category_theory.preadditive.projective_resolution

Changes since the initial port

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

Changes in mathlib3

324a7502

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

ef553359

bump to nightly-2024-02-05-08

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

516c6ec2

Diff

@@ -90,7 +90,7 @@ structure ProjectiveResolution (Z : C) where
 attribute [instance] ProjectiveResolution.projective ProjectiveResolution.epi
 
 #print CategoryTheory.HasProjectiveResolution /-
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
 /-- An object admits a projective resolution.
 -/
 class HasProjectiveResolution (Z : C) : Prop where

ef553359

bump to nightly-2023-12-23-06

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

b8c74971

Diff

@@ -90,7 +90,7 @@ structure ProjectiveResolution (Z : C) where
 attribute [instance] ProjectiveResolution.projective ProjectiveResolution.epi
 
 #print CategoryTheory.HasProjectiveResolution /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
 /-- An object admits a projective resolution.
 -/
 class HasProjectiveResolution (Z : C) : Prop where

ef553359

bump to nightly-2023-12-02-06

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

e637da5d

Diff

@@ -162,38 +162,38 @@ def self (Z : C) [CategoryTheory.Projective Z] : ProjectiveResolution Z
 #align category_theory.ProjectiveResolution.self CategoryTheory.ProjectiveResolution.self
 -/
 
-#print CategoryTheory.ProjectiveResolution.liftZero /-
+#print CategoryTheory.ProjectiveResolution.liftFZero /-
 /-- Auxiliary construction for `lift`. -/
-def liftZero {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) :
+def liftFZero {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) :
     P.complex.pt 0 ⟶ Q.complex.pt 0 :=
   factorThru (P.π.f 0 ≫ f) (Q.π.f 0)
-#align category_theory.ProjectiveResolution.lift_f_zero CategoryTheory.ProjectiveResolution.liftZero
+#align category_theory.ProjectiveResolution.lift_f_zero CategoryTheory.ProjectiveResolution.liftFZero
 -/
 
-#print CategoryTheory.ProjectiveResolution.liftOne /-
+#print CategoryTheory.ProjectiveResolution.liftFOne /-
 /-- Auxiliary construction for `lift`. -/
-def liftOne {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) :
+def liftFOne {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) :
     P.complex.pt 1 ⟶ Q.complex.pt 1 :=
-  Exact.lift (P.complex.d 1 0 ≫ liftZero f P Q) (Q.complex.d 1 0) (Q.π.f 0) Q.exact₀
+  Exact.lift (P.complex.d 1 0 ≫ liftFZero f P Q) (Q.complex.d 1 0) (Q.π.f 0) Q.exact₀
     (by simp [lift_f_zero, P.exact₀.w_assoc])
-#align category_theory.ProjectiveResolution.lift_f_one CategoryTheory.ProjectiveResolution.liftOne
+#align category_theory.ProjectiveResolution.lift_f_one CategoryTheory.ProjectiveResolution.liftFOne
 -/
 
-#print CategoryTheory.ProjectiveResolution.liftOne_zero_comm /-
+#print CategoryTheory.ProjectiveResolution.liftFOne_zero_comm /-
 /-- Auxiliary lemma for `lift`. -/
 @[simp]
-theorem liftOne_zero_comm {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
+theorem liftFOne_zero_comm {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
     (Q : ProjectiveResolution Z) :
-    liftOne f P Q ≫ Q.complex.d 1 0 = P.complex.d 1 0 ≫ liftZero f P Q :=
+    liftFOne f P Q ≫ Q.complex.d 1 0 = P.complex.d 1 0 ≫ liftFZero f P Q :=
   by
   dsimp [lift_f_zero, lift_f_one]
   simp
-#align category_theory.ProjectiveResolution.lift_f_one_zero_comm CategoryTheory.ProjectiveResolution.liftOne_zero_comm
+#align category_theory.ProjectiveResolution.lift_f_one_zero_comm CategoryTheory.ProjectiveResolution.liftFOne_zero_comm
 -/
 
-#print CategoryTheory.ProjectiveResolution.liftSucc /-
+#print CategoryTheory.ProjectiveResolution.liftFSucc /-
 /-- Auxiliary construction for `lift`. -/
-def liftSucc {Y Z : C} (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) (n : ℕ)
+def liftFSucc {Y Z : C} (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) (n : ℕ)
     (g : P.complex.pt n ⟶ Q.complex.pt n) (g' : P.complex.pt (n + 1) ⟶ Q.complex.pt (n + 1))
     (w : g' ≫ Q.complex.d (n + 1) n = P.complex.d (n + 1) n ≫ g) :
     Σ' g'' : P.complex.pt (n + 2) ⟶ Q.complex.pt (n + 2),
@@ -201,15 +201,15 @@ def liftSucc {Y Z : C} (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z)
   ⟨Exact.lift (P.complex.d (n + 2) (n + 1) ≫ g') (Q.complex.d (n + 2) (n + 1))
       (Q.complex.d (n + 1) n) (Q.exact _) (by simp [w]),
     by simp⟩
-#align category_theory.ProjectiveResolution.lift_f_succ CategoryTheory.ProjectiveResolution.liftSucc
+#align category_theory.ProjectiveResolution.lift_f_succ CategoryTheory.ProjectiveResolution.liftFSucc
 -/
 
 #print CategoryTheory.ProjectiveResolution.lift /-
 /-- A morphism in `C` lifts to a chain map between projective resolutions. -/
 def lift {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) :
     P.complex ⟶ Q.complex :=
-  ChainComplex.mkHom _ _ (liftZero f _ _) (liftOne f _ _) (liftOne_zero_comm f _ _)
-    fun n ⟨g, g', w⟩ => liftSucc P Q n g g' w
+  ChainComplex.mkHom _ _ (liftFZero f _ _) (liftFOne f _ _) (liftFOne_zero_comm f _ _)
+    fun n ⟨g, g', w⟩ => liftFSucc P Q n g g' w
 #align category_theory.ProjectiveResolution.lift CategoryTheory.ProjectiveResolution.lift
 -/
 
@@ -336,31 +336,25 @@ section
 
 variable [HasZeroMorphisms C] [HasZeroObject C] [HasEqualizers C] [HasImages C]
 
-#print CategoryTheory.projectiveResolution.complex /-
+#print CategoryTheory.projectiveResolution /-
 /-- An arbitrarily chosen projective resolution of an object. -/
-abbrev CategoryTheory.projectiveResolution.complex (Z : C) [HasProjectiveResolution Z] :
-    ChainComplex C ℕ :=
+abbrev projectiveResolution (Z : C) [HasProjectiveResolution Z] : ChainComplex C ℕ :=
   (HasProjectiveResolution.out Z).some.complex
-#align category_theory.projective_resolution CategoryTheory.projectiveResolution.complex
+#align category_theory.projective_resolution CategoryTheory.projectiveResolution
 -/
 
-#print CategoryTheory.projectiveResolution.π /-
 /-- The chain map from the arbitrarily chosen projective resolution `projective_resolution Z`
 back to the chain complex consisting of `Z` supported in degree `0`. -/
 abbrev projectiveResolution.π (Z : C) [HasProjectiveResolution Z] :
-    CategoryTheory.projectiveResolution.complex Z ⟶ (ChainComplex.single₀ C).obj Z :=
+    projectiveResolution Z ⟶ (ChainComplex.single₀ C).obj Z :=
   (HasProjectiveResolution.out Z).some.π
 #align category_theory.projective_resolution.π CategoryTheory.projectiveResolution.π
--/
 
-#print CategoryTheory.projectiveResolution.lift /-
 /-- The lift of a morphism to a chain map between the arbitrarily chosen projective resolutions. -/
 abbrev projectiveResolution.lift {X Y : C} (f : X ⟶ Y) [HasProjectiveResolution X]
-    [HasProjectiveResolution Y] :
-    CategoryTheory.projectiveResolution.complex X ⟶ CategoryTheory.projectiveResolution.complex Y :=
+    [HasProjectiveResolution Y] : projectiveResolution X ⟶ projectiveResolution Y :=
   ProjectiveResolution.lift f _ _
 #align category_theory.projective_resolution.lift CategoryTheory.projectiveResolution.lift
--/
 
 end
 
@@ -374,7 +368,7 @@ if considered with target the homotopy category
 -/
 def projectiveResolutions : C ⥤ HomotopyCategory C (ComplexShape.down ℕ)
     where
-  obj X := (HomotopyCategory.quotient _ _).obj (CategoryTheory.projectiveResolution.complex X)
+  obj X := (HomotopyCategory.quotient _ _).obj (projectiveResolution X)
   map X Y f := (HomotopyCategory.quotient _ _).map (projectiveResolution.lift f)
   map_id' X := by
     rw [← (HomotopyCategory.quotient _ _).map_id]

ef553359

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 -/
-import Mathbin.CategoryTheory.Preadditive.Projective
-import Mathbin.Algebra.Homology.Single
-import Mathbin.Algebra.Homology.HomotopyCategory
+import CategoryTheory.Preadditive.Projective
+import Algebra.Homology.Single
+import Algebra.Homology.HomotopyCategory
 
 #align_import category_theory.preadditive.projective_resolution from "leanprover-community/mathlib"@"ef55335933293309ff8c0b1d20ffffeecbe5c39f"
 
@@ -90,7 +90,7 @@ structure ProjectiveResolution (Z : C) where
 attribute [instance] ProjectiveResolution.projective ProjectiveResolution.epi
 
 #print CategoryTheory.HasProjectiveResolution /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
 /-- An object admits a projective resolution.
 -/
 class HasProjectiveResolution (Z : C) : Prop where

ef553359

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.preadditive.projective_resolution
-! leanprover-community/mathlib commit ef55335933293309ff8c0b1d20ffffeecbe5c39f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Preadditive.Projective
 import Mathbin.Algebra.Homology.Single
 import Mathbin.Algebra.Homology.HomotopyCategory
 
+#align_import category_theory.preadditive.projective_resolution from "leanprover-community/mathlib"@"ef55335933293309ff8c0b1d20ffffeecbe5c39f"
+
 /-!
 # Projective resolutions

ef553359

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -93,7 +93,7 @@ structure ProjectiveResolution (Z : C) where
 attribute [instance] ProjectiveResolution.projective ProjectiveResolution.epi
 
 #print CategoryTheory.HasProjectiveResolution /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
 /-- An object admits a projective resolution.
 -/
 class HasProjectiveResolution (Z : C) : Prop where
@@ -121,18 +121,22 @@ end
 
 namespace ProjectiveResolution
 
+#print CategoryTheory.ProjectiveResolution.π_f_succ /-
 @[simp]
 theorem π_f_succ {Z : C} (P : ProjectiveResolution Z) (n : ℕ) : P.π.f (n + 1) = 0 :=
   by
   apply zero_of_target_iso_zero
   dsimp; rfl
 #align category_theory.ProjectiveResolution.π_f_succ CategoryTheory.ProjectiveResolution.π_f_succ
+-/
 
+#print CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero /-
 @[simp]
 theorem complex_d_comp_π_f_zero {Z : C} (P : ProjectiveResolution Z) :
     P.complex.d 1 0 ≫ P.π.f 0 = 0 :=
   P.exact₀.w
 #align category_theory.ProjectiveResolution.complex_d_comp_π_f_zero CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero
+-/
 
 #print CategoryTheory.ProjectiveResolution.complex_d_succ_comp /-
 @[simp]
@@ -212,12 +216,14 @@ def lift {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveRes
 #align category_theory.ProjectiveResolution.lift CategoryTheory.ProjectiveResolution.lift
 -/
 
+#print CategoryTheory.ProjectiveResolution.lift_commutes /-
 /-- The resolution maps intertwine the lift of a morphism and that morphism. -/
 @[simp, reassoc]
 theorem lift_commutes {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
     (Q : ProjectiveResolution Z) : lift f P Q ≫ Q.π = P.π ≫ (ChainComplex.single₀ C).map f := by
   ext; dsimp [lift, lift_f_zero]; apply factor_thru_comp
 #align category_theory.ProjectiveResolution.lift_commutes CategoryTheory.ProjectiveResolution.lift_commutes
+-/
 
 -- Now that we've checked this property of the lift,
 -- we can seal away the actual definition.
@@ -229,20 +235,25 @@ namespace ProjectiveResolution
 
 variable [HasZeroObject C] [Preadditive C] [HasEqualizers C] [HasImages C]
 
+#print CategoryTheory.ProjectiveResolution.liftHomotopyZeroZero /-
 /-- An auxiliary definition for `lift_homotopy_zero`. -/
 def liftHomotopyZeroZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
     (f : P.complex ⟶ Q.complex) (comm : f ≫ Q.π = 0) : P.complex.pt 0 ⟶ Q.complex.pt 1 :=
   Exact.lift (f.f 0) (Q.complex.d 1 0) (Q.π.f 0) Q.exact₀
     (congr_fun (congr_arg HomologicalComplex.Hom.f comm) 0)
 #align category_theory.ProjectiveResolution.lift_homotopy_zero_zero CategoryTheory.ProjectiveResolution.liftHomotopyZeroZero
+-/
 
+#print CategoryTheory.ProjectiveResolution.liftHomotopyZeroOne /-
 /-- An auxiliary definition for `lift_homotopy_zero`. -/
 def liftHomotopyZeroOne {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
     (f : P.complex ⟶ Q.complex) (comm : f ≫ Q.π = 0) : P.complex.pt 1 ⟶ Q.complex.pt 2 :=
   Exact.lift (f.f 1 - P.complex.d 1 0 ≫ liftHomotopyZeroZero f comm) (Q.complex.d 2 1)
     (Q.complex.d 1 0) (Q.exact _) (by simp [lift_homotopy_zero_zero])
 #align category_theory.ProjectiveResolution.lift_homotopy_zero_one CategoryTheory.ProjectiveResolution.liftHomotopyZeroOne
+-/
 
+#print CategoryTheory.ProjectiveResolution.liftHomotopyZeroSucc /-
 /-- An auxiliary definition for `lift_homotopy_zero`. -/
 def liftHomotopyZeroSucc {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
     (f : P.complex ⟶ Q.complex) (n : ℕ) (g : P.complex.pt n ⟶ Q.complex.pt (n + 1))
@@ -252,7 +263,9 @@ def liftHomotopyZeroSucc {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveR
   Exact.lift (f.f (n + 2) - P.complex.d (n + 2) (n + 1) ≫ g') (Q.complex.d (n + 3) (n + 2))
     (Q.complex.d (n + 2) (n + 1)) (Q.exact _) (by simp [w])
 #align category_theory.ProjectiveResolution.lift_homotopy_zero_succ CategoryTheory.ProjectiveResolution.liftHomotopyZeroSucc
+-/
 
+#print CategoryTheory.ProjectiveResolution.liftHomotopyZero /-
 /-- Any lift of the zero morphism is homotopic to zero. -/
 def liftHomotopyZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
     (f : P.complex ⟶ Q.complex) (comm : f ≫ Q.π = 0) : Homotopy f 0 :=
@@ -260,13 +273,16 @@ def liftHomotopyZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResol
     (liftHomotopyZeroOne f comm) (by simp [lift_homotopy_zero_one]) fun n ⟨g, g', w⟩ =>
     ⟨liftHomotopyZeroSucc f n g g' w, by simp [lift_homotopy_zero_succ, w]⟩
 #align category_theory.ProjectiveResolution.lift_homotopy_zero CategoryTheory.ProjectiveResolution.liftHomotopyZero
+-/
 
+#print CategoryTheory.ProjectiveResolution.liftHomotopy /-
 /-- Two lifts of the same morphism are homotopic. -/
 def liftHomotopy {Y Z : C} (f : Y ⟶ Z) {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
     (g h : P.complex ⟶ Q.complex) (g_comm : g ≫ Q.π = P.π ≫ (ChainComplex.single₀ C).map f)
     (h_comm : h ≫ Q.π = P.π ≫ (ChainComplex.single₀ C).map f) : Homotopy g h :=
   Homotopy.equivSubZero.invFun (liftHomotopyZero _ (by simp [g_comm, h_comm]))
 #align category_theory.ProjectiveResolution.lift_homotopy CategoryTheory.ProjectiveResolution.liftHomotopy
+-/
 
 #print CategoryTheory.ProjectiveResolution.liftIdHomotopy /-
 /-- The lift of the identity morphism is homotopic to the identity chain map. -/
@@ -303,15 +319,19 @@ def homotopyEquiv {X : C} (P Q : ProjectiveResolution X) : HomotopyEquiv P.compl
 #align category_theory.ProjectiveResolution.homotopy_equiv CategoryTheory.ProjectiveResolution.homotopyEquiv
 -/
 
+#print CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π /-
 @[simp, reassoc]
 theorem homotopyEquiv_hom_π {X : C} (P Q : ProjectiveResolution X) :
     (homotopyEquiv P Q).Hom ≫ Q.π = P.π := by simp [HomotopyEquiv]
 #align category_theory.ProjectiveResolution.homotopy_equiv_hom_π CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π
+-/
 
+#print CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_π /-
 @[simp, reassoc]
 theorem homotopyEquiv_inv_π {X : C} (P Q : ProjectiveResolution X) :
     (homotopyEquiv P Q).inv ≫ P.π = Q.π := by simp [HomotopyEquiv]
 #align category_theory.ProjectiveResolution.homotopy_equiv_inv_π CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_π
+-/
 
 end ProjectiveResolution
 
@@ -327,12 +347,14 @@ abbrev CategoryTheory.projectiveResolution.complex (Z : C) [HasProjectiveResolut
 #align category_theory.projective_resolution CategoryTheory.projectiveResolution.complex
 -/
 
+#print CategoryTheory.projectiveResolution.π /-
 /-- The chain map from the arbitrarily chosen projective resolution `projective_resolution Z`
 back to the chain complex consisting of `Z` supported in degree `0`. -/
 abbrev projectiveResolution.π (Z : C) [HasProjectiveResolution Z] :
     CategoryTheory.projectiveResolution.complex Z ⟶ (ChainComplex.single₀ C).obj Z :=
   (HasProjectiveResolution.out Z).some.π
 #align category_theory.projective_resolution.π CategoryTheory.projectiveResolution.π
+-/
 
 #print CategoryTheory.projectiveResolution.lift /-
 /-- The lift of a morphism to a chain map between the arbitrarily chosen projective resolutions. -/

ef553359

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -93,7 +93,7 @@ structure ProjectiveResolution (Z : C) where
 attribute [instance] ProjectiveResolution.projective ProjectiveResolution.epi
 
 #print CategoryTheory.HasProjectiveResolution /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
 /-- An object admits a projective resolution.
 -/
 class HasProjectiveResolution (Z : C) : Prop where

ef553359

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -195,7 +195,7 @@ theorem liftOne_zero_comm {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
 def liftSucc {Y Z : C} (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) (n : ℕ)
     (g : P.complex.pt n ⟶ Q.complex.pt n) (g' : P.complex.pt (n + 1) ⟶ Q.complex.pt (n + 1))
     (w : g' ≫ Q.complex.d (n + 1) n = P.complex.d (n + 1) n ≫ g) :
-    Σ'g'' : P.complex.pt (n + 2) ⟶ Q.complex.pt (n + 2),
+    Σ' g'' : P.complex.pt (n + 2) ⟶ Q.complex.pt (n + 2),
       g'' ≫ Q.complex.d (n + 2) (n + 1) = P.complex.d (n + 2) (n + 1) ≫ g' :=
   ⟨Exact.lift (P.complex.d (n + 2) (n + 1) ≫ g') (Q.complex.d (n + 2) (n + 1))
       (Q.complex.d (n + 1) n) (Q.exact _) (by simp [w]),

ef553359

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -121,9 +121,6 @@ end
 
 namespace ProjectiveResolution
 
-/- warning: category_theory.ProjectiveResolution.π_f_succ -> CategoryTheory.ProjectiveResolution.π_f_succ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.π_f_succ CategoryTheory.ProjectiveResolution.π_f_succₓ'. -/
 @[simp]
 theorem π_f_succ {Z : C} (P : ProjectiveResolution Z) (n : ℕ) : P.π.f (n + 1) = 0 :=
   by
@@ -131,9 +128,6 @@ theorem π_f_succ {Z : C} (P : ProjectiveResolution Z) (n : ℕ) : P.π.f (n + 1
   dsimp; rfl
 #align category_theory.ProjectiveResolution.π_f_succ CategoryTheory.ProjectiveResolution.π_f_succ
 
-/- warning: category_theory.ProjectiveResolution.complex_d_comp_π_f_zero -> CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.complex_d_comp_π_f_zero CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zeroₓ'. -/
 @[simp]
 theorem complex_d_comp_π_f_zero {Z : C} (P : ProjectiveResolution Z) :
     P.complex.d 1 0 ≫ P.π.f 0 = 0 :=
@@ -218,9 +212,6 @@ def lift {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveRes
 #align category_theory.ProjectiveResolution.lift CategoryTheory.ProjectiveResolution.lift
 -/
 
-/- warning: category_theory.ProjectiveResolution.lift_commutes -> CategoryTheory.ProjectiveResolution.lift_commutes is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_commutes CategoryTheory.ProjectiveResolution.lift_commutesₓ'. -/
 /-- The resolution maps intertwine the lift of a morphism and that morphism. -/
 @[simp, reassoc]
 theorem lift_commutes {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
@@ -238,9 +229,6 @@ namespace ProjectiveResolution
 
 variable [HasZeroObject C] [Preadditive C] [HasEqualizers C] [HasImages C]
 
-/- warning: category_theory.ProjectiveResolution.lift_homotopy_zero_zero -> CategoryTheory.ProjectiveResolution.liftHomotopyZeroZero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_homotopy_zero_zero CategoryTheory.ProjectiveResolution.liftHomotopyZeroZeroₓ'. -/
 /-- An auxiliary definition for `lift_homotopy_zero`. -/
 def liftHomotopyZeroZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
     (f : P.complex ⟶ Q.complex) (comm : f ≫ Q.π = 0) : P.complex.pt 0 ⟶ Q.complex.pt 1 :=
@@ -248,9 +236,6 @@ def liftHomotopyZeroZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveR
     (congr_fun (congr_arg HomologicalComplex.Hom.f comm) 0)
 #align category_theory.ProjectiveResolution.lift_homotopy_zero_zero CategoryTheory.ProjectiveResolution.liftHomotopyZeroZero
 
-/- warning: category_theory.ProjectiveResolution.lift_homotopy_zero_one -> CategoryTheory.ProjectiveResolution.liftHomotopyZeroOne is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_homotopy_zero_one CategoryTheory.ProjectiveResolution.liftHomotopyZeroOneₓ'. -/
 /-- An auxiliary definition for `lift_homotopy_zero`. -/
 def liftHomotopyZeroOne {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
     (f : P.complex ⟶ Q.complex) (comm : f ≫ Q.π = 0) : P.complex.pt 1 ⟶ Q.complex.pt 2 :=
@@ -258,9 +243,6 @@ def liftHomotopyZeroOne {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveRe
     (Q.complex.d 1 0) (Q.exact _) (by simp [lift_homotopy_zero_zero])
 #align category_theory.ProjectiveResolution.lift_homotopy_zero_one CategoryTheory.ProjectiveResolution.liftHomotopyZeroOne
 
-/- warning: category_theory.ProjectiveResolution.lift_homotopy_zero_succ -> CategoryTheory.ProjectiveResolution.liftHomotopyZeroSucc is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_homotopy_zero_succ CategoryTheory.ProjectiveResolution.liftHomotopyZeroSuccₓ'. -/
 /-- An auxiliary definition for `lift_homotopy_zero`. -/
 def liftHomotopyZeroSucc {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
     (f : P.complex ⟶ Q.complex) (n : ℕ) (g : P.complex.pt n ⟶ Q.complex.pt (n + 1))
@@ -271,9 +253,6 @@ def liftHomotopyZeroSucc {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveR
     (Q.complex.d (n + 2) (n + 1)) (Q.exact _) (by simp [w])
 #align category_theory.ProjectiveResolution.lift_homotopy_zero_succ CategoryTheory.ProjectiveResolution.liftHomotopyZeroSucc
 
-/- warning: category_theory.ProjectiveResolution.lift_homotopy_zero -> CategoryTheory.ProjectiveResolution.liftHomotopyZero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_homotopy_zero CategoryTheory.ProjectiveResolution.liftHomotopyZeroₓ'. -/
 /-- Any lift of the zero morphism is homotopic to zero. -/
 def liftHomotopyZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
     (f : P.complex ⟶ Q.complex) (comm : f ≫ Q.π = 0) : Homotopy f 0 :=
@@ -282,9 +261,6 @@ def liftHomotopyZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResol
     ⟨liftHomotopyZeroSucc f n g g' w, by simp [lift_homotopy_zero_succ, w]⟩
 #align category_theory.ProjectiveResolution.lift_homotopy_zero CategoryTheory.ProjectiveResolution.liftHomotopyZero
 
-/- warning: category_theory.ProjectiveResolution.lift_homotopy -> CategoryTheory.ProjectiveResolution.liftHomotopy is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_homotopy CategoryTheory.ProjectiveResolution.liftHomotopyₓ'. -/
 /-- Two lifts of the same morphism are homotopic. -/
 def liftHomotopy {Y Z : C} (f : Y ⟶ Z) {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
     (g h : P.complex ⟶ Q.complex) (g_comm : g ≫ Q.π = P.π ≫ (ChainComplex.single₀ C).map f)
@@ -327,17 +303,11 @@ def homotopyEquiv {X : C} (P Q : ProjectiveResolution X) : HomotopyEquiv P.compl
 #align category_theory.ProjectiveResolution.homotopy_equiv CategoryTheory.ProjectiveResolution.homotopyEquiv
 -/
 
-/- warning: category_theory.ProjectiveResolution.homotopy_equiv_hom_π -> CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.homotopy_equiv_hom_π CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_πₓ'. -/
 @[simp, reassoc]
 theorem homotopyEquiv_hom_π {X : C} (P Q : ProjectiveResolution X) :
     (homotopyEquiv P Q).Hom ≫ Q.π = P.π := by simp [HomotopyEquiv]
 #align category_theory.ProjectiveResolution.homotopy_equiv_hom_π CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π
 
-/- warning: category_theory.ProjectiveResolution.homotopy_equiv_inv_π -> CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_π is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.homotopy_equiv_inv_π CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_πₓ'. -/
 @[simp, reassoc]
 theorem homotopyEquiv_inv_π {X : C} (P Q : ProjectiveResolution X) :
     (homotopyEquiv P Q).inv ≫ P.π = Q.π := by simp [HomotopyEquiv]
@@ -357,12 +327,6 @@ abbrev CategoryTheory.projectiveResolution.complex (Z : C) [HasProjectiveResolut
 #align category_theory.projective_resolution CategoryTheory.projectiveResolution.complex
 -/
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.projective_resolution.π CategoryTheory.projectiveResolution.πₓ'. -/
 /-- The chain map from the arbitrarily chosen projective resolution `projective_resolution Z`
 back to the chain complex consisting of `Z` supported in degree `0`. -/
 abbrev projectiveResolution.π (Z : C) [HasProjectiveResolution Z] :

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

6797a637

Diff

@@ -159,19 +159,11 @@ def self (Z : C) [CategoryTheory.Projective Z] : ProjectiveResolution Z
   π := 𝟙 ((ChainComplex.single₀ C).obj Z)
   Projective n := by
     cases n
-    · dsimp
-      infer_instance
-    · dsimp
-      infer_instance
-  exact₀ := by
-    dsimp
-    exact exact_zero_mono _
-  exact n := by
-    dsimp
-    exact exact_of_zero _ _
-  Epi := by
-    dsimp
-    infer_instance
+    · dsimp; infer_instance
+    · dsimp; infer_instance
+  exact₀ := by dsimp; exact exact_zero_mono _
+  exact n := by dsimp; exact exact_of_zero _ _
+  Epi := by dsimp; infer_instance
 #align category_theory.ProjectiveResolution.self CategoryTheory.ProjectiveResolution.self
 -/
 
@@ -232,11 +224,8 @@ Case conversion may be inaccurate. Consider using '#align category_theory.Projec
 /-- The resolution maps intertwine the lift of a morphism and that morphism. -/
 @[simp, reassoc]
 theorem lift_commutes {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
-    (Q : ProjectiveResolution Z) : lift f P Q ≫ Q.π = P.π ≫ (ChainComplex.single₀ C).map f :=
-  by
-  ext
-  dsimp [lift, lift_f_zero]
-  apply factor_thru_comp
+    (Q : ProjectiveResolution Z) : lift f P Q ≫ Q.π = P.π ≫ (ChainComplex.single₀ C).map f := by
+  ext; dsimp [lift, lift_f_zero]; apply factor_thru_comp
 #align category_theory.ProjectiveResolution.lift_commutes CategoryTheory.ProjectiveResolution.lift_commutes
 
 -- Now that we've checked this property of the lift,

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

6c6011cf

Diff

@@ -122,10 +122,7 @@ end
 namespace ProjectiveResolution
 
 /- warning: category_theory.ProjectiveResolution.π_f_succ -> CategoryTheory.ProjectiveResolution.π_f_succ is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.π_f_succ CategoryTheory.ProjectiveResolution.π_f_succₓ'. -/
 @[simp]
 theorem π_f_succ {Z : C} (P : ProjectiveResolution Z) (n : ℕ) : P.π.f (n + 1) = 0 :=
@@ -135,10 +132,7 @@ theorem π_f_succ {Z : C} (P : ProjectiveResolution Z) (n : ℕ) : P.π.f (n + 1
 #align category_theory.ProjectiveResolution.π_f_succ CategoryTheory.ProjectiveResolution.π_f_succ
 
 /- warning: category_theory.ProjectiveResolution.complex_d_comp_π_f_zero -> CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.complex_d_comp_π_f_zero CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zeroₓ'. -/
 @[simp]
 theorem complex_d_comp_π_f_zero {Z : C} (P : ProjectiveResolution Z) :
@@ -233,10 +227,7 @@ def lift {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveRes
 -/
 
 /- warning: category_theory.ProjectiveResolution.lift_commutes -> CategoryTheory.ProjectiveResolution.lift_commutes is a dubious translation:
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_inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Y P) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 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 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 _inst_3 _inst_2) Z)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 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} (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 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} (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 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 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Y P) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 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 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 _inst_3 _inst_2) Y Z f))
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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 _inst_3 _inst_2)) Y Z f))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_commutes CategoryTheory.ProjectiveResolution.lift_commutesₓ'. -/
 /-- The resolution maps intertwine the lift of a morphism and that morphism. -/
 @[simp, reassoc]
@@ -259,10 +250,7 @@ namespace ProjectiveResolution
 variable [HasZeroObject C] [Preadditive C] [HasEqualizers C] [HasImages C]
 
 /- warning: category_theory.ProjectiveResolution.lift_homotopy_zero_zero -> CategoryTheory.ProjectiveResolution.liftHomotopyZeroZero is a dubious translation:
-lean 3 declaration is
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_inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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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(OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat 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(HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) 0 (Zero.toOfNat0.{u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) (HomologicalComplex.instZeroHomHomologicalComplexPreadditiveHasZeroMorphismsToQuiverToCategoryStructInstCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z))))) -> (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_homotopy_zero_zero CategoryTheory.ProjectiveResolution.liftHomotopyZeroZeroₓ'. -/
 /-- An auxiliary definition for `lift_homotopy_zero`. -/
 def liftHomotopyZeroZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
@@ -272,10 +260,7 @@ def liftHomotopyZeroZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveR
 #align category_theory.ProjectiveResolution.lift_homotopy_zero_zero CategoryTheory.ProjectiveResolution.liftHomotopyZeroZero
 
 /- warning: category_theory.ProjectiveResolution.lift_homotopy_zero_one -> CategoryTheory.ProjectiveResolution.liftHomotopyZeroOne is a dubious translation:
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_inst_5 Z Q)), (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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) 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(CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q)), (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) 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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))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat 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(HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) 0 (Zero.toOfNat0.{u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{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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(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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) 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_inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_homotopy_zero_one CategoryTheory.ProjectiveResolution.liftHomotopyZeroOneₓ'. -/
 /-- An auxiliary definition for `lift_homotopy_zero`. -/
 def liftHomotopyZeroOne {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
@@ -285,10 +270,7 @@ def liftHomotopyZeroOne {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveRe
 #align category_theory.ProjectiveResolution.lift_homotopy_zero_one CategoryTheory.ProjectiveResolution.liftHomotopyZeroOne
 
 /- warning: category_theory.ProjectiveResolution.lift_homotopy_zero_succ -> CategoryTheory.ProjectiveResolution.liftHomotopyZeroSucc is a dubious translation:
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_inst_5 Z Q)) (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) n) (HomologicalComplex.x.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat 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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_homotopy_zero_succ CategoryTheory.ProjectiveResolution.liftHomotopyZeroSuccₓ'. -/
 /-- An auxiliary definition for `lift_homotopy_zero`. -/
 def liftHomotopyZeroSucc {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
@@ -301,10 +283,7 @@ def liftHomotopyZeroSucc {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveR
 #align category_theory.ProjectiveResolution.lift_homotopy_zero_succ CategoryTheory.ProjectiveResolution.liftHomotopyZeroSucc
 
 /- warning: category_theory.ProjectiveResolution.lift_homotopy_zero -> CategoryTheory.ProjectiveResolution.liftHomotopyZero is a dubious translation:
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Nat.strictOrderedSemiring))))) Nat.hasOne)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q)) (HomologicalComplex.Quiver.Hom.hasZero.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q))))))
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(CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) 0 (Zero.toOfNat0.{u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) (HomologicalComplex.instZeroHomHomologicalComplexPreadditiveHasZeroMorphismsToQuiverToCategoryStructInstCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z))))) -> (Homotopy.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) f (OfNat.ofNat.{u1} (Quiver.Hom.{succ u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, 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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_homotopy_zero CategoryTheory.ProjectiveResolution.liftHomotopyZeroₓ'. -/
 /-- Any lift of the zero morphism is homotopic to zero. -/
 def liftHomotopyZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
@@ -315,10 +294,7 @@ def liftHomotopyZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResol
 #align category_theory.ProjectiveResolution.lift_homotopy_zero CategoryTheory.ProjectiveResolution.liftHomotopyZero
 
 /- warning: category_theory.ProjectiveResolution.lift_homotopy -> CategoryTheory.ProjectiveResolution.liftHomotopy is a dubious translation:
-lean 3 declaration is
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(CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q)), (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z) g (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Y) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Y Z f))) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z) h (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 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Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat 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_inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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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(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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Y Z f))) -> (Homotopy.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) g h)
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_homotopy CategoryTheory.ProjectiveResolution.liftHomotopyₓ'. -/
 /-- Two lifts of the same morphism are homotopic. -/
 def liftHomotopy {Y Z : C} (f : Y ⟶ Z) {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
@@ -363,10 +339,7 @@ def homotopyEquiv {X : C} (P Q : ProjectiveResolution X) : HomotopyEquiv P.compl
 -/
 
 /- warning: category_theory.ProjectiveResolution.homotopy_equiv_hom_π -> CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π is a dubious translation:
-lean 3 declaration is
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_inst_4 _inst_5 X Q)) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P)
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.homotopy_equiv_hom_π CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_πₓ'. -/
 @[simp, reassoc]
 theorem homotopyEquiv_hom_π {X : C} (P Q : ProjectiveResolution X) :
@@ -374,10 +347,7 @@ theorem homotopyEquiv_hom_π {X : C} (P Q : ProjectiveResolution X) :
 #align category_theory.ProjectiveResolution.homotopy_equiv_hom_π CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π
 
 /- warning: category_theory.ProjectiveResolution.homotopy_equiv_inv_π -> CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_π is a dubious translation:
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(ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2) X)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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(CategoryTheory.ProjectiveResolution.homotopyEquiv.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 X P Q)) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P)) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q)
-but is expected to have type
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_inst_4 _inst_5 X P)) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q)
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.homotopy_equiv_inv_π CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_πₓ'. -/
 @[simp, reassoc]
 theorem homotopyEquiv_inv_π {X : C} (P Q : ProjectiveResolution X) :

ef553359

bump to nightly-2023-05-23-03

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

ed98987c

Diff

@@ -239,7 +239,7 @@ but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{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) (P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Y) (Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Z), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 Nat 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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)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 Nat 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(ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Z Q) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 _inst_3 _inst_2)) Y Z f))
 Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_commutes CategoryTheory.ProjectiveResolution.lift_commutesₓ'. -/
 /-- The resolution maps intertwine the lift of a morphism and that morphism. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem lift_commutes {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
     (Q : ProjectiveResolution Z) : lift f P Q ≫ Q.π = P.π ≫ (ChainComplex.single₀ C).map f :=
   by
@@ -368,7 +368,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] {X : C} (P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X) (Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) X)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) X) (HomotopyEquiv.hom.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q) (CategoryTheory.ProjectiveResolution.homotopyEquiv.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 X P Q)) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q)) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P)
 Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.homotopy_equiv_hom_π CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_πₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem homotopyEquiv_hom_π {X : C} (P Q : ProjectiveResolution X) :
     (homotopyEquiv P Q).Hom ≫ Q.π = P.π := by simp [HomotopyEquiv]
 #align category_theory.ProjectiveResolution.homotopy_equiv_hom_π CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π
@@ -379,7 +379,7 @@ lean 3 declaration is
 but is expected to have type
   forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] {X : C} (P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X) (Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) X)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) X) (HomotopyEquiv.inv.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q) (CategoryTheory.ProjectiveResolution.homotopyEquiv.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 X P Q)) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P)) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q)
 Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.homotopy_equiv_inv_π CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_πₓ'. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
 theorem homotopyEquiv_inv_π {X : C} (P Q : ProjectiveResolution X) :
     (homotopyEquiv P Q).inv ≫ P.π = Q.π := by simp [HomotopyEquiv]
 #align category_theory.ProjectiveResolution.homotopy_equiv_inv_π CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_π

ef553359

bump to nightly-2023-05-03-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

5ced3cdd

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
 
 ! This file was ported from Lean 3 source module category_theory.preadditive.projective_resolution
-! leanprover-community/mathlib commit 324a7502510e835cdbd3de1519b6c66b51fb2467
+! leanprover-community/mathlib commit ef55335933293309ff8c0b1d20ffffeecbe5c39f
 ! 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
 /-!
 # Projective resolutions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A projective resolution `P : ProjectiveResolution Z` of an object `Z : C` consists of
 a `ℕ`-indexed chain complex `P.complex` of projective objects,
 along with a chain map `P.π` from `C` to the chain complex consisting just of `Z` in degree zero,

324a7502

bump to nightly-2023-05-01-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/8b8ba04e2f326f3f7cf24ad129beda58531ada61

81091cba

Diff

@@ -58,6 +58,7 @@ section
 
 variable [HasZeroObject C] [HasZeroMorphisms C] [HasEqualizers C] [HasImages C]
 
+#print CategoryTheory.ProjectiveResolution /-
 /--
 A `ProjectiveResolution Z` consists of a bundled `ℕ`-indexed chain complex of projective objects,
 along with a quasi-isomorphism to the complex consisting of just `Z` supported in degree `0`.
@@ -84,20 +85,24 @@ structure ProjectiveResolution (Z : C) where
   exact : ∀ n, Exact (Complex.d (n + 2) (n + 1)) (Complex.d (n + 1) n)
   Epi : Epi (π.f 0) := by infer_instance
 #align category_theory.ProjectiveResolution CategoryTheory.ProjectiveResolution
+-/
 
 attribute [instance] ProjectiveResolution.projective ProjectiveResolution.epi
 
+#print CategoryTheory.HasProjectiveResolution /-
 /- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
 /-- An object admits a projective resolution.
 -/
 class HasProjectiveResolution (Z : C) : Prop where
   out : Nonempty (ProjectiveResolution Z)
 #align category_theory.has_projective_resolution CategoryTheory.HasProjectiveResolution
+-/
 
 section
 
 variable (C)
 
+#print CategoryTheory.HasProjectiveResolutions /-
 /-- You will rarely use this typeclass directly: it is implied by the combination
 `[enough_projectives C]` and `[abelian C]`.
 By itself it's enough to set up the basic theory of derived functors.
@@ -105,6 +110,7 @@ By itself it's enough to set up the basic theory of derived functors.
 class HasProjectiveResolutions : Prop where
   out : ∀ Z : C, HasProjectiveResolution Z
 #align category_theory.has_projective_resolutions CategoryTheory.HasProjectiveResolutions
+-/
 
 attribute [instance 100] has_projective_resolutions.out
 
@@ -112,6 +118,12 @@ end
 
 namespace ProjectiveResolution
 
+/- warning: category_theory.ProjectiveResolution.π_f_succ -> CategoryTheory.ProjectiveResolution.π_f_succ is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] {Z : C} (P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Z) (n : Nat), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (HomologicalComplex.x.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) 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(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 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 _inst_3 _inst_2) Z) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)))) 0 (Zero.zero.{u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) 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(CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 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 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 _inst_3 _inst_2) Z) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne)))) (CategoryTheory.Limits.HasZeroMorphisms.hasZero.{u1, u2} C _inst_1 _inst_3 (HomologicalComplex.x.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Z P) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (One.one.{0} Nat Nat.hasOne))) (HomologicalComplex.x.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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Z) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (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.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] {Z : C} (P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Z) (n : Nat), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (HomologicalComplex.X.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) 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+Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.π_f_succ CategoryTheory.ProjectiveResolution.π_f_succₓ'. -/
 @[simp]
 theorem π_f_succ {Z : C} (P : ProjectiveResolution Z) (n : ℕ) : P.π.f (n + 1) = 0 :=
   by
@@ -119,21 +131,30 @@ theorem π_f_succ {Z : C} (P : ProjectiveResolution Z) (n : ℕ) : P.π.f (n + 1
   dsimp; rfl
 #align category_theory.ProjectiveResolution.π_f_succ CategoryTheory.ProjectiveResolution.π_f_succ
 
+/- warning: category_theory.ProjectiveResolution.complex_d_comp_π_f_zero -> CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero is a dubious translation:
+lean 3 declaration is
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(OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 _inst_3 _inst_2) Z) (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.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] {Z : C} (P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Z), Eq.{succ u1} (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 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) 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+Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.complex_d_comp_π_f_zero CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zeroₓ'. -/
 @[simp]
 theorem complex_d_comp_π_f_zero {Z : C} (P : ProjectiveResolution Z) :
     P.complex.d 1 0 ≫ P.π.f 0 = 0 :=
   P.exact₀.w
 #align category_theory.ProjectiveResolution.complex_d_comp_π_f_zero CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero
 
+#print CategoryTheory.ProjectiveResolution.complex_d_succ_comp /-
 @[simp]
 theorem complex_d_succ_comp {Z : C} (P : ProjectiveResolution Z) (n : ℕ) :
     P.complex.d (n + 2) (n + 1) ≫ P.complex.d (n + 1) n = 0 :=
   (P.exact _).w
 #align category_theory.ProjectiveResolution.complex_d_succ_comp CategoryTheory.ProjectiveResolution.complex_d_succ_comp
+-/
 
 instance {Z : C} (P : ProjectiveResolution Z) (n : ℕ) : CategoryTheory.Epi (P.π.f n) := by
   cases n <;> infer_instance
 
+#print CategoryTheory.ProjectiveResolution.self /-
 /-- A projective object admits a trivial projective resolution: itself in degree 0. -/
 def self (Z : C) [CategoryTheory.Projective Z] : ProjectiveResolution Z
     where
@@ -155,32 +176,40 @@ def self (Z : C) [CategoryTheory.Projective Z] : ProjectiveResolution Z
     dsimp
     infer_instance
 #align category_theory.ProjectiveResolution.self CategoryTheory.ProjectiveResolution.self
+-/
 
+#print CategoryTheory.ProjectiveResolution.liftZero /-
 /-- Auxiliary construction for `lift`. -/
-def liftFZero {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) :
+def liftZero {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) :
     P.complex.pt 0 ⟶ Q.complex.pt 0 :=
   factorThru (P.π.f 0 ≫ f) (Q.π.f 0)
-#align category_theory.ProjectiveResolution.lift_f_zero CategoryTheory.ProjectiveResolution.liftFZero
+#align category_theory.ProjectiveResolution.lift_f_zero CategoryTheory.ProjectiveResolution.liftZero
+-/
 
+#print CategoryTheory.ProjectiveResolution.liftOne /-
 /-- Auxiliary construction for `lift`. -/
-def liftFOne {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) :
+def liftOne {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) :
     P.complex.pt 1 ⟶ Q.complex.pt 1 :=
-  Exact.lift (P.complex.d 1 0 ≫ liftFZero f P Q) (Q.complex.d 1 0) (Q.π.f 0) Q.exact₀
+  Exact.lift (P.complex.d 1 0 ≫ liftZero f P Q) (Q.complex.d 1 0) (Q.π.f 0) Q.exact₀
     (by simp [lift_f_zero, P.exact₀.w_assoc])
-#align category_theory.ProjectiveResolution.lift_f_one CategoryTheory.ProjectiveResolution.liftFOne
+#align category_theory.ProjectiveResolution.lift_f_one CategoryTheory.ProjectiveResolution.liftOne
+-/
 
+#print CategoryTheory.ProjectiveResolution.liftOne_zero_comm /-
 /-- Auxiliary lemma for `lift`. -/
 @[simp]
-theorem liftFOne_zero_comm {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
+theorem liftOne_zero_comm {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
     (Q : ProjectiveResolution Z) :
-    liftFOne f P Q ≫ Q.complex.d 1 0 = P.complex.d 1 0 ≫ liftFZero f P Q :=
+    liftOne f P Q ≫ Q.complex.d 1 0 = P.complex.d 1 0 ≫ liftZero f P Q :=
   by
   dsimp [lift_f_zero, lift_f_one]
   simp
-#align category_theory.ProjectiveResolution.lift_f_one_zero_comm CategoryTheory.ProjectiveResolution.liftFOne_zero_comm
+#align category_theory.ProjectiveResolution.lift_f_one_zero_comm CategoryTheory.ProjectiveResolution.liftOne_zero_comm
+-/
 
+#print CategoryTheory.ProjectiveResolution.liftSucc /-
 /-- Auxiliary construction for `lift`. -/
-def liftFSucc {Y Z : C} (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) (n : ℕ)
+def liftSucc {Y Z : C} (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) (n : ℕ)
     (g : P.complex.pt n ⟶ Q.complex.pt n) (g' : P.complex.pt (n + 1) ⟶ Q.complex.pt (n + 1))
     (w : g' ≫ Q.complex.d (n + 1) n = P.complex.d (n + 1) n ≫ g) :
     Σ'g'' : P.complex.pt (n + 2) ⟶ Q.complex.pt (n + 2),
@@ -188,15 +217,24 @@ def liftFSucc {Y Z : C} (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z
   ⟨Exact.lift (P.complex.d (n + 2) (n + 1) ≫ g') (Q.complex.d (n + 2) (n + 1))
       (Q.complex.d (n + 1) n) (Q.exact _) (by simp [w]),
     by simp⟩
-#align category_theory.ProjectiveResolution.lift_f_succ CategoryTheory.ProjectiveResolution.liftFSucc
+#align category_theory.ProjectiveResolution.lift_f_succ CategoryTheory.ProjectiveResolution.liftSucc
+-/
 
+#print CategoryTheory.ProjectiveResolution.lift /-
 /-- A morphism in `C` lifts to a chain map between projective resolutions. -/
 def lift {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) :
     P.complex ⟶ Q.complex :=
-  ChainComplex.mkHom _ _ (liftFZero f _ _) (liftFOne f _ _) (liftFOne_zero_comm f _ _)
-    fun n ⟨g, g', w⟩ => liftFSucc P Q n g g' w
+  ChainComplex.mkHom _ _ (liftZero f _ _) (liftOne f _ _) (liftOne_zero_comm f _ _)
+    fun n ⟨g, g', w⟩ => liftSucc P Q n g g' w
 #align category_theory.ProjectiveResolution.lift CategoryTheory.ProjectiveResolution.lift
+-/
 
+/- warning: category_theory.ProjectiveResolution.lift_commutes -> CategoryTheory.ProjectiveResolution.lift_commutes is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{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) (P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Y) (Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Z), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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_inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Y P) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 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 _inst_3 (ComplexShape.down.{0} Nat 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+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{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) (P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Y) (Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Z), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 _inst_3 Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 _inst_3 _inst_2)) Y Z f))
+Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_commutes CategoryTheory.ProjectiveResolution.lift_commutesₓ'. -/
 /-- The resolution maps intertwine the lift of a morphism and that morphism. -/
 @[simp, reassoc.1]
 theorem lift_commutes {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
@@ -217,6 +255,12 @@ namespace ProjectiveResolution
 
 variable [HasZeroObject C] [Preadditive C] [HasEqualizers C] [HasImages C]
 
+/- warning: category_theory.ProjectiveResolution.lift_homotopy_zero_zero -> CategoryTheory.ProjectiveResolution.liftHomotopyZeroZero is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] {Y : C} {Z : C} {P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y} {Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z} (f : Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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_inst_3) 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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat 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(ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2) Z)) 0 (Zero.zero.{u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2) Z)) (HomologicalComplex.Quiver.Hom.hasZero.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2) Z)))))) -> (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HomologicalComplex.x.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (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.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] {Y : C} {Z : C} {P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y} {Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z} (f : Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q)), (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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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(OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat 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(HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) 0 (Zero.toOfNat0.{u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) (HomologicalComplex.instZeroHomHomologicalComplexPreadditiveHasZeroMorphismsToQuiverToCategoryStructInstCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z))))) -> (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))
+Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_homotopy_zero_zero CategoryTheory.ProjectiveResolution.liftHomotopyZeroZeroₓ'. -/
 /-- An auxiliary definition for `lift_homotopy_zero`. -/
 def liftHomotopyZeroZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
     (f : P.complex ⟶ Q.complex) (comm : f ≫ Q.π = 0) : P.complex.pt 0 ⟶ Q.complex.pt 1 :=
@@ -224,6 +268,12 @@ def liftHomotopyZeroZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveR
     (congr_fun (congr_arg HomologicalComplex.Hom.f comm) 0)
 #align category_theory.ProjectiveResolution.lift_homotopy_zero_zero CategoryTheory.ProjectiveResolution.liftHomotopyZeroZero
 
+/- warning: category_theory.ProjectiveResolution.lift_homotopy_zero_one -> CategoryTheory.ProjectiveResolution.liftHomotopyZeroOne is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] {Y : C} {Z : C} {P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y} {Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z} (f : Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q)), (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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) 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Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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_inst_3) 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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat 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(ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2) Z)) 0 (Zero.zero.{u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2) Z)))))) -> (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (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.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] {Y : C} {Z : C} {P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y} {Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z} (f : Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q)), (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) 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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))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat 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(HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) 0 (Zero.toOfNat0.{u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{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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(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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) (HomologicalComplex.instZeroHomHomologicalComplexPreadditiveHasZeroMorphismsToQuiverToCategoryStructInstCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z))))) -> (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_homotopy_zero_one CategoryTheory.ProjectiveResolution.liftHomotopyZeroOneₓ'. -/
 /-- An auxiliary definition for `lift_homotopy_zero`. -/
 def liftHomotopyZeroOne {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
     (f : P.complex ⟶ Q.complex) (comm : f ≫ Q.π = 0) : P.complex.pt 1 ⟶ Q.complex.pt 2 :=
@@ -231,6 +281,12 @@ def liftHomotopyZeroOne {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveRe
     (Q.complex.d 1 0) (Q.exact _) (by simp [lift_homotopy_zero_zero])
 #align category_theory.ProjectiveResolution.lift_homotopy_zero_one CategoryTheory.ProjectiveResolution.liftHomotopyZeroOne
 
+/- warning: category_theory.ProjectiveResolution.lift_homotopy_zero_succ -> CategoryTheory.ProjectiveResolution.liftHomotopyZeroSucc is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] {Y : C} {Z : C} {P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y} {Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z} (f : Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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_inst_5 Z Q)) (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) n) (HomologicalComplex.x.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (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)))))))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] {Y : C} {Z : C} {P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y} {Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z} (f : Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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.ProjectiveResolution.lift_homotopy_zero_succ CategoryTheory.ProjectiveResolution.liftHomotopyZeroSuccₓ'. -/
 /-- An auxiliary definition for `lift_homotopy_zero`. -/
 def liftHomotopyZeroSucc {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
     (f : P.complex ⟶ Q.complex) (n : ℕ) (g : P.complex.pt n ⟶ Q.complex.pt (n + 1))
@@ -241,6 +297,12 @@ def liftHomotopyZeroSucc {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveR
     (Q.complex.d (n + 2) (n + 1)) (Q.exact _) (by simp [w])
 #align category_theory.ProjectiveResolution.lift_homotopy_zero_succ CategoryTheory.ProjectiveResolution.liftHomotopyZeroSucc
 
+/- warning: category_theory.ProjectiveResolution.lift_homotopy_zero -> CategoryTheory.ProjectiveResolution.liftHomotopyZero is a dubious translation:
+lean 3 declaration is
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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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q)) (HomologicalComplex.Quiver.Hom.hasZero.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q))))))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] {Y : C} {Z : C} {P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y} {Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z} (f : Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q)), (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z) f (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q)) (OfNat.ofNat.{u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) 0 (Zero.toOfNat0.{u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) (HomologicalComplex.instZeroHomHomologicalComplexPreadditiveHasZeroMorphismsToQuiverToCategoryStructInstCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z))))) -> (Homotopy.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) f (OfNat.ofNat.{u1} (Quiver.Hom.{succ u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, 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+Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_homotopy_zero CategoryTheory.ProjectiveResolution.liftHomotopyZeroₓ'. -/
 /-- Any lift of the zero morphism is homotopic to zero. -/
 def liftHomotopyZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
     (f : P.complex ⟶ Q.complex) (comm : f ≫ Q.π = 0) : Homotopy f 0 :=
@@ -249,6 +311,12 @@ def liftHomotopyZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResol
     ⟨liftHomotopyZeroSucc f n g g' w, by simp [lift_homotopy_zero_succ, w]⟩
 #align category_theory.ProjectiveResolution.lift_homotopy_zero CategoryTheory.ProjectiveResolution.liftHomotopyZero
 
+/- warning: category_theory.ProjectiveResolution.lift_homotopy -> CategoryTheory.ProjectiveResolution.liftHomotopy is a dubious translation:
+lean 3 declaration is
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(OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2) Y Z f))) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2) Z)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2) Z) h (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2) Y) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2) Z) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.Functor.map.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2) Y Z f))) -> (Homotopy.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) g h)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{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) {P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y} {Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z} (g : Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q)) (h : Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q)), (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z) g (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Y) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Y Z f))) -> (Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z) h (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Y) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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_inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Z) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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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(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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) Y Z f))) -> (Homotopy.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Y P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 Z Q) g h)
+Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.lift_homotopy CategoryTheory.ProjectiveResolution.liftHomotopyₓ'. -/
 /-- Two lifts of the same morphism are homotopic. -/
 def liftHomotopy {Y Z : C} (f : Y ⟶ Z) {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
     (g h : P.complex ⟶ Q.complex) (g_comm : g ≫ Q.π = P.π ≫ (ChainComplex.single₀ C).map f)
@@ -256,17 +324,22 @@ def liftHomotopy {Y Z : C} (f : Y ⟶ Z) {P : ProjectiveResolution Y} {Q : Proje
   Homotopy.equivSubZero.invFun (liftHomotopyZero _ (by simp [g_comm, h_comm]))
 #align category_theory.ProjectiveResolution.lift_homotopy CategoryTheory.ProjectiveResolution.liftHomotopy
 
+#print CategoryTheory.ProjectiveResolution.liftIdHomotopy /-
 /-- The lift of the identity morphism is homotopic to the identity chain map. -/
 def liftIdHomotopy (X : C) (P : ProjectiveResolution X) : Homotopy (lift (𝟙 X) P P) (𝟙 P.complex) :=
   by apply lift_homotopy (𝟙 X) <;> simp
 #align category_theory.ProjectiveResolution.lift_id_homotopy CategoryTheory.ProjectiveResolution.liftIdHomotopy
+-/
 
+#print CategoryTheory.ProjectiveResolution.liftCompHomotopy /-
 /-- The lift of a composition is homotopic to the composition of the lifts. -/
 def liftCompHomotopy {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z) (P : ProjectiveResolution X)
     (Q : ProjectiveResolution Y) (R : ProjectiveResolution Z) :
     Homotopy (lift (f ≫ g) P R) (lift f P Q ≫ lift g Q R) := by apply lift_homotopy (f ≫ g) <;> simp
 #align category_theory.ProjectiveResolution.lift_comp_homotopy CategoryTheory.ProjectiveResolution.liftCompHomotopy
+-/
 
+#print CategoryTheory.ProjectiveResolution.homotopyEquiv /-
 -- We don't care about the actual definitions of these homotopies.
 /-- Any two projective resolutions are homotopy equivalent. -/
 def homotopyEquiv {X : C} (P Q : ProjectiveResolution X) : HomotopyEquiv P.complex Q.complex
@@ -284,12 +357,25 @@ def homotopyEquiv {X : C} (P Q : ProjectiveResolution X) : HomotopyEquiv P.compl
     simp [category.id_comp]
     apply lift_id_homotopy
 #align category_theory.ProjectiveResolution.homotopy_equiv CategoryTheory.ProjectiveResolution.homotopyEquiv
+-/
 
+/- warning: category_theory.ProjectiveResolution.homotopy_equiv_hom_π -> CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] {X : C} (P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X) (Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2) X)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2) X) (HomotopyEquiv.hom.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q) (CategoryTheory.ProjectiveResolution.homotopyEquiv.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 X P Q)) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q)) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] {X : C} (P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X) (Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) X)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 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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.Category.toCategoryStruct.{u1, max u2 u1} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) X) (HomotopyEquiv.hom.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q) (CategoryTheory.ProjectiveResolution.homotopyEquiv.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 X P Q)) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q)) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P)
+Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.homotopy_equiv_hom_π CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_πₓ'. -/
 @[simp, reassoc.1]
 theorem homotopyEquiv_hom_π {X : C} (P Q : ProjectiveResolution X) :
     (homotopyEquiv P Q).Hom ≫ Q.π = P.π := by simp [HomotopyEquiv]
 #align category_theory.ProjectiveResolution.homotopy_equiv_hom_π CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π
 
+/- warning: category_theory.ProjectiveResolution.homotopy_equiv_inv_π -> CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_π is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] {X : C} (P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X) (Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2) X)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) 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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2) X) (HomotopyEquiv.inv.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q) (CategoryTheory.ProjectiveResolution.homotopyEquiv.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 X P Q)) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P)) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] {X : C} (P : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X) (Q : CategoryTheory.ProjectiveResolution.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X), Eq.{succ u1} (Quiver.Hom.{succ u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) X)) (CategoryTheory.CategoryStruct.comp.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P) (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)) (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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} (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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 _inst_3) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_2)) X) (HomotopyEquiv.inv.{u1, u2, 0} Nat C _inst_1 _inst_3 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P) (CategoryTheory.ProjectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q) (CategoryTheory.ProjectiveResolution.homotopyEquiv.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 X P Q)) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X P)) (CategoryTheory.ProjectiveResolution.π.{u1, u2} C _inst_1 _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 _inst_3) _inst_4 _inst_5 X Q)
+Case conversion may be inaccurate. Consider using '#align category_theory.ProjectiveResolution.homotopy_equiv_inv_π CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_πₓ'. -/
 @[simp, reassoc.1]
 theorem homotopyEquiv_inv_π {X : C} (P Q : ProjectiveResolution X) :
     (homotopyEquiv P Q).inv ≫ P.π = Q.π := by simp [HomotopyEquiv]
@@ -301,36 +387,49 @@ section
 
 variable [HasZeroMorphisms C] [HasZeroObject C] [HasEqualizers C] [HasImages C]
 
+#print CategoryTheory.projectiveResolution.complex /-
 /-- An arbitrarily chosen projective resolution of an object. -/
-abbrev projectiveResolution (Z : C) [HasProjectiveResolution Z] : ChainComplex C ℕ :=
+abbrev CategoryTheory.projectiveResolution.complex (Z : C) [HasProjectiveResolution Z] :
+    ChainComplex C ℕ :=
   (HasProjectiveResolution.out Z).some.complex
-#align category_theory.projective_resolution CategoryTheory.projectiveResolution
+#align category_theory.projective_resolution CategoryTheory.projectiveResolution.complex
+-/
 
+/- warning: category_theory.projective_resolution.π -> CategoryTheory.projectiveResolution.π is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] (Z : C) [_inst_6 : CategoryTheory.HasProjectiveResolution.{u1, u2} C _inst_1 _inst_3 _inst_2 _inst_4 _inst_5 Z], Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} 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} (ChainComplex.{u1, u2, 0} 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} (ChainComplex.{u1, u2, 0} 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 _inst_2 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) (CategoryTheory.projectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Z _inst_6) (CategoryTheory.Functor.obj.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} 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 _inst_2 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (ChainComplex.single₀.{u1, u2} C _inst_1 _inst_2 _inst_3) Z)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} C _inst_1] [_inst_3 : CategoryTheory.Limits.HasZeroObject.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} C _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} C _inst_1] (Z : C) [_inst_6 : CategoryTheory.HasProjectiveResolution.{u1, u2} C _inst_1 _inst_3 _inst_2 _inst_4 _inst_5 Z], Quiver.Hom.{succ u1, max u2 u1} (ChainComplex.{u1, u2, 0} 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} (ChainComplex.{u1, u2, 0} 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} (ChainComplex.{u1, u2, 0} 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 _inst_2 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.projectiveResolution.complex.{u1, u2} C _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 Z _inst_6) (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)) (ChainComplex.{u1, u2, 0} 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} (ChainComplex.{u1, u2, 0} 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} (ChainComplex.{u1, u2, 0} 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 _inst_2 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (ChainComplex.{u1, u2, 0} 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 _inst_2 (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u1, u2} C _inst_1 _inst_2 _inst_3)) Z)
+Case conversion may be inaccurate. Consider using '#align category_theory.projective_resolution.π CategoryTheory.projectiveResolution.πₓ'. -/
 /-- The chain map from the arbitrarily chosen projective resolution `projective_resolution Z`
 back to the chain complex consisting of `Z` supported in degree `0`. -/
 abbrev projectiveResolution.π (Z : C) [HasProjectiveResolution Z] :
-    projectiveResolution Z ⟶ (ChainComplex.single₀ C).obj Z :=
+    CategoryTheory.projectiveResolution.complex Z ⟶ (ChainComplex.single₀ C).obj Z :=
   (HasProjectiveResolution.out Z).some.π
 #align category_theory.projective_resolution.π CategoryTheory.projectiveResolution.π
 
+#print CategoryTheory.projectiveResolution.lift /-
 /-- The lift of a morphism to a chain map between the arbitrarily chosen projective resolutions. -/
 abbrev projectiveResolution.lift {X Y : C} (f : X ⟶ Y) [HasProjectiveResolution X]
-    [HasProjectiveResolution Y] : projectiveResolution X ⟶ projectiveResolution Y :=
+    [HasProjectiveResolution Y] :
+    CategoryTheory.projectiveResolution.complex X ⟶ CategoryTheory.projectiveResolution.complex Y :=
   ProjectiveResolution.lift f _ _
 #align category_theory.projective_resolution.lift CategoryTheory.projectiveResolution.lift
+-/
 
 end
 
 variable (C) [Preadditive C] [HasZeroObject C] [HasEqualizers C] [HasImages C]
   [HasProjectiveResolutions C]
 
+#print CategoryTheory.projectiveResolutions /-
 /-- Taking projective resolutions is functorial,
 if considered with target the homotopy category
 (`ℕ`-indexed chain complexes and chain maps up to homotopy).
 -/
 def projectiveResolutions : C ⥤ HomotopyCategory C (ComplexShape.down ℕ)
     where
-  obj X := (HomotopyCategory.quotient _ _).obj (projectiveResolution X)
+  obj X := (HomotopyCategory.quotient _ _).obj (CategoryTheory.projectiveResolution.complex X)
   map X Y f := (HomotopyCategory.quotient _ _).map (projectiveResolution.lift f)
   map_id' X := by
     rw [← (HomotopyCategory.quotient _ _).map_id]
@@ -341,6 +440,7 @@ def projectiveResolutions : C ⥤ HomotopyCategory C (ComplexShape.down ℕ)
     apply HomotopyCategory.eq_of_homotopy
     apply ProjectiveResolution.lift_comp_homotopy
 #align category_theory.projective_resolutions CategoryTheory.projectiveResolutions
+-/
 
 end CategoryTheory

324a7502

bump to nightly-2023-04-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

ff662d55

Diff

@@ -87,7 +87,7 @@ structure ProjectiveResolution (Z : C) where
 
 attribute [instance] ProjectiveResolution.projective ProjectiveResolution.epi
 
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`out] [] -/
 /-- An object admits a projective resolution.
 -/
 class HasProjectiveResolution (Z : C) : Prop where
@@ -106,7 +106,7 @@ class HasProjectiveResolutions : Prop where
   out : ∀ Z : C, HasProjectiveResolution Z
 #align category_theory.has_projective_resolutions CategoryTheory.HasProjectiveResolutions
 
-attribute [instance] has_projective_resolutions.out
+attribute [instance 100] has_projective_resolutions.out
 
 end

324a7502

bump to nightly-2023-03-10-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/ddec54a71a0dd025c05445d467f1a2b7d586a3ba

24f14899

Diff

@@ -78,10 +78,10 @@ you will not typically need to use this bundled object, and will instead use
 @[nolint has_nonempty_instance]
 structure ProjectiveResolution (Z : C) where
   complex : ChainComplex C ℕ
-  π : HomologicalComplex.Hom complex ((ChainComplex.single₀ C).obj Z)
-  Projective : ∀ n, Projective (complex.pt n) := by infer_instance
-  exact₀ : Exact (complex.d 1 0) (π.f 0)
-  exact : ∀ n, Exact (complex.d (n + 2) (n + 1)) (complex.d (n + 1) n)
+  π : HomologicalComplex.Hom Complex ((ChainComplex.single₀ C).obj Z)
+  Projective : ∀ n, Projective (Complex.pt n) := by infer_instance
+  exact₀ : Exact (Complex.d 1 0) (π.f 0)
+  exact : ∀ n, Exact (Complex.d (n + 2) (n + 1)) (Complex.d (n + 1) n)
   Epi : Epi (π.f 0) := by infer_instance
 #align category_theory.ProjectiveResolution CategoryTheory.ProjectiveResolution

324a7502

bump to nightly-2023-02-28-22

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

1fb1623f

Diff

@@ -79,7 +79,7 @@ you will not typically need to use this bundled object, and will instead use
 structure ProjectiveResolution (Z : C) where
   complex : ChainComplex C ℕ
   π : HomologicalComplex.Hom complex ((ChainComplex.single₀ C).obj Z)
-  Projective : ∀ n, Projective (complex.x n) := by infer_instance
+  Projective : ∀ n, Projective (complex.pt n) := by infer_instance
   exact₀ : Exact (complex.d 1 0) (π.f 0)
   exact : ∀ n, Exact (complex.d (n + 2) (n + 1)) (complex.d (n + 1) n)
   Epi : Epi (π.f 0) := by infer_instance
@@ -158,13 +158,13 @@ def self (Z : C) [CategoryTheory.Projective Z] : ProjectiveResolution Z
 
 /-- Auxiliary construction for `lift`. -/
 def liftFZero {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) :
-    P.complex.x 0 ⟶ Q.complex.x 0 :=
+    P.complex.pt 0 ⟶ Q.complex.pt 0 :=
   factorThru (P.π.f 0 ≫ f) (Q.π.f 0)
 #align category_theory.ProjectiveResolution.lift_f_zero CategoryTheory.ProjectiveResolution.liftFZero
 
 /-- Auxiliary construction for `lift`. -/
 def liftFOne {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) :
-    P.complex.x 1 ⟶ Q.complex.x 1 :=
+    P.complex.pt 1 ⟶ Q.complex.pt 1 :=
   Exact.lift (P.complex.d 1 0 ≫ liftFZero f P Q) (Q.complex.d 1 0) (Q.π.f 0) Q.exact₀
     (by simp [lift_f_zero, P.exact₀.w_assoc])
 #align category_theory.ProjectiveResolution.lift_f_one CategoryTheory.ProjectiveResolution.liftFOne
@@ -181,9 +181,9 @@ theorem liftFOne_zero_comm {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
 
 /-- Auxiliary construction for `lift`. -/
 def liftFSucc {Y Z : C} (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) (n : ℕ)
-    (g : P.complex.x n ⟶ Q.complex.x n) (g' : P.complex.x (n + 1) ⟶ Q.complex.x (n + 1))
+    (g : P.complex.pt n ⟶ Q.complex.pt n) (g' : P.complex.pt (n + 1) ⟶ Q.complex.pt (n + 1))
     (w : g' ≫ Q.complex.d (n + 1) n = P.complex.d (n + 1) n ≫ g) :
-    Σ'g'' : P.complex.x (n + 2) ⟶ Q.complex.x (n + 2),
+    Σ'g'' : P.complex.pt (n + 2) ⟶ Q.complex.pt (n + 2),
       g'' ≫ Q.complex.d (n + 2) (n + 1) = P.complex.d (n + 2) (n + 1) ≫ g' :=
   ⟨Exact.lift (P.complex.d (n + 2) (n + 1) ≫ g') (Q.complex.d (n + 2) (n + 1))
       (Q.complex.d (n + 1) n) (Q.exact _) (by simp [w]),
@@ -219,24 +219,24 @@ variable [HasZeroObject C] [Preadditive C] [HasEqualizers C] [HasImages C]
 
 /-- An auxiliary definition for `lift_homotopy_zero`. -/
 def liftHomotopyZeroZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
-    (f : P.complex ⟶ Q.complex) (comm : f ≫ Q.π = 0) : P.complex.x 0 ⟶ Q.complex.x 1 :=
+    (f : P.complex ⟶ Q.complex) (comm : f ≫ Q.π = 0) : P.complex.pt 0 ⟶ Q.complex.pt 1 :=
   Exact.lift (f.f 0) (Q.complex.d 1 0) (Q.π.f 0) Q.exact₀
     (congr_fun (congr_arg HomologicalComplex.Hom.f comm) 0)
 #align category_theory.ProjectiveResolution.lift_homotopy_zero_zero CategoryTheory.ProjectiveResolution.liftHomotopyZeroZero
 
 /-- An auxiliary definition for `lift_homotopy_zero`. -/
 def liftHomotopyZeroOne {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
-    (f : P.complex ⟶ Q.complex) (comm : f ≫ Q.π = 0) : P.complex.x 1 ⟶ Q.complex.x 2 :=
+    (f : P.complex ⟶ Q.complex) (comm : f ≫ Q.π = 0) : P.complex.pt 1 ⟶ Q.complex.pt 2 :=
   Exact.lift (f.f 1 - P.complex.d 1 0 ≫ liftHomotopyZeroZero f comm) (Q.complex.d 2 1)
     (Q.complex.d 1 0) (Q.exact _) (by simp [lift_homotopy_zero_zero])
 #align category_theory.ProjectiveResolution.lift_homotopy_zero_one CategoryTheory.ProjectiveResolution.liftHomotopyZeroOne
 
 /-- An auxiliary definition for `lift_homotopy_zero`. -/
 def liftHomotopyZeroSucc {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
-    (f : P.complex ⟶ Q.complex) (n : ℕ) (g : P.complex.x n ⟶ Q.complex.x (n + 1))
-    (g' : P.complex.x (n + 1) ⟶ Q.complex.x (n + 2))
+    (f : P.complex ⟶ Q.complex) (n : ℕ) (g : P.complex.pt n ⟶ Q.complex.pt (n + 1))
+    (g' : P.complex.pt (n + 1) ⟶ Q.complex.pt (n + 2))
     (w : f.f (n + 1) = P.complex.d (n + 1) n ≫ g + g' ≫ Q.complex.d (n + 2) (n + 1)) :
-    P.complex.x (n + 2) ⟶ Q.complex.x (n + 3) :=
+    P.complex.pt (n + 2) ⟶ Q.complex.pt (n + 3) :=
   Exact.lift (f.f (n + 2) - P.complex.d (n + 2) (n + 1) ≫ g') (Q.complex.d (n + 3) (n + 2))
     (Q.complex.d (n + 2) (n + 1)) (Q.exact _) (by simp [w])
 #align category_theory.ProjectiveResolution.lift_homotopy_zero_succ CategoryTheory.ProjectiveResolution.liftHomotopyZeroSucc

324a7502

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

324a7502

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

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

c5b5490c

Diff

@@ -30,7 +30,7 @@ open Projective
 
 variable [HasZeroObject C] [HasZeroMorphisms C]
 
--- porting note (#10927): removed @[nolint has_nonempty_instance]
+-- porting note (#5171): removed @[nolint has_nonempty_instance]
 /--
 A `ProjectiveResolution Z` consists of a bundled `ℕ`-indexed chain complex of projective objects,
 along with a quasi-isomorphism to the complex consisting of just `Z` supported in degree `0`.

324a7502

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

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

2599c3bb

Diff

@@ -30,7 +30,7 @@ open Projective
 
 variable [HasZeroObject C] [HasZeroMorphisms C]
 
--- porting note: removed @[nolint has_nonempty_instance]
+-- porting note (#10927): removed @[nolint has_nonempty_instance]
 /--
 A `ProjectiveResolution Z` consists of a bundled `ℕ`-indexed chain complex of projective objects,
 along with a quasi-isomorphism to the complex consisting of just `Z` supported in degree `0`.

324a7502

chore: classify simp can do this porting notes (#10619)

Classify by adding issue number (#10618) to porting notes claiming anything semantically equivalent to simp can prove this or simp can simplify this.

de765f60

Diff

@@ -98,7 +98,7 @@ theorem complex_d_comp_π_f_zero :
 set_option linter.uppercaseLean3 false in
 #align category_theory.ProjectiveResolution.complex_d_comp_π_f_zero CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero
 
--- Porting note: removed @[simp] simp can prove this
+-- Porting note (#10618): removed @[simp] simp can prove this
 theorem complex_d_succ_comp (n : ℕ) :
     P.complex.d n (n + 1) ≫ P.complex.d (n + 1) (n + 2) = 0 := by
   simp

324a7502

feat(Algebra/Homology): the class of quasi-isomorphisms in the homotopy category (#9686)

This PR introduces the class of quasi-isomorphisms in the homotopy category of homological complexes.

df4dbd30

Diff

@@ -50,7 +50,7 @@ set_option linter.uppercaseLean3 false in
 #align category_theory.ProjectiveResolution CategoryTheory.ProjectiveResolution
 
 open ProjectiveResolution in
-attribute [instance] projective quasiIso hasHomology
+attribute [instance] projective hasHomology ProjectiveResolution.quasiIso
 
 /-- An object admits a projective resolution.
 -/

324a7502

refactor(Algebra/Homology): use the new homology API (#8706)

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>

41529d1e

Diff

@@ -1,11 +1,9 @@
 /-
 Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Scott Morrison
+Authors: Scott Morrison, Joël Riou
 -/
-import Mathlib.CategoryTheory.Preadditive.Projective
-import Mathlib.Algebra.Homology.Single
-import Mathlib.Algebra.Homology.HomotopyCategory
+import Mathlib.Algebra.Homology.QuasiIso
 
 #align_import category_theory.preadditive.projective_resolution from "leanprover-community/mathlib"@"324a7502510e835cdbd3de1519b6c66b51fb2467"
 
@@ -14,74 +12,45 @@ import Mathlib.Algebra.Homology.HomotopyCategory
 
 A projective resolution `P : ProjectiveResolution Z` of an object `Z : C` consists of
 an `ℕ`-indexed chain complex `P.complex` of projective objects,
-along with a chain map `P.π` from `C` to the chain complex consisting just of `Z` in degree zero,
-so that the augmented chain complex is exact.
+along with a quasi-isomorphism `P.π` from `C` to the chain complex consisting just
+of `Z` in degree zero.
 
-When `C` is abelian, this exactness condition is equivalent to `π` being a quasi-isomorphism.
-It turns out that this formulation allows us to set up the basic theory of derived functors
-without even assuming `C` is abelian.
-
-(Typically, however, to show `HasProjectiveResolutions C`
-one will assume `EnoughProjectives C` and `Abelian C`.
-This construction appears in `CategoryTheory.Abelian.Projective`.)
-
-We show that given `P : ProjectiveResolution X` and `Q : ProjectiveResolution Y`,
-any morphism `X ⟶ Y` admits a lift to a chain map `P.complex ⟶ Q.complex`.
-(It is a lift in the sense that
-the projection maps `P.π` and `Q.π` intertwine the lift and the original morphism.)
-
-Moreover, we show that any two such lifts are homotopic.
-
-As a consequence, if every object admits a projective resolution,
-we can construct a functor `projectiveResolutions C : C ⥤ HomotopyCategory C`.
 -/
 
 
-noncomputable section
-
 universe v u
 
 namespace CategoryTheory
 
-open Limits
+open Category Limits ChainComplex HomologicalComplex
 
 variable {C : Type u} [Category.{v} C]
 
 open Projective
 
-section
-
-variable [HasZeroObject C] [HasZeroMorphisms C] [HasEqualizers C] [HasImages C]
+variable [HasZeroObject C] [HasZeroMorphisms C]
 
 -- porting note: removed @[nolint has_nonempty_instance]
 /--
 A `ProjectiveResolution Z` consists of a bundled `ℕ`-indexed chain complex of projective objects,
 along with a quasi-isomorphism to the complex consisting of just `Z` supported in degree `0`.
-
-(We don't actually ask here that the chain map is a quasi-iso, just exactness everywhere:
-that `π` is a quasi-iso is a lemma when the category is abelian.
-Should we just ask for it here?)
-
-Except in situations where you want to provide a particular projective resolution
-(for example to compute a derived functor),
-you will not typically need to use this bundled object, and will instead use
-* `ProjectiveResolution Z`: the `ℕ`-indexed chain complex
-  (equipped with `Projective` and `Exact` instances)
-* `ProjectiveResolution.π Z`: the chain map from `ProjectiveResolution Z` to
-  `(ChainComplex.single₀ C).obj Z` (all the components are equipped with `Epi` instances,
-  and when the category is `Abelian` we will show `π` is a quasi-iso).
 -/
 structure ProjectiveResolution (Z : C) where
+  /-- the chain complex involved in the resolution -/
   complex : ChainComplex C ℕ
-  π : complex ⟶ ((ChainComplex.single₀ C).obj Z)
+  /-- the chain complex must be degreewise projective -/
   projective : ∀ n, Projective (complex.X n) := by infer_instance
-  exact₀ : Exact (complex.d 1 0) (π.f 0)
-  exact : ∀ n, Exact (complex.d (n + 2) (n + 1)) (complex.d (n + 1) n)
-  epi : Epi (π.f 0) := by infer_instance
+  /-- the chain complex must have homology -/
+  [hasHomology : ∀ i, complex.HasHomology i]
+  /-- the morphism to the single chain complex with `Z` in degree `0` -/
+  π : complex ⟶ (ChainComplex.single₀ C).obj Z
+  /-- the morphism to the single chain complex with `Z` in degree `0` is a quasi-isomorphism -/
+  quasiIso : QuasiIso π := by infer_instance
 set_option linter.uppercaseLean3 false in
 #align category_theory.ProjectiveResolution CategoryTheory.ProjectiveResolution
 
-attribute [instance] ProjectiveResolution.projective ProjectiveResolution.epi
+open ProjectiveResolution in
+attribute [instance] projective quasiIso hasHomology
 
 /-- An object admits a projective resolution.
 -/
@@ -89,8 +58,6 @@ class HasProjectiveResolution (Z : C) : Prop where
   out : Nonempty (ProjectiveResolution Z)
 #align category_theory.has_projective_resolution CategoryTheory.HasProjectiveResolution
 
-section
-
 variable (C)
 
 /-- You will rarely use this typeclass directly: it is implied by the combination
@@ -103,268 +70,80 @@ class HasProjectiveResolutions : Prop where
 
 attribute [instance 100] HasProjectiveResolutions.out
 
-end
-
 namespace ProjectiveResolution
 
+variable {C}
+variable {Z : C} (P : ProjectiveResolution Z)
+
+lemma complex_exactAt_succ (n : ℕ) :
+    P.complex.ExactAt (n + 1) := by
+  rw [← quasiIsoAt_iff_exactAt' P.π (n + 1) (exactAt_succ_single_obj _ _)]
+  · infer_instance
+
+lemma exact_succ (n : ℕ):
+    (ShortComplex.mk _ _ (P.complex.d_comp_d (n + 2) (n + 1) n)).Exact :=
+  ((HomologicalComplex.exactAt_iff' _ (n + 2) (n + 1) n) (by simp only [prev]; rfl)
+    (by simp)).1 (P.complex_exactAt_succ n)
+
 @[simp]
-theorem π_f_succ {Z : C} (P : ProjectiveResolution Z) (n : ℕ) : P.π.f (n + 1) = 0 := by
-  apply zero_of_target_iso_zero
-  dsimp; rfl
+theorem π_f_succ (n : ℕ) : P.π.f (n + 1) = 0 :=
+  (isZero_single_obj_X _ _ _ _ (by simp)).eq_of_tgt _ _
 set_option linter.uppercaseLean3 false in
 #align category_theory.ProjectiveResolution.π_f_succ CategoryTheory.ProjectiveResolution.π_f_succ
 
-@[simp]
-theorem complex_d_comp_π_f_zero {Z : C} (P : ProjectiveResolution Z) :
-    P.complex.d 1 0 ≫ P.π.f 0 = 0 :=
-  P.exact₀.w
+@[reassoc (attr := simp)]
+theorem complex_d_comp_π_f_zero :
+    P.complex.d 1 0 ≫ P.π.f 0 = 0 := by
+  rw [← P.π.comm 1 0, single_obj_d, comp_zero]
 set_option linter.uppercaseLean3 false in
 #align category_theory.ProjectiveResolution.complex_d_comp_π_f_zero CategoryTheory.ProjectiveResolution.complex_d_comp_π_f_zero
 
-@[simp 1100]
-theorem complex_d_succ_comp {Z : C} (P : ProjectiveResolution Z) (n : ℕ) :
-    P.complex.d (n + 2) (n + 1) ≫ P.complex.d (n + 1) n = 0 :=
-  (P.exact _).w
+-- Porting note: removed @[simp] simp can prove this
+theorem complex_d_succ_comp (n : ℕ) :
+    P.complex.d n (n + 1) ≫ P.complex.d (n + 1) (n + 2) = 0 := by
+  simp
 set_option linter.uppercaseLean3 false in
 #align category_theory.ProjectiveResolution.complex_d_succ_comp CategoryTheory.ProjectiveResolution.complex_d_succ_comp
 
-instance {Z : C} (P : ProjectiveResolution Z) (n : ℕ) : CategoryTheory.Epi (P.π.f n) := by
+/-- The (limit) cokernel cofork given by the composition
+`P.complex.X 1 ⟶ P.complex.X 0 ⟶ Z` when `P : ProjectiveResolution Z`. -/
+@[simp]
+noncomputable def cokernelCofork : CokernelCofork (P.complex.d 1 0) :=
+  CokernelCofork.ofπ _ P.complex_d_comp_π_f_zero
+
+/-- `Z` is the cokernel of `P.complex.X 1 ⟶ P.complex.X 0` when `P : ProjectiveResolution Z`. -/
+noncomputable def isColimitCokernelCofork : IsColimit (P.cokernelCofork) := by
+  refine IsColimit.ofIsoColimit (P.complex.opcyclesIsCokernel 1 0 (by simp)) ?_
+  refine Cofork.ext (P.complex.isoHomologyι₀.symm ≪≫ isoOfQuasiIsoAt P.π 0 ≪≫
+    singleObjHomologySelfIso _ _ _) ?_
+  rw [← cancel_mono (singleObjHomologySelfIso (ComplexShape.down ℕ) 0 _).inv,
+    ← cancel_mono (isoHomologyι₀ _).hom]
+  dsimp
+  simp only [isoHomologyι₀_inv_naturality_assoc, p_opcyclesMap_assoc, single₀_obj_zero, assoc,
+    Iso.hom_inv_id, comp_id, isoHomologyι_inv_hom_id, singleObjHomologySelfIso_inv_homologyι,
+    singleObjOpcyclesSelfIso_hom, single₀ObjXSelf, Iso.refl_inv, id_comp]
+
+instance (n : ℕ) : Epi (P.π.f n) := by
   cases n
-  · dsimp
-    infer_instance
-  · constructor
-    intros
-    apply (HomologicalComplex.isZero_single_obj_X _ _ _ _ (Nat.succ_ne_zero _)).eq_of_src
+  · exact epi_of_isColimit_cofork P.isColimitCokernelCofork
+  · rw [π_f_succ]; infer_instance
+
+variable (Z)
 
 /-- A projective object admits a trivial projective resolution: itself in degree 0. -/
-def self (Z : C) [CategoryTheory.Projective Z] : ProjectiveResolution Z where
+@[simps]
+noncomputable def self [Projective Z] : ProjectiveResolution Z where
   complex := (ChainComplex.single₀ C).obj Z
   π := 𝟙 ((ChainComplex.single₀ C).obj Z)
   projective n := by
     cases n
     · simpa
-    · exact ((HomologicalComplex.isZero_single_obj_X (ComplexShape.down ℕ) 0 Z) _
-        (Nat.succ_ne_zero _)).projective
-  exact₀ := by
-    dsimp
-    exact exact_zero_mono _
-  exact n := by
-    dsimp
-    exact exact_of_zero _ _
-  epi := by
-    dsimp
-    infer_instance
+    · apply IsZero.projective
+      apply HomologicalComplex.isZero_single_obj_X
+      simp
 set_option linter.uppercaseLean3 false in
 #align category_theory.ProjectiveResolution.self CategoryTheory.ProjectiveResolution.self
 
-/-- Auxiliary construction for `lift`. -/
-def liftZero {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) :
-    P.complex.X 0 ⟶ Q.complex.X 0 :=
-  factorThru (P.π.f 0 ≫ f) (Q.π.f 0)
-set_option linter.uppercaseLean3 false in
-#align category_theory.ProjectiveResolution.lift_f_zero CategoryTheory.ProjectiveResolution.liftZero
-
-/-- Auxiliary construction for `lift`. -/
-def liftOne {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) :
-    P.complex.X 1 ⟶ Q.complex.X 1 :=
-  Exact.lift (P.complex.d 1 0 ≫ liftZero f P Q) (Q.complex.d 1 0) (Q.π.f 0) Q.exact₀
-    (by simp [liftZero, P.exact₀.w_assoc])
-set_option linter.uppercaseLean3 false in
-#align category_theory.ProjectiveResolution.lift_f_one CategoryTheory.ProjectiveResolution.liftOne
-
-/-- Auxiliary lemma for `lift`. -/
-@[simp]
-theorem liftOne_zero_comm {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
-    (Q : ProjectiveResolution Z) :
-    liftOne f P Q ≫ Q.complex.d 1 0 = P.complex.d 1 0 ≫ liftZero f P Q := by
-  dsimp [liftZero, liftOne]
-  simp
-set_option linter.uppercaseLean3 false in
-#align category_theory.ProjectiveResolution.lift_f_one_zero_comm CategoryTheory.ProjectiveResolution.liftOne_zero_comm
-
-/-- Auxiliary construction for `lift`. -/
-def liftSucc {Y Z : C} (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) (n : ℕ)
-    (g : P.complex.X n ⟶ Q.complex.X n) (g' : P.complex.X (n + 1) ⟶ Q.complex.X (n + 1))
-    (w : g' ≫ Q.complex.d (n + 1) n = P.complex.d (n + 1) n ≫ g) :
-    Σ' g'' : P.complex.X (n + 2) ⟶ Q.complex.X (n + 2),
-      g'' ≫ Q.complex.d (n + 2) (n + 1) = P.complex.d (n + 2) (n + 1) ≫ g' :=
-  ⟨Exact.lift (P.complex.d (n + 2) (n + 1) ≫ g') (Q.complex.d (n + 2) (n + 1))
-      (Q.complex.d (n + 1) n) (Q.exact _) (by simp [w]), by simp⟩
-set_option linter.uppercaseLean3 false in
-#align category_theory.ProjectiveResolution.lift_f_succ CategoryTheory.ProjectiveResolution.liftSucc
-
-/-- A morphism in `C` lifts to a chain map between projective resolutions. -/
-def lift {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y) (Q : ProjectiveResolution Z) :
-    P.complex ⟶ Q.complex :=
-  ChainComplex.mkHom _ _ (liftZero f _ _) (liftOne f _ _) (liftOne_zero_comm f _ _)
-    fun n ⟨g, g', w⟩ => liftSucc P Q n g g' w
-set_option linter.uppercaseLean3 false in
-#align category_theory.ProjectiveResolution.lift CategoryTheory.ProjectiveResolution.lift
-
-/-- The resolution maps intertwine the lift of a morphism and that morphism. -/
-@[reassoc (attr := simp)]
-theorem lift_commutes {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
-    (Q : ProjectiveResolution Z) : lift f P Q ≫ Q.π = P.π ≫ (ChainComplex.single₀ C).map f := by
-  ext; simp [lift, liftZero]
-set_option linter.uppercaseLean3 false in
-#align category_theory.ProjectiveResolution.lift_commutes CategoryTheory.ProjectiveResolution.lift_commutes
-
-@[reassoc (attr := simp)]
-theorem lift_commutes_zero {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
-    (Q : ProjectiveResolution Z) :
-    (lift f P Q).f 0 ≫ Q.π.f 0 = P.π.f 0 ≫ f :=
-  (HomologicalComplex.congr_hom (lift_commutes f P Q) 0).trans (by simp)
-
--- Now that we've checked this property of the lift,
--- we can seal away the actual definition.
-end ProjectiveResolution
-
-end
-
-namespace ProjectiveResolution
-
-variable [HasZeroObject C] [Preadditive C] [HasEqualizers C] [HasImages C]
-
-/-- An auxiliary definition for `liftHomotopyZero`. -/
-def liftHomotopyZeroZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
-    (f : P.complex ⟶ Q.complex) (comm : f ≫ Q.π = 0) : P.complex.X 0 ⟶ Q.complex.X 1 :=
-  Exact.lift (f.f 0) (Q.complex.d 1 0) (Q.π.f 0) Q.exact₀
-    (congr_fun (congr_arg HomologicalComplex.Hom.f comm) 0)
-set_option linter.uppercaseLean3 false in
-#align category_theory.ProjectiveResolution.lift_homotopy_zero_zero CategoryTheory.ProjectiveResolution.liftHomotopyZeroZero
-
-/-- An auxiliary definition for `liftHomotopyZero`. -/
-def liftHomotopyZeroOne {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
-    (f : P.complex ⟶ Q.complex) (comm : f ≫ Q.π = 0) : P.complex.X 1 ⟶ Q.complex.X 2 :=
-  Exact.lift (f.f 1 - P.complex.d 1 0 ≫ liftHomotopyZeroZero f comm) (Q.complex.d 2 1)
-    (Q.complex.d 1 0) (Q.exact _) (by simp [liftHomotopyZeroZero])
-set_option linter.uppercaseLean3 false in
-#align category_theory.ProjectiveResolution.lift_homotopy_zero_one CategoryTheory.ProjectiveResolution.liftHomotopyZeroOne
-
-/-- An auxiliary definition for `liftHomotopyZero`. -/
-def liftHomotopyZeroSucc {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
-    (f : P.complex ⟶ Q.complex) (n : ℕ) (g : P.complex.X n ⟶ Q.complex.X (n + 1))
-    (g' : P.complex.X (n + 1) ⟶ Q.complex.X (n + 2))
-    (w : f.f (n + 1) = P.complex.d (n + 1) n ≫ g + g' ≫ Q.complex.d (n + 2) (n + 1)) :
-    P.complex.X (n + 2) ⟶ Q.complex.X (n + 3) :=
-  Exact.lift (f.f (n + 2) - P.complex.d (n + 2) (n + 1) ≫ g') (Q.complex.d (n + 3) (n + 2))
-    (Q.complex.d (n + 2) (n + 1)) (Q.exact _) (by simp [w])
-set_option linter.uppercaseLean3 false in
-#align category_theory.ProjectiveResolution.lift_homotopy_zero_succ CategoryTheory.ProjectiveResolution.liftHomotopyZeroSucc
-
-/-- Any lift of the zero morphism is homotopic to zero. -/
-def liftHomotopyZero {Y Z : C} {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
-    (f : P.complex ⟶ Q.complex) (comm : f ≫ Q.π = 0) : Homotopy f 0 :=
-  Homotopy.mkInductive _ (liftHomotopyZeroZero f comm) (by simp [liftHomotopyZeroZero])
-    (liftHomotopyZeroOne f comm) (by simp [liftHomotopyZeroOne]) fun n ⟨g, g', w⟩ =>
-    ⟨liftHomotopyZeroSucc f n g g' w, by simp [liftHomotopyZeroSucc, w]⟩
-set_option linter.uppercaseLean3 false in
-#align category_theory.ProjectiveResolution.lift_homotopy_zero CategoryTheory.ProjectiveResolution.liftHomotopyZero
-
-/-- Two lifts of the same morphism are homotopic. -/
-def liftHomotopy {Y Z : C} (f : Y ⟶ Z) {P : ProjectiveResolution Y} {Q : ProjectiveResolution Z}
-    (g h : P.complex ⟶ Q.complex) (g_comm : g ≫ Q.π = P.π ≫ (ChainComplex.single₀ C).map f)
-    (h_comm : h ≫ Q.π = P.π ≫ (ChainComplex.single₀ C).map f) : Homotopy g h :=
-  Homotopy.equivSubZero.invFun (liftHomotopyZero _ (by simp [g_comm, h_comm]))
-set_option linter.uppercaseLean3 false in
-#align category_theory.ProjectiveResolution.lift_homotopy CategoryTheory.ProjectiveResolution.liftHomotopy
-
-/-- The lift of the identity morphism is homotopic to the identity chain map. -/
-def liftIdHomotopy (X : C) (P : ProjectiveResolution X) : Homotopy (lift (𝟙 X) P P) (𝟙 P.complex) :=
-  by apply liftHomotopy (𝟙 X) <;> simp
-set_option linter.uppercaseLean3 false in
-#align category_theory.ProjectiveResolution.lift_id_homotopy CategoryTheory.ProjectiveResolution.liftIdHomotopy
-
-/-- The lift of a composition is homotopic to the composition of the lifts. -/
-def liftCompHomotopy {X Y Z : C} (f : X ⟶ Y) (g : Y ⟶ Z) (P : ProjectiveResolution X)
-    (Q : ProjectiveResolution Y) (R : ProjectiveResolution Z) :
-    Homotopy (lift (f ≫ g) P R) (lift f P Q ≫ lift g Q R) := by
-  apply liftHomotopy (f ≫ g) <;> simp
-set_option linter.uppercaseLean3 false in
-#align category_theory.ProjectiveResolution.lift_comp_homotopy CategoryTheory.ProjectiveResolution.liftCompHomotopy
-
--- We don't care about the actual definitions of these homotopies.
-/-- Any two projective resolutions are homotopy equivalent. -/
-def homotopyEquiv {X : C} (P Q : ProjectiveResolution X) : HomotopyEquiv P.complex Q.complex where
-  hom := lift (𝟙 X) P Q
-  inv := lift (𝟙 X) Q P
-  homotopyHomInvId := by
-    refine' (liftCompHomotopy (𝟙 X) (𝟙 X) P Q P).symm.trans _
-    simp only [Category.id_comp]
-    apply liftIdHomotopy
-  homotopyInvHomId := by
-    refine' (liftCompHomotopy (𝟙 X) (𝟙 X) Q P Q).symm.trans _
-    simp only [Category.id_comp]
-    apply liftIdHomotopy
-set_option linter.uppercaseLean3 false in
-#align category_theory.ProjectiveResolution.homotopy_equiv CategoryTheory.ProjectiveResolution.homotopyEquiv
-
-@[reassoc (attr := simp)]
-theorem homotopyEquiv_hom_π {X : C} (P Q : ProjectiveResolution X) :
-    (homotopyEquiv P Q).hom ≫ Q.π = P.π := by simp [homotopyEquiv]
-set_option linter.uppercaseLean3 false in
-#align category_theory.ProjectiveResolution.homotopy_equiv_hom_π CategoryTheory.ProjectiveResolution.homotopyEquiv_hom_π
-
-@[reassoc (attr := simp)]
-theorem homotopyEquiv_inv_π {X : C} (P Q : ProjectiveResolution X) :
-    (homotopyEquiv P Q).inv ≫ P.π = Q.π := by simp [homotopyEquiv]
-set_option linter.uppercaseLean3 false in
-#align category_theory.ProjectiveResolution.homotopy_equiv_inv_π CategoryTheory.ProjectiveResolution.homotopyEquiv_inv_π
-
 end ProjectiveResolution
 
-section
-
-variable [HasZeroMorphisms C] [HasZeroObject C] [HasEqualizers C] [HasImages C]
-
-def projectiveResolution (Z : C) [HasProjectiveResolution Z] : ProjectiveResolution Z :=
-  HasProjectiveResolution.out.some
-
--- porting note: this was named `projective_resolution` in mathlib 3. As there was also a need
--- for a definition of `ProjectiveResolution Z` given `(Z : projectiveResolution Z)`, it
--- seemed more consistent to have `projectiveResolution Z : ProjectiveResolution Z`
--- and `projectiveResolution.complex Z : ChainComplex C ℕ`
-/-- An arbitrarily chosen projective resolution of an object. -/
-abbrev projectiveResolution.complex (Z : C) [HasProjectiveResolution Z] : ChainComplex C ℕ :=
-  (projectiveResolution Z).complex
-#align category_theory.projective_resolution CategoryTheory.projectiveResolution.complex
-
-/-- The chain map from the arbitrarily chosen projective resolution
-`projectiveResolution.complex Z` back to the chain complex consisting
-of `Z` supported in degree `0`. -/
-abbrev projectiveResolution.π (Z : C) [HasProjectiveResolution Z] :
-    projectiveResolution.complex Z ⟶ (ChainComplex.single₀ C).obj Z :=
-  (projectiveResolution Z).π
-#align category_theory.projective_resolution.π CategoryTheory.projectiveResolution.π
-
-/-- The lift of a morphism to a chain map between the arbitrarily chosen projective resolutions. -/
-abbrev projectiveResolution.lift {X Y : C} (f : X ⟶ Y) [HasProjectiveResolution X]
-    [HasProjectiveResolution Y] :
-    projectiveResolution.complex X ⟶ projectiveResolution.complex Y :=
-  ProjectiveResolution.lift f _ _
-#align category_theory.projective_resolution.lift CategoryTheory.projectiveResolution.lift
-
-end
-
-variable (C)
-variable [Preadditive C] [HasZeroObject C] [HasEqualizers C] [HasImages C]
-  [HasProjectiveResolutions C]
-
-/-- Taking projective resolutions is functorial,
-if considered with target the homotopy category
-(`ℕ`-indexed chain complexes and chain maps up to homotopy).
--/
-def projectiveResolutions : C ⥤ HomotopyCategory C (ComplexShape.down ℕ) where
-  obj X := (HomotopyCategory.quotient _ _).obj (projectiveResolution.complex X)
-  map f := (HomotopyCategory.quotient _ _).map (projectiveResolution.lift f)
-  map_id X := by
-    rw [← (HomotopyCategory.quotient _ _).map_id]
-    apply HomotopyCategory.eq_of_homotopy
-    apply ProjectiveResolution.liftIdHomotopy
-  map_comp f g := by
-    rw [← (HomotopyCategory.quotient _ _).map_comp]
-    apply HomotopyCategory.eq_of_homotopy
-    apply ProjectiveResolution.liftCompHomotopy
-#align category_theory.projective_resolutions CategoryTheory.projectiveResolutions
-
 end CategoryTheory

324a7502

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

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

ecdd87a3

Diff

@@ -39,14 +39,12 @@ we can construct a functor `projectiveResolutions C : C ⥤ HomotopyCategory C`.
 
 noncomputable section
 
-open CategoryTheory
-
-open CategoryTheory.Limits
-
 universe v u
 
 namespace CategoryTheory
 
+open Limits
+
 variable {C : Type u} [Category.{v} C]
 
 open Projective
@@ -131,7 +129,12 @@ set_option linter.uppercaseLean3 false in
 #align category_theory.ProjectiveResolution.complex_d_succ_comp CategoryTheory.ProjectiveResolution.complex_d_succ_comp
 
 instance {Z : C} (P : ProjectiveResolution Z) (n : ℕ) : CategoryTheory.Epi (P.π.f n) := by
-  cases n <;> dsimp <;> infer_instance
+  cases n
+  · dsimp
+    infer_instance
+  · constructor
+    intros
+    apply (HomologicalComplex.isZero_single_obj_X _ _ _ _ (Nat.succ_ne_zero _)).eq_of_src
 
 /-- A projective object admits a trivial projective resolution: itself in degree 0. -/
 def self (Z : C) [CategoryTheory.Projective Z] : ProjectiveResolution Z where
@@ -139,10 +142,9 @@ def self (Z : C) [CategoryTheory.Projective Z] : ProjectiveResolution Z where
   π := 𝟙 ((ChainComplex.single₀ C).obj Z)
   projective n := by
     cases n
-    · dsimp
-      infer_instance
-    · dsimp
-      infer_instance
+    · simpa
+    · exact ((HomologicalComplex.isZero_single_obj_X (ComplexShape.down ℕ) 0 Z) _
+        (Nat.succ_ne_zero _)).projective
   exact₀ := by
     dsimp
     exact exact_zero_mono _
@@ -207,6 +209,12 @@ theorem lift_commutes {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
 set_option linter.uppercaseLean3 false in
 #align category_theory.ProjectiveResolution.lift_commutes CategoryTheory.ProjectiveResolution.lift_commutes
 
+@[reassoc (attr := simp)]
+theorem lift_commutes_zero {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
+    (Q : ProjectiveResolution Z) :
+    (lift f P Q).f 0 ≫ Q.π.f 0 = P.π.f 0 ≫ f :=
+  (HomologicalComplex.congr_hom (lift_commutes f P Q) 0).trans (by simp)
+
 -- Now that we've checked this property of the lift,
 -- we can seal away the actual definition.
 end ProjectiveResolution

324a7502

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.preadditive.projective_resolution
-! leanprover-community/mathlib commit 324a7502510e835cdbd3de1519b6c66b51fb2467
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Preadditive.Projective
 import Mathlib.Algebra.Homology.Single
 import Mathlib.Algebra.Homology.HomotopyCategory
 
+#align_import category_theory.preadditive.projective_resolution from "leanprover-community/mathlib"@"324a7502510e835cdbd3de1519b6c66b51fb2467"
+
 /-!
 # Projective resolutions

324a7502

chore: fix grammar in docs (#5668)

15cdb8ec

Diff

@@ -16,7 +16,7 @@ import Mathlib.Algebra.Homology.HomotopyCategory
 # Projective resolutions
 
 A projective resolution `P : ProjectiveResolution Z` of an object `Z : C` consists of
-a `ℕ`-indexed chain complex `P.complex` of projective objects,
+an `ℕ`-indexed chain complex `P.complex` of projective objects,
 along with a chain map `P.π` from `C` to the chain complex consisting just of `Z` in degree zero,
 so that the augmented chain complex is exact.

324a7502

chore: bump to nightly-2023-05-31 (#4530)

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>

01da6a3c

Diff

@@ -206,7 +206,7 @@ set_option linter.uppercaseLean3 false in
 @[reassoc (attr := simp)]
 theorem lift_commutes {Y Z : C} (f : Y ⟶ Z) (P : ProjectiveResolution Y)
     (Q : ProjectiveResolution Z) : lift f P Q ≫ Q.π = P.π ≫ (ChainComplex.single₀ C).map f := by
-  ext (_|_) <;> simp [lift, liftZero]
+  ext; simp [lift, liftZero]
 set_option linter.uppercaseLean3 false in
 #align category_theory.ProjectiveResolution.lift_commutes CategoryTheory.ProjectiveResolution.lift_commutes

324a7502

feat: port CategoryTheory.Preadditive.ProjectiveResolution (#3740)

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

3d2204e1

`category_theory.preadditive.projective_resolution` ⟷ `Mathlib.CategoryTheory.Preadditive.ProjectiveResolution`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 3 + 331

category_theory.preadditive.projective_resolution ⟷ Mathlib.CategoryTheory.Preadditive.ProjectiveResolution

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 3 + 331

`category_theory.preadditive.projective_resolution` ⟷ `Mathlib.CategoryTheory.Preadditive.ProjectiveResolution`