomotopyZeroSucc {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
-    (f : I.cocomplex ⟶ J.cocomplex) (n : ℕ) (g : I.cocomplex.x (n + 1) ⟶ J.cocomplex.x n)
-    (g' : I.cocomplex.x (n + 2) ⟶ J.cocomplex.x (n + 1))
+    (f : I.cocomplex ⟶ J.cocomplex) (n : ℕ) (g : I.cocomplex.pt (n + 1) ⟶ J.cocomplex.pt n)
+    (g' : I.cocomplex.pt (n + 2) ⟶ J.cocomplex.pt (n + 1))
     (w : f.f (n + 1) = I.cocomplex.d (n + 1) (n + 2) ≫ g' + g ≫ J.cocomplex.d n (n + 1)) :
-    I.cocomplex.x (n + 3) ⟶ J.cocomplex.x (n + 2) :=
+    I.cocomplex.pt (n + 3) ⟶ J.cocomplex.pt (n + 2) :=
   Exact.desc (f.f (n + 2) - g' ≫ J.cocomplex.d _ _) (I.cocomplex.d (n + 1) (n + 2))
     (I.cocomplex.d (n + 2) (n + 3)) (Abelian.Exact.op _ _ (I.exact _))
     (by
@@ -312,7 +312,7 @@ variable {C : Type u} [Category.{v} C] [Abelian C]
 /-- If `X` is a cochain complex of injective objects and we have a quasi-isomorphism
 `f : Y[0] ⟶ X`, then `X` is an injective resolution of `Y.` -/
 def HomologicalComplex.Hom.fromSingle₀InjectiveResolution (X : CochainComplex C ℕ) (Y : C)
-    (f : (CochainComplex.single₀ C).obj Y ⟶ X) [QuasiIso f] (H : ∀ n, Injective (X.x n)) :
+    (f : (CochainComplex.single₀ C).obj Y ⟶ X) [QuasiIso f] (H : ∀ n, Injective (X.pt n)) :
     InjectiveResolution Y where
   cocomplex := X
   ι := f

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

Similar to the changes for ChainComplex.mkAux we remove the ad-hoc MkStruct and replace with it ShortComplex.

@@ -28,7 +28,6 @@ When the underlying category is abelian:
   is injective, we can apply `Injective.d` repeatedly to obtain an injective resolution of `X`.
 -/
 
-
 noncomputable section
 
 open CategoryTheory Category Limits
@@ -313,8 +312,7 @@ variable [Abelian C] [EnoughInjectives C] (Z : C)
 /-- Auxiliary definition for `InjectiveResolution.of`. -/
 def ofCocomplex : CochainComplex C ℕ :=
   CochainComplex.mk' (Injective.under Z) (Injective.syzygies (Injective.ι Z))
-    (Injective.d (Injective.ι Z)) fun ⟨_, _, f⟩ =>
-    ⟨Injective.syzygies f, Injective.d f, by simp⟩
+    (Injective.d (Injective.ι Z)) fun f => ⟨_, Injective.d f, by simp⟩
 set_option linter.uppercaseLean3 false in
 #align category_theory.InjectiveResolution.of_cocomplex CategoryTheory.InjectiveResolution.ofCocomplex
 
@@ -322,15 +320,18 @@ lemma ofCocomplex_d_0_1 :
     (ofCocomplex Z).d 0 1 = d (Injective.ι Z) := by
   simp [ofCocomplex]
 
+--Adaptation note: nightly-2024-03-11. This takes takes forever now
 lemma ofCocomplex_exactAt_succ (n : ℕ) :
     (ofCocomplex Z).ExactAt (n + 1) := by
   rw [HomologicalComplex.exactAt_iff' _ n (n + 1) (n + 1 + 1) (by simp) (by simp)]
-  cases n
-  all_goals
-    dsimp [ofCocomplex, HomologicalComplex.sc', HomologicalComplex.shortComplexFunctor',
-      CochainComplex.mk', CochainComplex.mk]
-    simp only [CochainComplex.of_d]
-    apply exact_f_d
+  dsimp [ofCocomplex, CochainComplex.mk', CochainComplex.mk, HomologicalComplex.sc',
+      HomologicalComplex.shortComplexFunctor']
+  simp only [CochainComplex.of_d]
+  match n with
+  | 0 => apply exact_f_d ((CochainComplex.mkAux _ _ _
+      (d (Injective.ι Z)) (d (d (Injective.ι Z))) _ _ 0).f)
+  | n+1 => apply exact_f_d ((CochainComplex.mkAux _ _ _
+      (d (Injective.ι Z)) (d (d (Injective.ι Z))) _ _ (n+1)).f)
 
 instance (n : ℕ) : Injective ((ofCocomplex Z).X n) := by
   obtain (_ | _ | _ | n) := n <;> apply Injective.injective_under

Adds a linter that detects calls to simp where the next line is at the same indentation level.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -329,7 +329,7 @@ lemma ofCocomplex_exactAt_succ (n : ℕ) :
   all_goals
     dsimp [ofCocomplex, HomologicalComplex.sc', HomologicalComplex.shortComplexFunctor',
       CochainComplex.mk', CochainComplex.mk]
-    simp
+    simp only [CochainComplex.of_d]
     apply exact_f_d
 
 instance (n : ℕ) : Injective ((ofCocomplex Z).X n) := by

This PR refactors the construction of left derived functors using the new homology API: this also affects the dependencies (Ext functors, group cohomology, local cohomology). As a result, the old homology API is no longer used in any significant way in mathlib. Then, with this PR, the homology refactor is essentially complete.

The organization of the files was made more coherent: the definition of a projective resolution is in Preadditive.ProjectiveResolution, the existence of resolutions when there are enough projectives is shown in Abelian.ProjectiveResolution, and the left derived functor is constructed in Abelian.LeftDerived; the dual results are in Preadditive.InjectiveResolution, Abelian.InjectiveResolution and Abelian.RightDerived.

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

@@ -9,8 +9,9 @@ import Mathlib.Algebra.Homology.HomotopyCategory
 #align_import category_theory.abelian.injective_resolution from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
 
 /-!
-# Main result
+# Abelian categories with enough injectives have injective resolutions
 
+## Main results
 When the underlying category is abelian:
 * `CategoryTheory.InjectiveResolution.desc`: Given `I : InjectiveResolution X` and
   `J : InjectiveResolution Y`, any morphism `X ⟶ Y` admits a descent to a chain map

Injective resolutions and right derived functors are redefined using the new homology API.

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

@@ -3,7 +3,6 @@ Copyright (c) 2022 Jujian Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jujian Zhang, Scott Morrison
 -/
-import Mathlib.Algebra.Homology.QuasiIso
 import Mathlib.CategoryTheory.Preadditive.InjectiveResolution
 import Mathlib.Algebra.Homology.HomotopyCategory
 
@@ -31,9 +30,7 @@ When the underlying category is abelian:
 
 noncomputable section
 
-open CategoryTheory
-
-open CategoryTheory.Limits
+open CategoryTheory Category Limits
 
 universe v u
 
@@ -48,7 +45,7 @@ set_option linter.uppercaseLean3 false -- `InjectiveResolution`
 
 section
 
-variable [HasZeroMorphisms C] [HasZeroObject C] [HasEqualizers C] [HasImages C]
+variable [HasZeroObject C] [HasZeroMorphisms C]
 
 /-- Auxiliary construction for `desc`. -/
 def descFZero {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y) (J : InjectiveResolution Z) :
@@ -62,18 +59,22 @@ section Abelian
 
 variable [Abelian C]
 
+lemma exact₀ {Z : C} (I : InjectiveResolution Z) :
+    (ShortComplex.mk _ _ I.ι_f_zero_comp_complex_d).Exact :=
+  ShortComplex.exact_of_f_is_kernel _ I.isLimitKernelFork
+
 /-- Auxiliary construction for `desc`. -/
 def descFOne {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y) (J : InjectiveResolution Z) :
     J.cocomplex.X 1 ⟶ I.cocomplex.X 1 :=
-  Exact.desc (descFZero f I J ≫ I.cocomplex.d 0 1) (J.ι.f 0) (J.cocomplex.d 0 1)
-    (Abelian.Exact.op _ _ J.exact₀) (by simp [← Category.assoc, descFZero])
+  J.exact₀.descToInjective (descFZero f I J ≫ I.cocomplex.d 0 1)
+    (by dsimp; simp [← assoc, descFZero])
 #align category_theory.InjectiveResolution.desc_f_one CategoryTheory.InjectiveResolution.descFOne
 
 @[simp]
 theorem descFOne_zero_comm {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y)
     (J : InjectiveResolution Z) :
     J.cocomplex.d 0 1 ≫ descFOne f I J = descFZero f I J ≫ I.cocomplex.d 0 1 := by
-  simp [descFZero, descFOne]
+  apply J.exact₀.comp_descToInjective
 #align category_theory.InjectiveResolution.desc_f_one_zero_comm CategoryTheory.InjectiveResolution.descFOne_zero_comm
 
 /-- Auxiliary construction for `desc`. -/
@@ -82,10 +83,9 @@ def descFSucc {Y Z : C} (I : InjectiveResolution Y) (J : InjectiveResolution Z)
     (w : J.cocomplex.d n (n + 1) ≫ g' = g ≫ I.cocomplex.d n (n + 1)) :
     Σ'g'' : J.cocomplex.X (n + 2) ⟶ I.cocomplex.X (n + 2),
       J.cocomplex.d (n + 1) (n + 2) ≫ g'' = g' ≫ I.cocomplex.d (n + 1) (n + 2) :=
-  ⟨@Exact.desc C _ _ _ _ _ _ _ _ _ (g' ≫ I.cocomplex.d (n + 1) (n + 2)) (J.cocomplex.d n (n + 1))
-      (J.cocomplex.d (n + 1) (n + 2)) (Abelian.Exact.op _ _ (J.exact _))
-      (by simp [← Category.assoc, w]),
-    by simp⟩
+  ⟨(J.exact_succ n).descToInjective
+    (g' ≫ I.cocomplex.d (n + 1) (n + 2)) (by simp [reassoc_of% w]),
+      (J.exact_succ n).comp_descToInjective _ _⟩
 #align category_theory.InjectiveResolution.desc_f_succ CategoryTheory.InjectiveResolution.descFSucc
 
 /-- A morphism in `C` descends to a chain map between injective resolutions. -/
@@ -113,40 +113,59 @@ lemma desc_commutes_zero {Y Z : C} (f : Z ⟶ Y)
 /-- An auxiliary definition for `descHomotopyZero`. -/
 def descHomotopyZeroZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (f : I.cocomplex ⟶ J.cocomplex) (comm : I.ι ≫ f = 0) : I.cocomplex.X 1 ⟶ J.cocomplex.X 0 :=
-  Exact.desc (f.f 0) (I.ι.f 0) (I.cocomplex.d 0 1) (Abelian.Exact.op _ _ I.exact₀)
-    (congr_fun (congr_arg HomologicalComplex.Hom.f comm) 0)
+  I.exact₀.descToInjective (f.f 0) (congr_fun (congr_arg HomologicalComplex.Hom.f comm) 0)
 #align category_theory.InjectiveResolution.desc_homotopy_zero_zero CategoryTheory.InjectiveResolution.descHomotopyZeroZero
 
+@[reassoc (attr := simp)]
+lemma comp_descHomotopyZeroZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
+    (f : I.cocomplex ⟶ J.cocomplex) (comm : I.ι ≫ f = 0) :
+    I.cocomplex.d 0 1 ≫ descHomotopyZeroZero f comm = f.f 0 :=
+  I.exact₀.comp_descToInjective  _ _
+
 /-- An auxiliary definition for `descHomotopyZero`. -/
 def descHomotopyZeroOne {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (f : I.cocomplex ⟶ J.cocomplex) (comm : I.ι ≫ f = (0 : _ ⟶ J.cocomplex)) :
     I.cocomplex.X 2 ⟶ J.cocomplex.X 1 :=
-  Exact.desc (f.f 1 - descHomotopyZeroZero f comm ≫ J.cocomplex.d 0 1) (I.cocomplex.d 0 1)
-    (I.cocomplex.d 1 2) (Abelian.Exact.op _ _ (I.exact _))
-    (by simp [descHomotopyZeroZero, ← Category.assoc])
+  (I.exact_succ 0).descToInjective (f.f 1 - descHomotopyZeroZero f comm ≫ J.cocomplex.d 0 1)
+    (by rw [Preadditive.comp_sub, comp_descHomotopyZeroZero_assoc f comm,
+          HomologicalComplex.Hom.comm, sub_self])
 #align category_theory.InjectiveResolution.desc_homotopy_zero_one CategoryTheory.InjectiveResolution.descHomotopyZeroOne
 
+@[reassoc (attr := simp)]
+lemma comp_descHomotopyZeroOne {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
+    (f : I.cocomplex ⟶ J.cocomplex) (comm : I.ι ≫ f = (0 : _ ⟶ J.cocomplex)) :
+    I.cocomplex.d 1 2 ≫ descHomotopyZeroOne f comm =
+      f.f 1 - descHomotopyZeroZero f comm ≫ J.cocomplex.d 0 1 :=
+  (I.exact_succ 0).comp_descToInjective _ _
+
 /-- An auxiliary definition for `descHomotopyZero`. -/
 def descHomotopyZeroSucc {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (f : I.cocomplex ⟶ J.cocomplex) (n : ℕ) (g : I.cocomplex.X (n + 1) ⟶ J.cocomplex.X n)
     (g' : I.cocomplex.X (n + 2) ⟶ J.cocomplex.X (n + 1))
     (w : f.f (n + 1) = I.cocomplex.d (n + 1) (n + 2) ≫ g' + g ≫ J.cocomplex.d n (n + 1)) :
     I.cocomplex.X (n + 3) ⟶ J.cocomplex.X (n + 2) :=
-  Exact.desc (f.f (n + 2) - g' ≫ J.cocomplex.d _ _) (I.cocomplex.d (n + 1) (n + 2))
-    (I.cocomplex.d (n + 2) (n + 3)) (Abelian.Exact.op _ _ (I.exact _))
-    (by
-      simp [Preadditive.comp_sub, ← Category.assoc, Preadditive.sub_comp,
-        show I.cocomplex.d (n + 1) (n + 2) ≫ g' = f.f (n + 1) - g ≫ J.cocomplex.d n (n + 1) by
-          rw [w]
-          simp only [add_sub_cancel]])
+  (I.exact_succ (n + 1)).descToInjective (f.f (n + 2) - g' ≫ J.cocomplex.d _ _) (by
+      dsimp
+      rw [Preadditive.comp_sub, ← HomologicalComplex.Hom.comm, w, Preadditive.add_comp,
+        Category.assoc, Category.assoc, HomologicalComplex.d_comp_d, comp_zero,
+        add_zero, sub_self])
 #align category_theory.InjectiveResolution.desc_homotopy_zero_succ CategoryTheory.InjectiveResolution.descHomotopyZeroSucc
 
+@[reassoc (attr := simp)]
+lemma comp_descHomotopyZeroSucc {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
+    (f : I.cocomplex ⟶ J.cocomplex) (n : ℕ) (g : I.cocomplex.X (n + 1) ⟶ J.cocomplex.X n)
+    (g' : I.cocomplex.X (n + 2) ⟶ J.cocomplex.X (n + 1))
+    (w : f.f (n + 1) = I.cocomplex.d (n + 1) (n + 2) ≫ g' + g ≫ J.cocomplex.d n (n + 1)) :
+    I.cocomplex.d (n+2) (n+3) ≫ descHomotopyZeroSucc f n g g' w =
+      f.f (n + 2) - g' ≫ J.cocomplex.d _ _ :=
+  (I.exact_succ (n+1)).comp_descToInjective  _ _
+
 /-- Any descent of the zero morphism is homotopic to zero. -/
 def descHomotopyZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}
     (f : I.cocomplex ⟶ J.cocomplex) (comm : I.ι ≫ f = 0) : Homotopy f 0 :=
-  Homotopy.mkCoinductive _ (descHomotopyZeroZero f comm) (by simp [descHomotopyZeroZero])
-    (descHomotopyZeroOne f comm) (by simp [descHomotopyZeroOne]) fun n ⟨g, g', w⟩ =>
-    ⟨descHomotopyZeroSucc f n g g' (by simp only [w, add_comm]), by simp [descHomotopyZeroSucc, w]⟩
+  Homotopy.mkCoinductive _ (descHomotopyZeroZero f comm) (by simp)
+    (descHomotopyZeroOne f comm) (by simp) (fun n ⟨g, g', w⟩ =>
+    ⟨descHomotopyZeroSucc f n g g' (by simp only [w, add_comm]), by simp⟩)
 #align category_theory.InjectiveResolution.desc_homotopy_zero CategoryTheory.InjectiveResolution.descHomotopyZero
 
 /-- Two descents of the same morphism are homotopic. -/
@@ -176,9 +195,9 @@ def homotopyEquiv {X : C} (I J : InjectiveResolution X) :
   hom := desc (𝟙 X) J I
   inv := desc (𝟙 X) I J
   homotopyHomInvId := (descCompHomotopy (𝟙 X) (𝟙 X) I J I).symm.trans <| by
-    simpa [Category.id_comp] using descIdHomotopy _ _
+    simpa [id_comp] using descIdHomotopy _ _
   homotopyInvHomId := (descCompHomotopy (𝟙 X) (𝟙 X) J I J).symm.trans <| by
-    simpa [Category.id_comp] using descIdHomotopy _ _
+    simpa [id_comp] using descIdHomotopy _ _
 #align category_theory.InjectiveResolution.homotopy_equiv CategoryTheory.InjectiveResolution.homotopyEquiv
 
 @[reassoc (attr := simp)] -- Porting note: Originally `@[simp, reassoc.1]`
@@ -200,24 +219,10 @@ section
 variable [Abelian C]
 
 /-- An arbitrarily chosen injective resolution of an object. -/
-abbrev injectiveResolution (Z : C) [HasInjectiveResolution Z] : CochainComplex C ℕ :=
-  (HasInjectiveResolution.out (Z := Z)).some.cocomplex
+abbrev injectiveResolution (Z : C) [HasInjectiveResolution Z] : InjectiveResolution Z :=
+  (HasInjectiveResolution.out (Z := Z)).some
 #align category_theory.injective_resolution CategoryTheory.injectiveResolution
 
-/-- The cochain map from cochain complex consisting of `Z` supported in degree `0`
-back to the arbitrarily chosen injective resolution `injectiveResolution Z`. -/
-abbrev injectiveResolution.ι (Z : C) [HasInjectiveResolution Z] :
-    (CochainComplex.single₀ C).obj Z ⟶ injectiveResolution Z :=
-  (HasInjectiveResolution.out (Z := Z)).some.ι
-#align category_theory.injective_resolution.ι CategoryTheory.injectiveResolution.ι
-
-/-- The descent of a morphism to a cochain map between the arbitrarily chosen injective resolutions.
--/
-abbrev injectiveResolution.desc {X Y : C} (f : X ⟶ Y) [HasInjectiveResolution X]
-    [HasInjectiveResolution Y] : injectiveResolution X ⟶ injectiveResolution Y :=
-  InjectiveResolution.desc f _ _
-#align category_theory.injective_resolution.desc CategoryTheory.injectiveResolution.desc
-
 variable (C)
 variable [HasInjectiveResolutions C]
 
@@ -226,8 +231,8 @@ if considered with target the homotopy category
 (`ℕ`-indexed cochain complexes and chain maps up to homotopy).
 -/
 def injectiveResolutions : C ⥤ HomotopyCategory C (ComplexShape.up ℕ) where
-  obj X := (HomotopyCategory.quotient _ _).obj (injectiveResolution X)
-  map f := (HomotopyCategory.quotient _ _).map (injectiveResolution.desc f)
+  obj X := (HomotopyCategory.quotient _ _).obj (injectiveResolution X).cocomplex
+  map f := (HomotopyCategory.quotient _ _).map (InjectiveResolution.desc f _ _)
   map_id X := by
     rw [← (HomotopyCategory.quotient _ _).map_id]
     apply HomotopyCategory.eq_of_homotopy
@@ -237,6 +242,33 @@ def injectiveResolutions : C ⥤ HomotopyCategory C (ComplexShape.up ℕ) where
     apply HomotopyCategory.eq_of_homotopy
     apply InjectiveResolution.descCompHomotopy
 #align category_theory.injective_resolutions CategoryTheory.injectiveResolutions
+variable {C}
+
+/-- If `I : InjectiveResolution X`, then the chosen `(injectiveResolutions C).obj X`
+is isomorphic (in the homotopy category) to `I.cocomplex`. -/
+def InjectiveResolution.iso {X : C} (I : InjectiveResolution X) :
+    (injectiveResolutions C).obj X ≅
+      (HomotopyCategory.quotient _ _).obj I.cocomplex :=
+  HomotopyCategory.isoOfHomotopyEquiv (homotopyEquiv _ _)
+
+@[reassoc]
+lemma InjectiveResolution.iso_hom_naturality {X Y : C} (f : X ⟶ Y)
+    (I : InjectiveResolution X) (J : InjectiveResolution Y)
+    (φ : I.cocomplex ⟶ J.cocomplex) (comm : I.ι.f 0 ≫ φ.f 0 = f ≫ J.ι.f 0) :
+    (injectiveResolutions C).map f ≫ J.iso.hom =
+      I.iso.hom ≫ (HomotopyCategory.quotient _ _).map φ := by
+  apply HomotopyCategory.eq_of_homotopy
+  apply descHomotopy f
+  all_goals aesop_cat
+
+@[reassoc]
+lemma InjectiveResolution.iso_inv_naturality {X Y : C} (f : X ⟶ Y)
+    (I : InjectiveResolution X) (J : InjectiveResolution Y)
+    (φ : I.cocomplex ⟶ J.cocomplex) (comm : I.ι.f 0 ≫ φ.f 0 = f ≫ J.ι.f 0) :
+    I.iso.inv ≫ (injectiveResolutions C).map f =
+      (HomotopyCategory.quotient _ _).map φ ≫ J.iso.inv := by
+  rw [← cancel_mono (J.iso).hom, Category.assoc, iso_hom_naturality f I J φ comm,
+    Iso.inv_hom_id_assoc, Category.assoc, Iso.inv_hom_id, Category.comp_id]
 
 end
 
@@ -244,9 +276,18 @@ section
 
 variable [Abelian C] [EnoughInjectives C]
 
-theorem exact_f_d {X Y : C} (f : X ⟶ Y) : Exact f (d f) :=
-  (Abelian.exact_iff _ _).2 <|
-    ⟨by simp, zero_of_comp_mono (ι _) <| by rw [Category.assoc, kernel.condition]⟩
+theorem exact_f_d {X Y : C} (f : X ⟶ Y) :
+    (ShortComplex.mk f (d f) (by simp)).Exact := by
+  let α : ShortComplex.mk f (cokernel.π f) (by simp) ⟶ ShortComplex.mk f (d f) (by simp) :=
+    { τ₁ := 𝟙 _
+      τ₂ := 𝟙 _
+      τ₃ := Injective.ι _  }
+  have : Epi α.τ₁ := by dsimp; infer_instance
+  have : IsIso α.τ₂ := by dsimp; infer_instance
+  have : Mono α.τ₃ := by dsimp; infer_instance
+  rw [← ShortComplex.exact_iff_of_epi_of_isIso_of_mono α]
+  apply ShortComplex.exact_of_g_is_cokernel
+  apply cokernelIsCokernel
 #align category_theory.exact_f_d CategoryTheory.exact_f_d
 
 end
@@ -263,63 +304,57 @@ and the map from the `n`-th object as `Injective.d`.
 -/
 
 
-variable [Abelian C] [EnoughInjectives C]
+variable [Abelian C] [EnoughInjectives C] (Z : C)
+
+-- The construction of the injective resolution `of` would be very, very slow
+-- if it were not broken into separate definitions and lemmas
 
 /-- Auxiliary definition for `InjectiveResolution.of`. -/
-@[simps!]
-def ofCocomplex (Z : C) : CochainComplex C ℕ :=
+def ofCocomplex : CochainComplex C ℕ :=
   CochainComplex.mk' (Injective.under Z) (Injective.syzygies (Injective.ι Z))
     (Injective.d (Injective.ι Z)) fun ⟨_, _, f⟩ =>
-    ⟨Injective.syzygies f, Injective.d f, (exact_f_d f).w⟩
+    ⟨Injective.syzygies f, Injective.d f, by simp⟩
 set_option linter.uppercaseLean3 false in
 #align category_theory.InjectiveResolution.of_cocomplex CategoryTheory.InjectiveResolution.ofCocomplex
 
--- Porting note: the ι field in `of` was very, very slow. To assist,
--- implicit arguments were filled in and this particular proof was broken
--- out into a separate result
-theorem ofCocomplex_sq_01_comm (Z : C) :
-    Injective.ι Z ≫ HomologicalComplex.d (ofCocomplex Z) 0 1 =
-    HomologicalComplex.d ((CochainComplex.single₀ C).obj Z) 0 1 ≫ 0 := by
-  simp only [ofCocomplex_d, eq_self_iff_true, eqToHom_refl, Category.comp_id,
-    dite_eq_ite, if_true, comp_zero]
-  exact (exact_f_d (Injective.ι Z)).w
-
--- Porting note: the `exact` in `of` was very, very slow. To assist,
--- the whole proof was broken out into a separate result
-theorem exact_ofCocomplex (Z : C) (n : ℕ) :
-    Exact (HomologicalComplex.d (ofCocomplex Z) n (n + 1))
-    (HomologicalComplex.d (ofCocomplex Z) (n + 1) (n + 2)) :=
-  match n with
--- Porting note: used to be simp; apply exact_f_d on both branches
-    | 0 => by simp; apply exact_f_d
-    | m+1 => by
-      simp only [ofCocomplex_X, ComplexShape.up_Rel, not_true, ofCocomplex_d,
-        eqToHom_refl, Category.comp_id, dite_eq_ite, ite_true]
-      erw [if_pos (c := m + 1 + 1 + 1 = m + 2 + 1) rfl]
-      apply exact_f_d
-
--- Porting note: still very slow but with `ofCocomplex_sq_01_comm` and
--- `exact_ofCocomplex` as separate results it is more reasonable
+lemma ofCocomplex_d_0_1 :
+    (ofCocomplex Z).d 0 1 = d (Injective.ι Z) := by
+  simp [ofCocomplex]
+
+lemma ofCocomplex_exactAt_succ (n : ℕ) :
+    (ofCocomplex Z).ExactAt (n + 1) := by
+  rw [HomologicalComplex.exactAt_iff' _ n (n + 1) (n + 1 + 1) (by simp) (by simp)]
+  cases n
+  all_goals
+    dsimp [ofCocomplex, HomologicalComplex.sc', HomologicalComplex.shortComplexFunctor',
+      CochainComplex.mk', CochainComplex.mk]
+    simp
+    apply exact_f_d
+
+instance (n : ℕ) : Injective ((ofCocomplex Z).X n) := by
+  obtain (_ | _ | _ | n) := n <;> apply Injective.injective_under
+
 /-- In any abelian category with enough injectives,
 `InjectiveResolution.of Z` constructs an injective resolution of the object `Z`.
 -/
-irreducible_def of (Z : C) : InjectiveResolution Z :=
-  { cocomplex := ofCocomplex Z
-    ι :=
-      CochainComplex.mkHom
-        ((CochainComplex.single₀ C).obj Z) (ofCocomplex Z) (Injective.ι Z) 0
-          (ofCocomplex_sq_01_comm Z) fun n _ => by
-          -- Porting note: used to be ⟨0, by ext⟩
-            use 0
-            apply HasZeroObject.from_zero_ext
-    injective := by rintro (_ | _ | _ | n) <;> · apply Injective.injective_under
-    exact₀ := by simpa using exact_f_d (Injective.ι Z)
-    exact := exact_ofCocomplex Z
-    mono := Injective.ι_mono Z }
+irreducible_def of : InjectiveResolution Z where
+  cocomplex := ofCocomplex Z
+  ι := (CochainComplex.fromSingle₀Equiv _ _).symm ⟨Injective.ι Z,
+    by rw [ofCocomplex_d_0_1, cokernel.condition_assoc, zero_comp]⟩
+  quasiIso := ⟨fun n => by
+    cases n
+    · rw [CochainComplex.quasiIsoAt₀_iff, ShortComplex.quasiIso_iff_of_zeros]
+      · refine' (ShortComplex.exact_and_mono_f_iff_of_iso _).2
+          ⟨exact_f_d (Injective.ι Z), by dsimp; infer_instance⟩
+        exact ShortComplex.isoMk (Iso.refl _) (Iso.refl _) (Iso.refl _) (by simp)
+          (by simp [ofCocomplex])
+      all_goals rfl
+    · rw [quasiIsoAt_iff_exactAt]
+      · apply ofCocomplex_exactAt_succ
+      · apply CochainComplex.exactAt_succ_single_obj⟩
 set_option linter.uppercaseLean3 false in
 #align category_theory.InjectiveResolution.of CategoryTheory.InjectiveResolution.of
 
-
 instance (priority := 100) (Z : C) : HasInjectiveResolution Z where out := ⟨of Z⟩
 
 instance (priority := 100) : HasInjectiveResolutions C where out _ := inferInstance
@@ -327,23 +362,3 @@ instance (priority := 100) : HasInjectiveResolutions C where out _ := inferInsta
 end InjectiveResolution
 
 end CategoryTheory
-
-namespace HomologicalComplex.Hom
-
-variable {C : Type u} [Category.{v} C] [Abelian C]
-
-/-- If `X` is a cochain complex of injective objects and we have a quasi-isomorphism
-`f : Y[0] ⟶ X`, then `X` is an injective resolution of `Y`. -/
-def HomologicalComplex.Hom.fromSingle₀InjectiveResolution (X : CochainComplex C ℕ) (Y : C)
-    (f : (CochainComplex.single₀ C).obj Y ⟶ X) [QuasiIso' f] (H : ∀ n, Injective (X.X n)) :
-    InjectiveResolution Y where
-  cocomplex := X
-  ι := f
-  injective := H
-  exact₀ := from_single₀_exact_f_d_at_zero f
-  exact := from_single₀_exact_at_succ f
-  mono := from_single₀_mono_at_zero f
-set_option linter.uppercaseLean3 false in
-#align homological_complex.hom.homological_complex.hom.from_single₀_InjectiveResolution HomologicalComplex.Hom.HomologicalComplex.Hom.fromSingle₀InjectiveResolution
-
-end HomologicalComplex.Hom

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

@@ -103,6 +103,12 @@ theorem desc_commutes {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y)
   simp [desc, descFOne, descFZero]
 #align category_theory.InjectiveResolution.desc_commutes CategoryTheory.InjectiveResolution.desc_commutes
 
+@[reassoc (attr := simp)]
+lemma desc_commutes_zero {Y Z : C} (f : Z ⟶ Y)
+    (I : InjectiveResolution Y) (J : InjectiveResolution Z) :
+    J.ι.f 0 ≫ (desc f I J).f 0 = f ≫ I.ι.f 0 :=
+  (HomologicalComplex.congr_hom (desc_commutes f I J) 0).trans (by simp)
+
 -- Now that we've checked this property of the descent, we can seal away the actual definition.
 /-- An auxiliary definition for `descHomotopyZero`. -/
 def descHomotopyZeroZero {Y Z : C} {I : InjectiveResolution Y} {J : InjectiveResolution Z}

This PR renames definitions of the current homology API (adding a ' to homology, cycles, QuasiIso) so as to create space for the development of the new homology API of homological complexes: this PR also contains the new definition of HomologicalComplex.homology which involves the homology theory of short complexes.

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

@@ -329,7 +329,7 @@ variable {C : Type u} [Category.{v} C] [Abelian C]
 /-- If `X` is a cochain complex of injective objects and we have a quasi-isomorphism
 `f : Y[0] ⟶ X`, then `X` is an injective resolution of `Y`. -/
 def HomologicalComplex.Hom.fromSingle₀InjectiveResolution (X : CochainComplex C ℕ) (Y : C)
-    (f : (CochainComplex.single₀ C).obj Y ⟶ X) [QuasiIso f] (H : ∀ n, Injective (X.X n)) :
+    (f : (CochainComplex.single₀ C).obj Y ⟶ X) [QuasiIso' f] (H : ∀ n, Injective (X.X n)) :
     InjectiveResolution Y where
   cocomplex := X
   ι := f

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Jujian Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jujian Zhang, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.abelian.injective_resolution
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Homology.QuasiIso
 import Mathlib.CategoryTheory.Preadditive.InjectiveResolution
 import Mathlib.Algebra.Homology.HomotopyCategory
 
+#align_import category_theory.abelian.injective_resolution from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
+
 /-!
 # Main result
 

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Alex J Best <alex.j.best@gmail.com>

@@ -99,13 +99,11 @@ def desc {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y) (J : InjectiveResol
 #align category_theory.InjectiveResolution.desc CategoryTheory.InjectiveResolution.desc
 
 /-- The resolution maps intertwine the descent of a morphism and that morphism. -/
-@[reassoc (attr := simp)] -- Porting note: Originally `@[simp, reassoc.1]`
+@[reassoc (attr := simp)]
 theorem desc_commutes {Y Z : C} (f : Z ⟶ Y) (I : InjectiveResolution Y)
     (J : InjectiveResolution Z) : J.ι ≫ desc f I J = (CochainComplex.single₀ C).map f ≫ I.ι := by
-  ext n
-  rcases n with (_ | _ | n) <;>
-    · dsimp [desc, descFOne, descFZero]
-      simp
+  ext
+  simp [desc, descFOne, descFZero]
 #align category_theory.InjectiveResolution.desc_commutes CategoryTheory.InjectiveResolution.desc_commutes
 
 -- Now that we've checked this property of the descent, we can seal away the actual definition.

Co-authored-by: Matthew Ballard <matt@mrb.email>