algebra.homology.quasi_iso | Mathlib porting status

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

956af7c7

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

50251fd6

bump to nightly-2024-04-14-09

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

f736ea6b

Diff

@@ -250,7 +250,8 @@ end ToSingle₀
 end HomologicalComplex.Hom
 
 variable {A : Type _} [Category A] [Abelian A] {B : Type _} [Category B] [Abelian B] (F : A ⥤ B)
-  [Functor.Additive F] [PreservesFiniteLimits F] [PreservesFiniteColimits F] [Faithful F]
+  [Functor.Additive F] [PreservesFiniteLimits F] [PreservesFiniteColimits F]
+  [CategoryTheory.Functor.Faithful F]
 
 #print CategoryTheory.Functor.quasiIso'_of_map_quasiIso' /-
 theorem CategoryTheory.Functor.quasiIso'_of_map_quasiIso' {C D : HomologicalComplex A c} (f : C ⟶ D)

50251fd6

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -148,7 +148,7 @@ theorem to_single₀_epi_at_zero [hf : QuasiIso' f] : Epi (f.f 0) :=
   constructor
   intro Z g h Hgh
   rw [← cokernel.π_desc (X.d 1 0) (f.f 0) (by rw [← f.2 1 0 rfl] <;> exact comp_zero), ←
-    to_single₀_cokernel_at_zero_iso_hom_eq] at Hgh 
+    to_single₀_cokernel_at_zero_iso_hom_eq] at Hgh
   rw [(@cancel_epi _ _ _ _ _ _ (epi_comp _ _) _ _).1 Hgh]
 #align homological_complex.hom.to_single₀_epi_at_zero HomologicalComplex.Hom.to_single₀_epi_at_zero
 -/
@@ -215,7 +215,7 @@ theorem from_single₀_mono_at_zero [hf : QuasiIso' f] : Mono (f.f 0) :=
   constructor
   intro Z g h Hgh
   rw [← kernel.lift_ι (X.d 0 1) (f.f 0) (by rw [f.2 0 1 rfl] <;> exact zero_comp), ←
-    from_single₀_kernel_at_zero_iso_inv_eq] at Hgh 
+    from_single₀_kernel_at_zero_iso_inv_eq] at Hgh
   rw [(@cancel_mono _ _ _ _ _ _ (mono_comp _ _) _ _).1 Hgh]
 #align homological_complex.hom.from_single₀_mono_at_zero HomologicalComplex.Hom.from_single₀_mono_at_zero
 -/

50251fd6

bump to nightly-2023-11-15-06

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

38c8ceef

Diff

@@ -158,7 +158,7 @@ theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso' f] : Exact (X.d 1 0) (f.f
   by
   rw [preadditive.exact_iff_homology_zero]
   have h : X.d 1 0 ≫ f.f 0 = 0 := by
-    simp only [← f.2 1 0 rfl, ChainComplex.single₀_obj_X_d, comp_zero]
+    simp only [← f.2 1 0 rfl, ChainComplex.single₀_obj_x_d, comp_zero]
   refine' ⟨h, Nonempty.intro (homology'IsoKernelDesc _ _ _ ≪≫ _)⟩
   · suffices is_iso (cokernel.desc _ _ h) by haveI := this; apply kernel.of_mono
     rw [← to_single₀_cokernel_at_zero_iso_hom_eq]
@@ -225,7 +225,7 @@ theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso' f] : Exact (f.f 0) (X.d
   by
   rw [preadditive.exact_iff_homology_zero]
   have h : f.f 0 ≫ X.d 0 1 = 0 := by
-    simp only [HomologicalComplex.Hom.comm, CochainComplex.single₀_obj_X_d, zero_comp]
+    simp only [HomologicalComplex.Hom.comm, CochainComplex.single₀_obj_x_d, zero_comp]
   refine' ⟨h, Nonempty.intro (homology'IsoCokernelLift _ _ _ ≪≫ _)⟩
   · suffices is_iso (kernel.lift (X.d 0 1) (f.f 0) h) by haveI := this; apply cokernel.of_epi
     rw [← from_single₀_kernel_at_zero_iso_inv_eq f]

50251fd6

bump to nightly-2023-10-29-06

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

abdd1870

Diff

@@ -36,45 +36,45 @@ variable [HasEqualizers V] [HasImages V] [HasImageMaps V] [HasCokernels V]
 
 variable {c : ComplexShape ι} {C D E : HomologicalComplex V c}
 
-#print QuasiIso /-
+#print QuasiIso' /-
 /-- A chain map is a quasi-isomorphism if it induces isomorphisms on homology.
 -/
-class QuasiIso (f : C ⟶ D) : Prop where
-  IsIso : ∀ i, IsIso ((homologyFunctor V c i).map f)
-#align quasi_iso QuasiIso
+class QuasiIso' (f : C ⟶ D) : Prop where
+  IsIso : ∀ i, IsIso ((homology'Functor V c i).map f)
+#align quasi_iso QuasiIso'
 -/
 
-attribute [instance] QuasiIso.isIso
+attribute [instance] QuasiIso'.isIso
 
-#print quasiIso_of_iso /-
-instance (priority := 100) quasiIso_of_iso (f : C ⟶ D) [IsIso f] : QuasiIso f
+#print quasiIso'_of_iso /-
+instance (priority := 100) quasiIso'_of_iso (f : C ⟶ D) [IsIso f] : QuasiIso' f
     where IsIso i :=
     by
-    change is_iso ((homologyFunctor V c i).mapIso (as_iso f)).Hom
+    change is_iso ((homology'Functor V c i).mapIso (as_iso f)).Hom
     infer_instance
-#align quasi_iso_of_iso quasiIso_of_iso
+#align quasi_iso_of_iso quasiIso'_of_iso
 -/
 
-#print quasiIso_comp /-
-instance quasiIso_comp (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso g] : QuasiIso (f ≫ g)
+#print quasiIso'_comp /-
+instance quasiIso'_comp (f : C ⟶ D) [QuasiIso' f] (g : D ⟶ E) [QuasiIso' g] : QuasiIso' (f ≫ g)
     where IsIso i := by
     rw [functor.map_comp]
     infer_instance
-#align quasi_iso_comp quasiIso_comp
+#align quasi_iso_comp quasiIso'_comp
 -/
 
-#print quasiIso_of_comp_left /-
-theorem quasiIso_of_comp_left (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso (f ≫ g)] :
-    QuasiIso g :=
-  { IsIso := fun i => IsIso.of_isIso_fac_left ((homologyFunctor V c i).map_comp f g).symm }
-#align quasi_iso_of_comp_left quasiIso_of_comp_left
+#print quasiIso'_of_comp_left /-
+theorem quasiIso'_of_comp_left (f : C ⟶ D) [QuasiIso' f] (g : D ⟶ E) [QuasiIso' (f ≫ g)] :
+    QuasiIso' g :=
+  { IsIso := fun i => IsIso.of_isIso_fac_left ((homology'Functor V c i).map_comp f g).symm }
+#align quasi_iso_of_comp_left quasiIso'_of_comp_left
 -/
 
-#print quasiIso_of_comp_right /-
-theorem quasiIso_of_comp_right (f : C ⟶ D) (g : D ⟶ E) [QuasiIso g] [QuasiIso (f ≫ g)] :
-    QuasiIso f :=
-  { IsIso := fun i => IsIso.of_isIso_fac_right ((homologyFunctor V c i).map_comp f g).symm }
-#align quasi_iso_of_comp_right quasiIso_of_comp_right
+#print quasiIso'_of_comp_right /-
+theorem quasiIso'_of_comp_right (f : C ⟶ D) (g : D ⟶ E) [QuasiIso' g] [QuasiIso' (f ≫ g)] :
+    QuasiIso' f :=
+  { IsIso := fun i => IsIso.of_isIso_fac_right ((homology'Functor V c i).map_comp f g).symm }
+#align quasi_iso_of_comp_right quasiIso'_of_comp_right
 -/
 
 namespace HomotopyEquiv
@@ -84,25 +84,25 @@ section
 variable {W : Type _} [Category W] [Preadditive W] [HasCokernels W] [HasImages W] [HasEqualizers W]
   [HasZeroObject W] [HasImageMaps W]
 
-#print HomotopyEquiv.toQuasiIso /-
+#print HomotopyEquiv.toQuasiIso' /-
 /-- An homotopy equivalence is a quasi-isomorphism. -/
-theorem toQuasiIso {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) : QuasiIso e.Hom :=
+theorem toQuasiIso' {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) : QuasiIso' e.Hom :=
   ⟨fun i => by
-    refine' ⟨⟨(homologyFunctor W c i).map e.inv, _⟩⟩
-    simp only [← functor.map_comp, ← (homologyFunctor W c i).map_id]
-    constructor <;> apply homology_map_eq_of_homotopy
+    refine' ⟨⟨(homology'Functor W c i).map e.inv, _⟩⟩
+    simp only [← functor.map_comp, ← (homology'Functor W c i).map_id]
+    constructor <;> apply homology'_map_eq_of_homotopy
     exacts [e.homotopy_hom_inv_id, e.homotopy_inv_hom_id]⟩
-#align homotopy_equiv.to_quasi_iso HomotopyEquiv.toQuasiIso
+#align homotopy_equiv.to_quasi_iso HomotopyEquiv.toQuasiIso'
 -/
 
-#print HomotopyEquiv.toQuasiIso_inv /-
-theorem toQuasiIso_inv {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) (i : ι) :
-    (@asIso _ _ _ _ _ (e.toQuasiIso.1 i)).inv = (homologyFunctor W c i).map e.inv :=
+#print HomotopyEquiv.toQuasiIso'_inv /-
+theorem toQuasiIso'_inv {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) (i : ι) :
+    (@asIso _ _ _ _ _ (e.toQuasiIso'.1 i)).inv = (homology'Functor W c i).map e.inv :=
   by
   symm
-  simp only [← iso.hom_comp_eq_id, as_iso_hom, ← functor.map_comp, ← (homologyFunctor W c i).map_id,
-    homology_map_eq_of_homotopy e.homotopy_hom_inv_id _]
-#align homotopy_equiv.to_quasi_iso_inv HomotopyEquiv.toQuasiIso_inv
+  simp only [← iso.hom_comp_eq_id, as_iso_hom, ← functor.map_comp, ←
+    (homology'Functor W c i).map_id, homology'_map_eq_of_homotopy e.homotopy_hom_inv_id _]
+#align homotopy_equiv.to_quasi_iso_inv HomotopyEquiv.toQuasiIso'_inv
 -/
 
 end
@@ -117,33 +117,33 @@ variable {W : Type _} [Category W] [Abelian W]
 
 section
 
-variable {X : ChainComplex W ℕ} {Y : W} (f : X ⟶ (ChainComplex.single₀ _).obj Y) [hf : QuasiIso f]
+variable {X : ChainComplex W ℕ} {Y : W} (f : X ⟶ (ChainComplex.single₀ _).obj Y) [hf : QuasiIso' f]
 
 #print HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso /-
 /-- If a chain map `f : X ⟶ Y[0]` is a quasi-isomorphism, then the cokernel of the differential
 `d : X₁ → X₀` is isomorphic to `Y.` -/
 noncomputable def toSingle₀CokernelAtZeroIso : cokernel (X.d 1 0) ≅ Y :=
-  X.homologyZeroIso.symm.trans
-    ((@asIso _ _ _ _ _ (hf.1 0)).trans ((ChainComplex.homologyFunctor0Single₀ W).app Y))
+  X.homology'ZeroIso.symm.trans
+    ((@asIso _ _ _ _ _ (hf.1 0)).trans ((ChainComplex.homology'Functor0Single₀ W).app Y))
 #align homological_complex.hom.to_single₀_cokernel_at_zero_iso HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso
 -/
 
 #print HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso_hom_eq /-
-theorem toSingle₀CokernelAtZeroIso_hom_eq [hf : QuasiIso f] :
+theorem toSingle₀CokernelAtZeroIso_hom_eq [hf : QuasiIso' f] :
     f.toSingle₀CokernelAtZeroIso.Hom =
       cokernel.desc (X.d 1 0) (f.f 0) (by rw [← f.2 1 0 rfl] <;> exact comp_zero) :=
   by
   ext
-  dsimp only [to_single₀_cokernel_at_zero_iso, ChainComplex.homologyZeroIso, homologyOfZeroRight,
-    homology.mapIso, ChainComplex.homologyFunctor0Single₀, cokernel.map]
+  dsimp only [to_single₀_cokernel_at_zero_iso, ChainComplex.homology'ZeroIso, homology'OfZeroRight,
+    homology'.mapIso, ChainComplex.homology'Functor0Single₀, cokernel.map]
   dsimp
-  simp only [cokernel.π_desc, category.assoc, homology.map_desc, cokernel.π_desc_assoc]
-  simp [homology.desc, iso.refl_inv (X.X 0)]
+  simp only [cokernel.π_desc, category.assoc, homology'.map_desc, cokernel.π_desc_assoc]
+  simp [homology'.desc, iso.refl_inv (X.X 0)]
 #align homological_complex.hom.to_single₀_cokernel_at_zero_iso_hom_eq HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso_hom_eq
 -/
 
 #print HomologicalComplex.Hom.to_single₀_epi_at_zero /-
-theorem to_single₀_epi_at_zero [hf : QuasiIso f] : Epi (f.f 0) :=
+theorem to_single₀_epi_at_zero [hf : QuasiIso' f] : Epi (f.f 0) :=
   by
   constructor
   intro Z g h Hgh
@@ -154,12 +154,12 @@ theorem to_single₀_epi_at_zero [hf : QuasiIso f] : Epi (f.f 0) :=
 -/
 
 #print HomologicalComplex.Hom.to_single₀_exact_d_f_at_zero /-
-theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f 0) :=
+theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso' f] : Exact (X.d 1 0) (f.f 0) :=
   by
   rw [preadditive.exact_iff_homology_zero]
   have h : X.d 1 0 ≫ f.f 0 = 0 := by
     simp only [← f.2 1 0 rfl, ChainComplex.single₀_obj_X_d, comp_zero]
-  refine' ⟨h, Nonempty.intro (homologyIsoKernelDesc _ _ _ ≪≫ _)⟩
+  refine' ⟨h, Nonempty.intro (homology'IsoKernelDesc _ _ _ ≪≫ _)⟩
   · suffices is_iso (cokernel.desc _ _ h) by haveI := this; apply kernel.of_mono
     rw [← to_single₀_cokernel_at_zero_iso_hom_eq]
     infer_instance
@@ -167,12 +167,12 @@ theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f
 -/
 
 #print HomologicalComplex.Hom.to_single₀_exact_at_succ /-
-theorem to_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
+theorem to_single₀_exact_at_succ [hf : QuasiIso' f] (n : ℕ) :
     Exact (X.d (n + 2) (n + 1)) (X.d (n + 1) n) :=
-  (Preadditive.exact_iff_homology_zero _ _).2
+  (Preadditive.exact_iff_homology'_zero _ _).2
     ⟨X.d_comp_d _ _ _,
-      ⟨(ChainComplex.homologySuccIso _ _).symm.trans
-          ((@asIso _ _ _ _ _ (hf.1 (n + 1))).trans homologyZeroZero)⟩⟩
+      ⟨(ChainComplex.homology'SuccIso _ _).symm.trans
+          ((@asIso _ _ _ _ _ (hf.1 (n + 1))).trans homology'ZeroZero)⟩⟩
 #align homological_complex.hom.to_single₀_exact_at_succ HomologicalComplex.Hom.to_single₀_exact_at_succ
 -/
 
@@ -185,32 +185,32 @@ variable {X : CochainComplex W ℕ} {Y : W} (f : (CochainComplex.single₀ _).ob
 #print HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso /-
 /-- If a cochain map `f : Y[0] ⟶ X` is a quasi-isomorphism, then the kernel of the differential
 `d : X₀ → X₁` is isomorphic to `Y.` -/
-noncomputable def fromSingle₀KernelAtZeroIso [hf : QuasiIso f] : kernel (X.d 0 1) ≅ Y :=
-  X.homologyZeroIso.symm.trans
+noncomputable def fromSingle₀KernelAtZeroIso [hf : QuasiIso' f] : kernel (X.d 0 1) ≅ Y :=
+  X.homology'ZeroIso.symm.trans
     ((@asIso _ _ _ _ _ (hf.1 0)).symm.trans ((CochainComplex.homologyFunctor0Single₀ W).app Y))
 #align homological_complex.hom.from_single₀_kernel_at_zero_iso HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso
 -/
 
 #print HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso_inv_eq /-
-theorem fromSingle₀KernelAtZeroIso_inv_eq [hf : QuasiIso f] :
+theorem fromSingle₀KernelAtZeroIso_inv_eq [hf : QuasiIso' f] :
     f.fromSingle₀KernelAtZeroIso.inv =
       kernel.lift (X.d 0 1) (f.f 0) (by rw [f.2 0 1 rfl] <;> exact zero_comp) :=
   by
   ext
-  dsimp only [from_single₀_kernel_at_zero_iso, CochainComplex.homologyZeroIso, homologyOfZeroLeft,
-    homology.mapIso, CochainComplex.homologyFunctor0Single₀, kernel.map]
+  dsimp only [from_single₀_kernel_at_zero_iso, CochainComplex.homology'ZeroIso, homology'OfZeroLeft,
+    homology'.mapIso, CochainComplex.homologyFunctor0Single₀, kernel.map]
   simp only [iso.trans_inv, iso.app_inv, iso.symm_inv, category.assoc, equalizer_as_kernel,
     kernel.lift_ι]
   dsimp
-  simp only [category.assoc, homology.π_map, cokernel_zero_iso_target_hom,
-    cokernel_iso_of_eq_hom_comp_desc, kernel_subobject_arrow, homology.π_map_assoc,
+  simp only [category.assoc, homology'.π_map, cokernel_zero_iso_target_hom,
+    cokernel_iso_of_eq_hom_comp_desc, kernel_subobject_arrow, homology'.π_map_assoc,
     is_iso.inv_comp_eq]
-  simp [homology.π, kernel_subobject_map_comp, iso.refl_hom (X.X 0), category.comp_id]
+  simp [homology'.π, kernel_subobject_map_comp, iso.refl_hom (X.X 0), category.comp_id]
 #align homological_complex.hom.from_single₀_kernel_at_zero_iso_inv_eq HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso_inv_eq
 -/
 
 #print HomologicalComplex.Hom.from_single₀_mono_at_zero /-
-theorem from_single₀_mono_at_zero [hf : QuasiIso f] : Mono (f.f 0) :=
+theorem from_single₀_mono_at_zero [hf : QuasiIso' f] : Mono (f.f 0) :=
   by
   constructor
   intro Z g h Hgh
@@ -221,12 +221,12 @@ theorem from_single₀_mono_at_zero [hf : QuasiIso f] : Mono (f.f 0) :=
 -/
 
 #print HomologicalComplex.Hom.from_single₀_exact_f_d_at_zero /-
-theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso f] : Exact (f.f 0) (X.d 0 1) :=
+theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso' f] : Exact (f.f 0) (X.d 0 1) :=
   by
   rw [preadditive.exact_iff_homology_zero]
   have h : f.f 0 ≫ X.d 0 1 = 0 := by
     simp only [HomologicalComplex.Hom.comm, CochainComplex.single₀_obj_X_d, zero_comp]
-  refine' ⟨h, Nonempty.intro (homologyIsoCokernelLift _ _ _ ≪≫ _)⟩
+  refine' ⟨h, Nonempty.intro (homology'IsoCokernelLift _ _ _ ≪≫ _)⟩
   · suffices is_iso (kernel.lift (X.d 0 1) (f.f 0) h) by haveI := this; apply cokernel.of_epi
     rw [← from_single₀_kernel_at_zero_iso_inv_eq f]
     infer_instance
@@ -234,12 +234,12 @@ theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso f] : Exact (f.f 0) (X.d
 -/
 
 #print HomologicalComplex.Hom.from_single₀_exact_at_succ /-
-theorem from_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
+theorem from_single₀_exact_at_succ [hf : QuasiIso' f] (n : ℕ) :
     Exact (X.d n (n + 1)) (X.d (n + 1) (n + 2)) :=
-  (Preadditive.exact_iff_homology_zero _ _).2
+  (Preadditive.exact_iff_homology'_zero _ _).2
     ⟨X.d_comp_d _ _ _,
-      ⟨(CochainComplex.homologySuccIso _ _).symm.trans
-          ((@asIso _ _ _ _ _ (hf.1 (n + 1))).symm.trans homologyZeroZero)⟩⟩
+      ⟨(CochainComplex.homology'SuccIso _ _).symm.trans
+          ((@asIso _ _ _ _ _ (hf.1 (n + 1))).symm.trans homology'ZeroZero)⟩⟩
 #align homological_complex.hom.from_single₀_exact_at_succ HomologicalComplex.Hom.from_single₀_exact_at_succ
 -/
 
@@ -252,15 +252,15 @@ end HomologicalComplex.Hom
 variable {A : Type _} [Category A] [Abelian A] {B : Type _} [Category B] [Abelian B] (F : A ⥤ B)
   [Functor.Additive F] [PreservesFiniteLimits F] [PreservesFiniteColimits F] [Faithful F]
 
-#print CategoryTheory.Functor.quasiIso_of_map_quasiIso /-
-theorem CategoryTheory.Functor.quasiIso_of_map_quasiIso {C D : HomologicalComplex A c} (f : C ⟶ D)
-    (hf : QuasiIso ((F.mapHomologicalComplex _).map f)) : QuasiIso f :=
+#print CategoryTheory.Functor.quasiIso'_of_map_quasiIso' /-
+theorem CategoryTheory.Functor.quasiIso'_of_map_quasiIso' {C D : HomologicalComplex A c} (f : C ⟶ D)
+    (hf : QuasiIso' ((F.mapHomologicalComplex _).map f)) : QuasiIso' f :=
   ⟨fun i =>
-    haveI : is_iso (F.map ((homologyFunctor A c i).map f)) :=
+    haveI : is_iso (F.map ((homology'Functor A c i).map f)) :=
       by
       rw [← functor.comp_map, ← nat_iso.naturality_2 (F.homology_functor_iso i) f, functor.comp_map]
       infer_instance
     is_iso_of_reflects_iso _ F⟩
-#align category_theory.functor.quasi_iso_of_map_quasi_iso CategoryTheory.Functor.quasiIso_of_map_quasiIso
+#align category_theory.functor.quasi_iso_of_map_quasi_iso CategoryTheory.Functor.quasiIso'_of_map_quasiIso'
 -/

50251fd6

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Joël Riou
 -/
-import Mathbin.Algebra.Homology.Homotopy
-import Mathbin.CategoryTheory.Abelian.Homology
+import Algebra.Homology.Homotopy
+import CategoryTheory.Abelian.Homology
 
 #align_import algebra.homology.quasi_iso from "leanprover-community/mathlib"@"50251fd6309cca5ca2e747882ffecd2729f38c5d"

50251fd6

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Joël Riou
-
-! This file was ported from Lean 3 source module algebra.homology.quasi_iso
-! leanprover-community/mathlib commit 50251fd6309cca5ca2e747882ffecd2729f38c5d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.Homology.Homotopy
 import Mathbin.CategoryTheory.Abelian.Homology
 
+#align_import algebra.homology.quasi_iso from "leanprover-community/mathlib"@"50251fd6309cca5ca2e747882ffecd2729f38c5d"
+
 /-!
 # Quasi-isomorphisms

50251fd6

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -39,36 +39,46 @@ variable [HasEqualizers V] [HasImages V] [HasImageMaps V] [HasCokernels V]
 
 variable {c : ComplexShape ι} {C D E : HomologicalComplex V c}
 
+#print QuasiIso /-
 /-- A chain map is a quasi-isomorphism if it induces isomorphisms on homology.
 -/
 class QuasiIso (f : C ⟶ D) : Prop where
   IsIso : ∀ i, IsIso ((homologyFunctor V c i).map f)
 #align quasi_iso QuasiIso
+-/
 
 attribute [instance] QuasiIso.isIso
 
+#print quasiIso_of_iso /-
 instance (priority := 100) quasiIso_of_iso (f : C ⟶ D) [IsIso f] : QuasiIso f
     where IsIso i :=
     by
     change is_iso ((homologyFunctor V c i).mapIso (as_iso f)).Hom
     infer_instance
 #align quasi_iso_of_iso quasiIso_of_iso
+-/
 
+#print quasiIso_comp /-
 instance quasiIso_comp (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso g] : QuasiIso (f ≫ g)
     where IsIso i := by
     rw [functor.map_comp]
     infer_instance
 #align quasi_iso_comp quasiIso_comp
+-/
 
+#print quasiIso_of_comp_left /-
 theorem quasiIso_of_comp_left (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso (f ≫ g)] :
     QuasiIso g :=
   { IsIso := fun i => IsIso.of_isIso_fac_left ((homologyFunctor V c i).map_comp f g).symm }
 #align quasi_iso_of_comp_left quasiIso_of_comp_left
+-/
 
+#print quasiIso_of_comp_right /-
 theorem quasiIso_of_comp_right (f : C ⟶ D) (g : D ⟶ E) [QuasiIso g] [QuasiIso (f ≫ g)] :
     QuasiIso f :=
   { IsIso := fun i => IsIso.of_isIso_fac_right ((homologyFunctor V c i).map_comp f g).symm }
 #align quasi_iso_of_comp_right quasiIso_of_comp_right
+-/
 
 namespace HomotopyEquiv
 
@@ -77,6 +87,7 @@ section
 variable {W : Type _} [Category W] [Preadditive W] [HasCokernels W] [HasImages W] [HasEqualizers W]
   [HasZeroObject W] [HasImageMaps W]
 
+#print HomotopyEquiv.toQuasiIso /-
 /-- An homotopy equivalence is a quasi-isomorphism. -/
 theorem toQuasiIso {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) : QuasiIso e.Hom :=
   ⟨fun i => by
@@ -85,7 +96,9 @@ theorem toQuasiIso {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) : Quas
     constructor <;> apply homology_map_eq_of_homotopy
     exacts [e.homotopy_hom_inv_id, e.homotopy_inv_hom_id]⟩
 #align homotopy_equiv.to_quasi_iso HomotopyEquiv.toQuasiIso
+-/
 
+#print HomotopyEquiv.toQuasiIso_inv /-
 theorem toQuasiIso_inv {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) (i : ι) :
     (@asIso _ _ _ _ _ (e.toQuasiIso.1 i)).inv = (homologyFunctor W c i).map e.inv :=
   by
@@ -93,6 +106,7 @@ theorem toQuasiIso_inv {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) (i
   simp only [← iso.hom_comp_eq_id, as_iso_hom, ← functor.map_comp, ← (homologyFunctor W c i).map_id,
     homology_map_eq_of_homotopy e.homotopy_hom_inv_id _]
 #align homotopy_equiv.to_quasi_iso_inv HomotopyEquiv.toQuasiIso_inv
+-/
 
 end
 
@@ -108,13 +122,16 @@ section
 
 variable {X : ChainComplex W ℕ} {Y : W} (f : X ⟶ (ChainComplex.single₀ _).obj Y) [hf : QuasiIso f]
 
+#print HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso /-
 /-- If a chain map `f : X ⟶ Y[0]` is a quasi-isomorphism, then the cokernel of the differential
 `d : X₁ → X₀` is isomorphic to `Y.` -/
 noncomputable def toSingle₀CokernelAtZeroIso : cokernel (X.d 1 0) ≅ Y :=
   X.homologyZeroIso.symm.trans
     ((@asIso _ _ _ _ _ (hf.1 0)).trans ((ChainComplex.homologyFunctor0Single₀ W).app Y))
 #align homological_complex.hom.to_single₀_cokernel_at_zero_iso HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso
+-/
 
+#print HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso_hom_eq /-
 theorem toSingle₀CokernelAtZeroIso_hom_eq [hf : QuasiIso f] :
     f.toSingle₀CokernelAtZeroIso.Hom =
       cokernel.desc (X.d 1 0) (f.f 0) (by rw [← f.2 1 0 rfl] <;> exact comp_zero) :=
@@ -126,7 +143,9 @@ theorem toSingle₀CokernelAtZeroIso_hom_eq [hf : QuasiIso f] :
   simp only [cokernel.π_desc, category.assoc, homology.map_desc, cokernel.π_desc_assoc]
   simp [homology.desc, iso.refl_inv (X.X 0)]
 #align homological_complex.hom.to_single₀_cokernel_at_zero_iso_hom_eq HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso_hom_eq
+-/
 
+#print HomologicalComplex.Hom.to_single₀_epi_at_zero /-
 theorem to_single₀_epi_at_zero [hf : QuasiIso f] : Epi (f.f 0) :=
   by
   constructor
@@ -135,7 +154,9 @@ theorem to_single₀_epi_at_zero [hf : QuasiIso f] : Epi (f.f 0) :=
     to_single₀_cokernel_at_zero_iso_hom_eq] at Hgh 
   rw [(@cancel_epi _ _ _ _ _ _ (epi_comp _ _) _ _).1 Hgh]
 #align homological_complex.hom.to_single₀_epi_at_zero HomologicalComplex.Hom.to_single₀_epi_at_zero
+-/
 
+#print HomologicalComplex.Hom.to_single₀_exact_d_f_at_zero /-
 theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f 0) :=
   by
   rw [preadditive.exact_iff_homology_zero]
@@ -146,7 +167,9 @@ theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f
     rw [← to_single₀_cokernel_at_zero_iso_hom_eq]
     infer_instance
 #align homological_complex.hom.to_single₀_exact_d_f_at_zero HomologicalComplex.Hom.to_single₀_exact_d_f_at_zero
+-/
 
+#print HomologicalComplex.Hom.to_single₀_exact_at_succ /-
 theorem to_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
     Exact (X.d (n + 2) (n + 1)) (X.d (n + 1) n) :=
   (Preadditive.exact_iff_homology_zero _ _).2
@@ -154,6 +177,7 @@ theorem to_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
       ⟨(ChainComplex.homologySuccIso _ _).symm.trans
           ((@asIso _ _ _ _ _ (hf.1 (n + 1))).trans homologyZeroZero)⟩⟩
 #align homological_complex.hom.to_single₀_exact_at_succ HomologicalComplex.Hom.to_single₀_exact_at_succ
+-/
 
 end
 
@@ -161,13 +185,16 @@ section
 
 variable {X : CochainComplex W ℕ} {Y : W} (f : (CochainComplex.single₀ _).obj Y ⟶ X)
 
+#print HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso /-
 /-- If a cochain map `f : Y[0] ⟶ X` is a quasi-isomorphism, then the kernel of the differential
 `d : X₀ → X₁` is isomorphic to `Y.` -/
 noncomputable def fromSingle₀KernelAtZeroIso [hf : QuasiIso f] : kernel (X.d 0 1) ≅ Y :=
   X.homologyZeroIso.symm.trans
     ((@asIso _ _ _ _ _ (hf.1 0)).symm.trans ((CochainComplex.homologyFunctor0Single₀ W).app Y))
 #align homological_complex.hom.from_single₀_kernel_at_zero_iso HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso
+-/
 
+#print HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso_inv_eq /-
 theorem fromSingle₀KernelAtZeroIso_inv_eq [hf : QuasiIso f] :
     f.fromSingle₀KernelAtZeroIso.inv =
       kernel.lift (X.d 0 1) (f.f 0) (by rw [f.2 0 1 rfl] <;> exact zero_comp) :=
@@ -183,7 +210,9 @@ theorem fromSingle₀KernelAtZeroIso_inv_eq [hf : QuasiIso f] :
     is_iso.inv_comp_eq]
   simp [homology.π, kernel_subobject_map_comp, iso.refl_hom (X.X 0), category.comp_id]
 #align homological_complex.hom.from_single₀_kernel_at_zero_iso_inv_eq HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso_inv_eq
+-/
 
+#print HomologicalComplex.Hom.from_single₀_mono_at_zero /-
 theorem from_single₀_mono_at_zero [hf : QuasiIso f] : Mono (f.f 0) :=
   by
   constructor
@@ -192,7 +221,9 @@ theorem from_single₀_mono_at_zero [hf : QuasiIso f] : Mono (f.f 0) :=
     from_single₀_kernel_at_zero_iso_inv_eq] at Hgh 
   rw [(@cancel_mono _ _ _ _ _ _ (mono_comp _ _) _ _).1 Hgh]
 #align homological_complex.hom.from_single₀_mono_at_zero HomologicalComplex.Hom.from_single₀_mono_at_zero
+-/
 
+#print HomologicalComplex.Hom.from_single₀_exact_f_d_at_zero /-
 theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso f] : Exact (f.f 0) (X.d 0 1) :=
   by
   rw [preadditive.exact_iff_homology_zero]
@@ -203,7 +234,9 @@ theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso f] : Exact (f.f 0) (X.d
     rw [← from_single₀_kernel_at_zero_iso_inv_eq f]
     infer_instance
 #align homological_complex.hom.from_single₀_exact_f_d_at_zero HomologicalComplex.Hom.from_single₀_exact_f_d_at_zero
+-/
 
+#print HomologicalComplex.Hom.from_single₀_exact_at_succ /-
 theorem from_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
     Exact (X.d n (n + 1)) (X.d (n + 1) (n + 2)) :=
   (Preadditive.exact_iff_homology_zero _ _).2
@@ -211,6 +244,7 @@ theorem from_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
       ⟨(CochainComplex.homologySuccIso _ _).symm.trans
           ((@asIso _ _ _ _ _ (hf.1 (n + 1))).symm.trans homologyZeroZero)⟩⟩
 #align homological_complex.hom.from_single₀_exact_at_succ HomologicalComplex.Hom.from_single₀_exact_at_succ
+-/
 
 end
 
@@ -221,6 +255,7 @@ end HomologicalComplex.Hom
 variable {A : Type _} [Category A] [Abelian A] {B : Type _} [Category B] [Abelian B] (F : A ⥤ B)
   [Functor.Additive F] [PreservesFiniteLimits F] [PreservesFiniteColimits F] [Faithful F]
 
+#print CategoryTheory.Functor.quasiIso_of_map_quasiIso /-
 theorem CategoryTheory.Functor.quasiIso_of_map_quasiIso {C D : HomologicalComplex A c} (f : C ⟶ D)
     (hf : QuasiIso ((F.mapHomologicalComplex _).map f)) : QuasiIso f :=
   ⟨fun i =>
@@ -230,4 +265,5 @@ theorem CategoryTheory.Functor.quasiIso_of_map_quasiIso {C D : HomologicalComple
       infer_instance
     is_iso_of_reflects_iso _ F⟩
 #align category_theory.functor.quasi_iso_of_map_quasi_iso CategoryTheory.Functor.quasiIso_of_map_quasiIso
+-/

50251fd6

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -83,7 +83,7 @@ theorem toQuasiIso {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) : Quas
     refine' ⟨⟨(homologyFunctor W c i).map e.inv, _⟩⟩
     simp only [← functor.map_comp, ← (homologyFunctor W c i).map_id]
     constructor <;> apply homology_map_eq_of_homotopy
-    exacts[e.homotopy_hom_inv_id, e.homotopy_inv_hom_id]⟩
+    exacts [e.homotopy_hom_inv_id, e.homotopy_inv_hom_id]⟩
 #align homotopy_equiv.to_quasi_iso HomotopyEquiv.toQuasiIso
 
 theorem toQuasiIso_inv {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) (i : ι) :
@@ -132,7 +132,7 @@ theorem to_single₀_epi_at_zero [hf : QuasiIso f] : Epi (f.f 0) :=
   constructor
   intro Z g h Hgh
   rw [← cokernel.π_desc (X.d 1 0) (f.f 0) (by rw [← f.2 1 0 rfl] <;> exact comp_zero), ←
-    to_single₀_cokernel_at_zero_iso_hom_eq] at Hgh
+    to_single₀_cokernel_at_zero_iso_hom_eq] at Hgh 
   rw [(@cancel_epi _ _ _ _ _ _ (epi_comp _ _) _ _).1 Hgh]
 #align homological_complex.hom.to_single₀_epi_at_zero HomologicalComplex.Hom.to_single₀_epi_at_zero
 
@@ -189,7 +189,7 @@ theorem from_single₀_mono_at_zero [hf : QuasiIso f] : Mono (f.f 0) :=
   constructor
   intro Z g h Hgh
   rw [← kernel.lift_ι (X.d 0 1) (f.f 0) (by rw [f.2 0 1 rfl] <;> exact zero_comp), ←
-    from_single₀_kernel_at_zero_iso_inv_eq] at Hgh
+    from_single₀_kernel_at_zero_iso_inv_eq] at Hgh 
   rw [(@cancel_mono _ _ _ _ _ _ (mono_comp _ _) _ _).1 Hgh]
 #align homological_complex.hom.from_single₀_mono_at_zero HomologicalComplex.Hom.from_single₀_mono_at_zero

50251fd6

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -39,12 +39,6 @@ variable [HasEqualizers V] [HasImages V] [HasImageMaps V] [HasCokernels V]
 
 variable {c : ComplexShape ι} {C D E : HomologicalComplex V c}
 
-/- warning: quasi_iso -> QuasiIso is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {ι : Type.{u3}} {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} V _inst_1] [_inst_3 : CategoryTheory.Limits.HasEqualizers.{u1, u2} V _inst_1] [_inst_4 : CategoryTheory.Limits.HasImages.{u1, u2} V _inst_1] [_inst_5 : CategoryTheory.Limits.HasImageMaps.{u1, u2} V _inst_1 _inst_4] [_inst_6 : CategoryTheory.Limits.HasCokernels.{u1, u2} V _inst_1 _inst_2] {_inst_7 : ComplexShape.{u3} ι} {c : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7} {C : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7}, (Quiver.Hom.{max (succ u1) (succ u3), max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7))) c C) -> Prop
-Case conversion may be inaccurate. Consider using '#align quasi_iso QuasiIsoₓ'. -/
 /-- A chain map is a quasi-isomorphism if it induces isomorphisms on homology.
 -/
 class QuasiIso (f : C ⟶ D) : Prop where
@@ -53,12 +47,6 @@ class QuasiIso (f : C ⟶ D) : Prop where
 
 attribute [instance] QuasiIso.isIso
 
-/- warning: quasi_iso_of_iso -> quasiIso_of_iso is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {ι : Type.{u3}} {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} V _inst_1] [_inst_3 : CategoryTheory.Limits.HasEqualizers.{u1, u2} V _inst_1] [_inst_4 : CategoryTheory.Limits.HasImages.{u1, u2} V _inst_1] [_inst_5 : CategoryTheory.Limits.HasImageMaps.{u1, u2} V _inst_1 _inst_4] [_inst_6 : CategoryTheory.Limits.HasCokernels.{u1, u2} V _inst_1 _inst_2] {_inst_7 : ComplexShape.{u3} ι} {c : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7} {C : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7} (D : Quiver.Hom.{max (succ u1) (succ u3), max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7))) c C) [f : CategoryTheory.IsIso.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) c C D], QuasiIso.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 c C D
-Case conversion may be inaccurate. Consider using '#align quasi_iso_of_iso quasiIso_of_isoₓ'. -/
 instance (priority := 100) quasiIso_of_iso (f : C ⟶ D) [IsIso f] : QuasiIso f
     where IsIso i :=
     by
@@ -66,26 +54,17 @@ instance (priority := 100) quasiIso_of_iso (f : C ⟶ D) [IsIso f] : QuasiIso f
     infer_instance
 #align quasi_iso_of_iso quasiIso_of_iso
 
-/- warning: quasi_iso_comp -> quasiIso_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quasi_iso_comp quasiIso_compₓ'. -/
 instance quasiIso_comp (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso g] : QuasiIso (f ≫ g)
     where IsIso i := by
     rw [functor.map_comp]
     infer_instance
 #align quasi_iso_comp quasiIso_comp
 
-/- warning: quasi_iso_of_comp_left -> quasiIso_of_comp_left is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quasi_iso_of_comp_left quasiIso_of_comp_leftₓ'. -/
 theorem quasiIso_of_comp_left (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso (f ≫ g)] :
     QuasiIso g :=
   { IsIso := fun i => IsIso.of_isIso_fac_left ((homologyFunctor V c i).map_comp f g).symm }
 #align quasi_iso_of_comp_left quasiIso_of_comp_left
 
-/- warning: quasi_iso_of_comp_right -> quasiIso_of_comp_right is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align quasi_iso_of_comp_right quasiIso_of_comp_rightₓ'. -/
 theorem quasiIso_of_comp_right (f : C ⟶ D) (g : D ⟶ E) [QuasiIso g] [QuasiIso (f ≫ g)] :
     QuasiIso f :=
   { IsIso := fun i => IsIso.of_isIso_fac_right ((homologyFunctor V c i).map_comp f g).symm }
@@ -98,12 +77,6 @@ section
 variable {W : Type _} [Category W] [Preadditive W] [HasCokernels W] [HasImages W] [HasEqualizers W]
   [HasZeroObject W] [HasImageMaps W]
 
-/- warning: homotopy_equiv.to_quasi_iso -> HomotopyEquiv.toQuasiIso is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {c : ComplexShape.{u1} ι} {W : Type.{u2}} [_inst_8 : CategoryTheory.Category.{u3, u2} W] [_inst_9 : CategoryTheory.Preadditive.{u3, u2} W _inst_8] [_inst_10 : CategoryTheory.Limits.HasCokernels.{u3, u2} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9)] [_inst_11 : CategoryTheory.Limits.HasImages.{u3, u2} W _inst_8] [_inst_12 : CategoryTheory.Limits.HasEqualizers.{u3, u2} W _inst_8] [_inst_13 : CategoryTheory.Limits.HasZeroObject.{u3, u2} W _inst_8] [_inst_14 : CategoryTheory.Limits.HasImageMaps.{u3, u2} W _inst_8 _inst_11] {C : HomologicalComplex.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c} {D : HomologicalComplex.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c} (e : HomotopyEquiv.{u3, u2, u1} ι W _inst_8 _inst_9 c C D), QuasiIso.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) _inst_13 _inst_12 _inst_11 _inst_14 _inst_10 c C D (HomotopyEquiv.hom.{u3, u2, u1} ι W _inst_8 _inst_9 c C D e)
-but is expected to have type
-  forall {ι : Type.{u1}} {c : ComplexShape.{u1} ι} {W : Type.{u2}} [_inst_8 : CategoryTheory.Category.{u3, u2} W] [_inst_9 : CategoryTheory.Preadditive.{u3, u2} W _inst_8] [_inst_10 : CategoryTheory.Limits.HasCokernels.{u3, u2} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9)] [_inst_11 : CategoryTheory.Limits.HasImages.{u3, u2} W _inst_8] [_inst_12 : CategoryTheory.Limits.HasEqualizers.{u3, u2} W _inst_8] [_inst_13 : CategoryTheory.Limits.HasImageMaps.{u3, u2} W _inst_8 _inst_11] {_inst_14 : HomologicalComplex.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c} {C : HomologicalComplex.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c} (D : HomotopyEquiv.{u3, u2, u1} ι W _inst_8 _inst_9 c _inst_14 C), QuasiIso.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) _inst_12 _inst_11 _inst_13 _inst_10 c _inst_14 C (HomotopyEquiv.hom.{u3, u2, u1} ι W _inst_8 _inst_9 c _inst_14 C D)
-Case conversion may be inaccurate. Consider using '#align homotopy_equiv.to_quasi_iso HomotopyEquiv.toQuasiIsoₓ'. -/
 /-- An homotopy equivalence is a quasi-isomorphism. -/
 theorem toQuasiIso {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) : QuasiIso e.Hom :=
   ⟨fun i => by
@@ -113,9 +86,6 @@ theorem toQuasiIso {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) : Quas
     exacts[e.homotopy_hom_inv_id, e.homotopy_inv_hom_id]⟩
 #align homotopy_equiv.to_quasi_iso HomotopyEquiv.toQuasiIso
 
-/- warning: homotopy_equiv.to_quasi_iso_inv -> HomotopyEquiv.toQuasiIso_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homotopy_equiv.to_quasi_iso_inv HomotopyEquiv.toQuasiIso_invₓ'. -/
 theorem toQuasiIso_inv {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) (i : ι) :
     (@asIso _ _ _ _ _ (e.toQuasiIso.1 i)).inv = (homologyFunctor W c i).map e.inv :=
   by
@@ -138,9 +108,6 @@ section
 
 variable {X : ChainComplex W ℕ} {Y : W} (f : X ⟶ (ChainComplex.single₀ _).obj Y) [hf : QuasiIso f]
 
-/- warning: homological_complex.hom.to_single₀_cokernel_at_zero_iso -> HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homological_complex.hom.to_single₀_cokernel_at_zero_iso HomologicalComplex.Hom.toSingle₀CokernelAtZeroIsoₓ'. -/
 /-- If a chain map `f : X ⟶ Y[0]` is a quasi-isomorphism, then the cokernel of the differential
 `d : X₁ → X₀` is isomorphic to `Y.` -/
 noncomputable def toSingle₀CokernelAtZeroIso : cokernel (X.d 1 0) ≅ Y :=
@@ -148,9 +115,6 @@ noncomputable def toSingle₀CokernelAtZeroIso : cokernel (X.d 1 0) ≅ Y :=
     ((@asIso _ _ _ _ _ (hf.1 0)).trans ((ChainComplex.homologyFunctor0Single₀ W).app Y))
 #align homological_complex.hom.to_single₀_cokernel_at_zero_iso HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso
 
-/- warning: homological_complex.hom.to_single₀_cokernel_at_zero_iso_hom_eq -> HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso_hom_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homological_complex.hom.to_single₀_cokernel_at_zero_iso_hom_eq HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso_hom_eqₓ'. -/
 theorem toSingle₀CokernelAtZeroIso_hom_eq [hf : QuasiIso f] :
     f.toSingle₀CokernelAtZeroIso.Hom =
       cokernel.desc (X.d 1 0) (f.f 0) (by rw [← f.2 1 0 rfl] <;> exact comp_zero) :=
@@ -163,9 +127,6 @@ theorem toSingle₀CokernelAtZeroIso_hom_eq [hf : QuasiIso f] :
   simp [homology.desc, iso.refl_inv (X.X 0)]
 #align homological_complex.hom.to_single₀_cokernel_at_zero_iso_hom_eq HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso_hom_eq
 
-/- warning: homological_complex.hom.to_single₀_epi_at_zero -> HomologicalComplex.Hom.to_single₀_epi_at_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homological_complex.hom.to_single₀_epi_at_zero HomologicalComplex.Hom.to_single₀_epi_at_zeroₓ'. -/
 theorem to_single₀_epi_at_zero [hf : QuasiIso f] : Epi (f.f 0) :=
   by
   constructor
@@ -175,9 +136,6 @@ theorem to_single₀_epi_at_zero [hf : QuasiIso f] : Epi (f.f 0) :=
   rw [(@cancel_epi _ _ _ _ _ _ (epi_comp _ _) _ _).1 Hgh]
 #align homological_complex.hom.to_single₀_epi_at_zero HomologicalComplex.Hom.to_single₀_epi_at_zero
 
-/- warning: homological_complex.hom.to_single₀_exact_d_f_at_zero -> HomologicalComplex.Hom.to_single₀_exact_d_f_at_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homological_complex.hom.to_single₀_exact_d_f_at_zero HomologicalComplex.Hom.to_single₀_exact_d_f_at_zeroₓ'. -/
 theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f 0) :=
   by
   rw [preadditive.exact_iff_homology_zero]
@@ -189,9 +147,6 @@ theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f
     infer_instance
 #align homological_complex.hom.to_single₀_exact_d_f_at_zero HomologicalComplex.Hom.to_single₀_exact_d_f_at_zero
 
-/- warning: homological_complex.hom.to_single₀_exact_at_succ -> HomologicalComplex.Hom.to_single₀_exact_at_succ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homological_complex.hom.to_single₀_exact_at_succ HomologicalComplex.Hom.to_single₀_exact_at_succₓ'. -/
 theorem to_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
     Exact (X.d (n + 2) (n + 1)) (X.d (n + 1) n) :=
   (Preadditive.exact_iff_homology_zero _ _).2
@@ -206,9 +161,6 @@ section
 
 variable {X : CochainComplex W ℕ} {Y : W} (f : (CochainComplex.single₀ _).obj Y ⟶ X)
 
-/- warning: homological_complex.hom.from_single₀_kernel_at_zero_iso -> HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homological_complex.hom.from_single₀_kernel_at_zero_iso HomologicalComplex.Hom.fromSingle₀KernelAtZeroIsoₓ'. -/
 /-- If a cochain map `f : Y[0] ⟶ X` is a quasi-isomorphism, then the kernel of the differential
 `d : X₀ → X₁` is isomorphic to `Y.` -/
 noncomputable def fromSingle₀KernelAtZeroIso [hf : QuasiIso f] : kernel (X.d 0 1) ≅ Y :=
@@ -216,9 +168,6 @@ noncomputable def fromSingle₀KernelAtZeroIso [hf : QuasiIso f] : kernel (X.d 0
     ((@asIso _ _ _ _ _ (hf.1 0)).symm.trans ((CochainComplex.homologyFunctor0Single₀ W).app Y))
 #align homological_complex.hom.from_single₀_kernel_at_zero_iso HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso
 
-/- warning: homological_complex.hom.from_single₀_kernel_at_zero_iso_inv_eq -> HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso_inv_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homological_complex.hom.from_single₀_kernel_at_zero_iso_inv_eq HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso_inv_eqₓ'. -/
 theorem fromSingle₀KernelAtZeroIso_inv_eq [hf : QuasiIso f] :
     f.fromSingle₀KernelAtZeroIso.inv =
       kernel.lift (X.d 0 1) (f.f 0) (by rw [f.2 0 1 rfl] <;> exact zero_comp) :=
@@ -235,9 +184,6 @@ theorem fromSingle₀KernelAtZeroIso_inv_eq [hf : QuasiIso f] :
   simp [homology.π, kernel_subobject_map_comp, iso.refl_hom (X.X 0), category.comp_id]
 #align homological_complex.hom.from_single₀_kernel_at_zero_iso_inv_eq HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso_inv_eq
 
-/- warning: homological_complex.hom.from_single₀_mono_at_zero -> HomologicalComplex.Hom.from_single₀_mono_at_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homological_complex.hom.from_single₀_mono_at_zero HomologicalComplex.Hom.from_single₀_mono_at_zeroₓ'. -/
 theorem from_single₀_mono_at_zero [hf : QuasiIso f] : Mono (f.f 0) :=
   by
   constructor
@@ -247,9 +193,6 @@ theorem from_single₀_mono_at_zero [hf : QuasiIso f] : Mono (f.f 0) :=
   rw [(@cancel_mono _ _ _ _ _ _ (mono_comp _ _) _ _).1 Hgh]
 #align homological_complex.hom.from_single₀_mono_at_zero HomologicalComplex.Hom.from_single₀_mono_at_zero
 
-/- warning: homological_complex.hom.from_single₀_exact_f_d_at_zero -> HomologicalComplex.Hom.from_single₀_exact_f_d_at_zero is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homological_complex.hom.from_single₀_exact_f_d_at_zero HomologicalComplex.Hom.from_single₀_exact_f_d_at_zeroₓ'. -/
 theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso f] : Exact (f.f 0) (X.d 0 1) :=
   by
   rw [preadditive.exact_iff_homology_zero]
@@ -261,9 +204,6 @@ theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso f] : Exact (f.f 0) (X.d
     infer_instance
 #align homological_complex.hom.from_single₀_exact_f_d_at_zero HomologicalComplex.Hom.from_single₀_exact_f_d_at_zero
 
-/- warning: homological_complex.hom.from_single₀_exact_at_succ -> HomologicalComplex.Hom.from_single₀_exact_at_succ is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align homological_complex.hom.from_single₀_exact_at_succ HomologicalComplex.Hom.from_single₀_exact_at_succₓ'. -/
 theorem from_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
     Exact (X.d n (n + 1)) (X.d (n + 1) (n + 2)) :=
   (Preadditive.exact_iff_homology_zero _ _).2
@@ -281,9 +221,6 @@ end HomologicalComplex.Hom
 variable {A : Type _} [Category A] [Abelian A] {B : Type _} [Category B] [Abelian B] (F : A ⥤ B)
   [Functor.Additive F] [PreservesFiniteLimits F] [PreservesFiniteColimits F] [Faithful F]
 
-/- warning: category_theory.functor.quasi_iso_of_map_quasi_iso -> CategoryTheory.Functor.quasiIso_of_map_quasiIso is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.functor.quasi_iso_of_map_quasi_iso CategoryTheory.Functor.quasiIso_of_map_quasiIsoₓ'. -/
 theorem CategoryTheory.Functor.quasiIso_of_map_quasiIso {C D : HomologicalComplex A c} (f : C ⟶ D)
     (hf : QuasiIso ((F.mapHomologicalComplex _).map f)) : QuasiIso f :=
   ⟨fun i =>

50251fd6

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -184,9 +184,7 @@ theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f
   have h : X.d 1 0 ≫ f.f 0 = 0 := by
     simp only [← f.2 1 0 rfl, ChainComplex.single₀_obj_X_d, comp_zero]
   refine' ⟨h, Nonempty.intro (homologyIsoKernelDesc _ _ _ ≪≫ _)⟩
-  · suffices is_iso (cokernel.desc _ _ h) by
-      haveI := this
-      apply kernel.of_mono
+  · suffices is_iso (cokernel.desc _ _ h) by haveI := this; apply kernel.of_mono
     rw [← to_single₀_cokernel_at_zero_iso_hom_eq]
     infer_instance
 #align homological_complex.hom.to_single₀_exact_d_f_at_zero HomologicalComplex.Hom.to_single₀_exact_d_f_at_zero
@@ -258,10 +256,7 @@ theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso f] : Exact (f.f 0) (X.d
   have h : f.f 0 ≫ X.d 0 1 = 0 := by
     simp only [HomologicalComplex.Hom.comm, CochainComplex.single₀_obj_X_d, zero_comp]
   refine' ⟨h, Nonempty.intro (homologyIsoCokernelLift _ _ _ ≪≫ _)⟩
-  · suffices is_iso (kernel.lift (X.d 0 1) (f.f 0) h)
-      by
-      haveI := this
-      apply cokernel.of_epi
+  · suffices is_iso (kernel.lift (X.d 0 1) (f.f 0) h) by haveI := this; apply cokernel.of_epi
     rw [← from_single₀_kernel_at_zero_iso_inv_eq f]
     infer_instance
 #align homological_complex.hom.from_single₀_exact_f_d_at_zero HomologicalComplex.Hom.from_single₀_exact_f_d_at_zero

50251fd6

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -67,10 +67,7 @@ instance (priority := 100) quasiIso_of_iso (f : C ⟶ D) [IsIso f] : QuasiIso f
 #align quasi_iso_of_iso quasiIso_of_iso
 
 /- warning: quasi_iso_comp -> quasiIso_comp is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u3}} {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} V _inst_1] [_inst_3 : CategoryTheory.Limits.HasZeroObject.{u1, u2} V _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} V _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} V _inst_1] [_inst_6 : CategoryTheory.Limits.HasImageMaps.{u1, u2} V _inst_1 _inst_5] [_inst_7 : CategoryTheory.Limits.HasCokernels.{u1, u2} V _inst_1 _inst_2] {c : ComplexShape.{u3} ι} {C : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c} {D : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c} {E : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c} (f : Quiver.Hom.{succ (max u3 u1), max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c) (HomologicalComplex.CategoryTheory.category.{u1, u2, u3} ι V _inst_1 _inst_2 c))) C D) [_inst_8 : QuasiIso.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 c C D f] (g : Quiver.Hom.{succ (max u3 u1), max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c) (HomologicalComplex.CategoryTheory.category.{u1, u2, u3} ι V _inst_1 _inst_2 c))) D E) [_inst_9 : QuasiIso.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 c D E g], QuasiIso.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 c C E (CategoryTheory.CategoryStruct.comp.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c) (HomologicalComplex.CategoryTheory.category.{u1, u2, u3} ι V _inst_1 _inst_2 c)) C D E f g)
-but is expected to have type
-  forall {ι : Type.{u3}} {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} V _inst_1] [_inst_3 : CategoryTheory.Limits.HasEqualizers.{u1, u2} V _inst_1] [_inst_4 : CategoryTheory.Limits.HasImages.{u1, u2} V _inst_1] [_inst_5 : CategoryTheory.Limits.HasImageMaps.{u1, u2} V _inst_1 _inst_4] [_inst_6 : CategoryTheory.Limits.HasCokernels.{u1, u2} V _inst_1 _inst_2] {_inst_7 : ComplexShape.{u3} ι} {c : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7} {C : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7} {D : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7} (E : Quiver.Hom.{max (succ u1) (succ u3), max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7))) c C) [f : QuasiIso.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 c C E] (_inst_8 : Quiver.Hom.{max (succ u1) (succ u3), max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7))) C D) [g : QuasiIso.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 C D _inst_8], QuasiIso.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 c D (CategoryTheory.CategoryStruct.comp.{max u3 u1, max (max u3 u2) u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max (max u3 u2) u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7)) c C D E _inst_8)
+<too large>
 Case conversion may be inaccurate. Consider using '#align quasi_iso_comp quasiIso_compₓ'. -/
 instance quasiIso_comp (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso g] : QuasiIso (f ≫ g)
     where IsIso i := by
@@ -79,10 +76,7 @@ instance quasiIso_comp (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso g] : Q
 #align quasi_iso_comp quasiIso_comp
 
 /- warning: quasi_iso_of_comp_left -> quasiIso_of_comp_left is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align quasi_iso_of_comp_left quasiIso_of_comp_leftₓ'. -/
 theorem quasiIso_of_comp_left (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso (f ≫ g)] :
     QuasiIso g :=
@@ -90,10 +84,7 @@ theorem quasiIso_of_comp_left (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso
 #align quasi_iso_of_comp_left quasiIso_of_comp_left
 
 /- warning: quasi_iso_of_comp_right -> quasiIso_of_comp_right is a dubious translation:
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 Case conversion may be inaccurate. Consider using '#align quasi_iso_of_comp_right quasiIso_of_comp_rightₓ'. -/
 theorem quasiIso_of_comp_right (f : C ⟶ D) (g : D ⟶ E) [QuasiIso g] [QuasiIso (f ≫ g)] :
     QuasiIso f :=
@@ -123,10 +114,7 @@ theorem toQuasiIso {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) : Quas
 #align homotopy_equiv.to_quasi_iso HomotopyEquiv.toQuasiIso
 
 /- warning: homotopy_equiv.to_quasi_iso_inv -> HomotopyEquiv.toQuasiIso_inv is a dubious translation:
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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c) (HomologicalComplex.instCategoryHomologicalComplex.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c) W _inst_8 (homologyFunctor.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c _inst_12 _inst_11 _inst_13 _inst_10 e)) C _inst_14 (HomotopyEquiv.inv.{u3, u2, u1} ι W _inst_8 _inst_9 c _inst_14 C D))
+<too large>
 Case conversion may be inaccurate. Consider using '#align homotopy_equiv.to_quasi_iso_inv HomotopyEquiv.toQuasiIso_invₓ'. -/
 theorem toQuasiIso_inv {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) (i : ι) :
     (@asIso _ _ _ _ _ (e.toQuasiIso.1 i)).inv = (homologyFunctor W c i).map e.inv :=
@@ -151,10 +139,7 @@ section
 variable {X : ChainComplex W ℕ} {Y : W} (f : X ⟶ (ChainComplex.single₀ _).obj Y) [hf : QuasiIso f]
 
 /- warning: homological_complex.hom.to_single₀_cokernel_at_zero_iso -> HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso is a dubious translation:
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Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Y
+<too large>
 Case conversion may be inaccurate. Consider using '#align homological_complex.hom.to_single₀_cokernel_at_zero_iso HomologicalComplex.Hom.toSingle₀CokernelAtZeroIsoₓ'. -/
 /-- If a chain map `f : X ⟶ Y[0]` is a quasi-isomorphism, then the cokernel of the differential
 `d : X₁ → X₀` is isomorphic to `Y.` -/
@@ -164,10 +149,7 @@ noncomputable def toSingle₀CokernelAtZeroIso : cokernel (X.d 1 0) ≅ Y :=
 #align homological_complex.hom.to_single₀_cokernel_at_zero_iso HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso
 
 /- warning: homological_complex.hom.to_single₀_cokernel_at_zero_iso_hom_eq -> HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso_hom_eq is a dubious translation:
-lean 3 declaration is
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(AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max 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(CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y)) [hf : QuasiIso.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, 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Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => Eq.{1} Prop (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (CategoryTheory.CategoryStruct.comp.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.d.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 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(AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Eq.refl.{1} Prop (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (CategoryTheory.CategoryStruct.comp.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.d.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) 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(AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 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Nat.canonicallyOrderedCommSemiring))))))))) (CategoryTheory.Limits.comp_zero.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} 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.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat 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u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align homological_complex.hom.to_single₀_cokernel_at_zero_iso_hom_eq HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso_hom_eqₓ'. -/
 theorem toSingle₀CokernelAtZeroIso_hom_eq [hf : QuasiIso f] :
     f.toSingle₀CokernelAtZeroIso.Hom =
@@ -182,10 +164,7 @@ theorem toSingle₀CokernelAtZeroIso_hom_eq [hf : QuasiIso f] :
 #align homological_complex.hom.to_single₀_cokernel_at_zero_iso_hom_eq HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso_hom_eq
 
 /- warning: homological_complex.hom.to_single₀_epi_at_zero -> HomologicalComplex.Hom.to_single₀_epi_at_zero is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homological_complex.hom.to_single₀_epi_at_zero HomologicalComplex.Hom.to_single₀_epi_at_zeroₓ'. -/
 theorem to_single₀_epi_at_zero [hf : QuasiIso f] : Epi (f.f 0) :=
   by
@@ -197,10 +176,7 @@ theorem to_single₀_epi_at_zero [hf : QuasiIso f] : Epi (f.f 0) :=
 #align homological_complex.hom.to_single₀_epi_at_zero HomologicalComplex.Hom.to_single₀_epi_at_zero
 
 /- warning: homological_complex.hom.to_single₀_exact_d_f_at_zero -> HomologicalComplex.Hom.to_single₀_exact_d_f_at_zero is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homological_complex.hom.to_single₀_exact_d_f_at_zero HomologicalComplex.Hom.to_single₀_exact_d_f_at_zeroₓ'. -/
 theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f 0) :=
   by
@@ -216,10 +192,7 @@ theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f
 #align homological_complex.hom.to_single₀_exact_d_f_at_zero HomologicalComplex.Hom.to_single₀_exact_d_f_at_zero
 
 /- warning: homological_complex.hom.to_single₀_exact_at_succ -> HomologicalComplex.Hom.to_single₀_exact_at_succ is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homological_complex.hom.to_single₀_exact_at_succ HomologicalComplex.Hom.to_single₀_exact_at_succₓ'. -/
 theorem to_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
     Exact (X.d (n + 2) (n + 1)) (X.d (n + 1) n) :=
@@ -236,10 +209,7 @@ section
 variable {X : CochainComplex W ℕ} {Y : W} (f : (CochainComplex.single₀ _).obj Y ⟶ X)
 
 /- warning: homological_complex.hom.from_single₀_kernel_at_zero_iso -> HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso is a dubious translation:
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Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) Y
+<too large>
 Case conversion may be inaccurate. Consider using '#align homological_complex.hom.from_single₀_kernel_at_zero_iso HomologicalComplex.Hom.fromSingle₀KernelAtZeroIsoₓ'. -/
 /-- If a cochain map `f : Y[0] ⟶ X` is a quasi-isomorphism, then the kernel of the differential
 `d : X₀ → X₁` is isomorphic to `Y.` -/
@@ -249,10 +219,7 @@ noncomputable def fromSingle₀KernelAtZeroIso [hf : QuasiIso f] : kernel (X.d 0
 #align homological_complex.hom.from_single₀_kernel_at_zero_iso HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso
 
 /- warning: homological_complex.hom.from_single₀_kernel_at_zero_iso_inv_eq -> HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso_inv_eq is a dubious translation:
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Nat.hasOne)) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9)) Y) X) [hf : QuasiIso.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 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(OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Eq.{1} Prop (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (CategoryTheory.CategoryStruct.comp.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) 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(AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{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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Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))) (Eq.refl.{1} Prop (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (CategoryTheory.CategoryStruct.comp.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) 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+<too large>
 Case conversion may be inaccurate. Consider using '#align homological_complex.hom.from_single₀_kernel_at_zero_iso_inv_eq HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso_inv_eqₓ'. -/
 theorem fromSingle₀KernelAtZeroIso_inv_eq [hf : QuasiIso f] :
     f.fromSingle₀KernelAtZeroIso.inv =
@@ -271,10 +238,7 @@ theorem fromSingle₀KernelAtZeroIso_inv_eq [hf : QuasiIso f] :
 #align homological_complex.hom.from_single₀_kernel_at_zero_iso_inv_eq HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso_inv_eq
 
 /- warning: homological_complex.hom.from_single₀_mono_at_zero -> HomologicalComplex.Hom.from_single₀_mono_at_zero is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homological_complex.hom.from_single₀_mono_at_zero HomologicalComplex.Hom.from_single₀_mono_at_zeroₓ'. -/
 theorem from_single₀_mono_at_zero [hf : QuasiIso f] : Mono (f.f 0) :=
   by
@@ -286,10 +250,7 @@ theorem from_single₀_mono_at_zero [hf : QuasiIso f] : Mono (f.f 0) :=
 #align homological_complex.hom.from_single₀_mono_at_zero HomologicalComplex.Hom.from_single₀_mono_at_zero
 
 /- warning: homological_complex.hom.from_single₀_exact_f_d_at_zero -> HomologicalComplex.Hom.from_single₀_exact_f_d_at_zero is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align homological_complex.hom.from_single₀_exact_f_d_at_zero HomologicalComplex.Hom.from_single₀_exact_f_d_at_zeroₓ'. -/
 theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso f] : Exact (f.f 0) (X.d 0 1) :=
   by
@@ -306,10 +267,7 @@ theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso f] : Exact (f.f 0) (X.d
 #align homological_complex.hom.from_single₀_exact_f_d_at_zero HomologicalComplex.Hom.from_single₀_exact_f_d_at_zero
 
 /- warning: homological_complex.hom.from_single₀_exact_at_succ -> HomologicalComplex.Hom.from_single₀_exact_at_succ is a dubious translation:
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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) X) [hf : QuasiIso.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasPullbacks.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9))) (CategoryTheory.Limits.hasCokernels_of_hasCoequalizers.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasCoequalizers.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HomologicalComplex.d.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.d.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align homological_complex.hom.from_single₀_exact_at_succ HomologicalComplex.Hom.from_single₀_exact_at_succₓ'. -/
 theorem from_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
     Exact (X.d n (n + 1)) (X.d (n + 1) (n + 2)) :=
@@ -329,10 +287,7 @@ variable {A : Type _} [Category A] [Abelian A] {B : Type _} [Category B] [Abelia
   [Functor.Additive F] [PreservesFiniteLimits F] [PreservesFiniteColimits F] [Faithful F]
 
 /- warning: category_theory.functor.quasi_iso_of_map_quasi_iso -> CategoryTheory.Functor.quasiIso_of_map_quasiIso is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {c : ComplexShape.{u1} ι} {A : Type.{u2}} [_inst_8 : CategoryTheory.Category.{u3, u2} A] [_inst_9 : CategoryTheory.Abelian.{u3, u2} A _inst_8] {B : Type.{u4}} [_inst_10 : CategoryTheory.Category.{u5, u4} B] [_inst_11 : CategoryTheory.Abelian.{u5, u4} B _inst_10] (F : CategoryTheory.Functor.{u3, u5, u2, u4} A _inst_8 B _inst_10) [_inst_12 : CategoryTheory.Functor.Additive.{u2, u4, u3, u5} A B _inst_8 _inst_10 (CategoryTheory.Abelian.toPreadditive.{u3, u2} A _inst_8 _inst_9) (CategoryTheory.Abelian.toPreadditive.{u5, u4} B _inst_10 _inst_11) F] [_inst_13 : CategoryTheory.Limits.PreservesFiniteLimits.{u3, u5, u2, u4} A _inst_8 B _inst_10 F] [_inst_14 : CategoryTheory.Limits.PreservesFiniteColimits.{u3, u5, u2, u4} A _inst_8 B _inst_10 F] [_inst_15 : CategoryTheory.Faithful.{u3, u5, u2, u4} A _inst_8 B _inst_10 F] {C : HomologicalComplex.{u3, u2, u1} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} A _inst_8 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9)) c))) (HomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max (max u1 u2) u3} (HomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max (max u1 u2) u3} (HomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c))) (CategoryTheory.Functor.toPrefunctor.{max u5 u3, max u2 u3, max (max u4 u5) u3, max (max u1 u2) u3} (HomologicalComplex.{u5, u4, u3} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9)) c) (HomologicalComplex.instCategoryHomologicalComplex.{u5, u4, u3} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9)) c) (HomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c) (CategoryTheory.Functor.mapHomologicalComplex.{u5, u4, u3, u1, u2} ι A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9) B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11) F _inst_12 c)) C D f)) -> (QuasiIso.{u5, u4, u3} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9)) (CategoryTheory.Abelian.hasEqualizers.{u5, u4} A _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u5, u4} A _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u5, u4} A _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u5, u4} A _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u5, u4} A _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u5, u4} A _inst_8 _inst_9)) (CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers.{u5, u4} A _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u5, u4} A _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u5, u4} A _inst_8 _inst_9)) (CategoryTheory.Abelian.hasPullbacks.{u5, u4} A _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u5, u4} A _inst_8 _inst_9))) (CategoryTheory.Limits.hasCokernels_of_hasCoequalizers.{u5, u4} A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9)) (CategoryTheory.Abelian.hasCoequalizers.{u5, u4} A _inst_8 _inst_9)) c C D f)
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.functor.quasi_iso_of_map_quasi_iso CategoryTheory.Functor.quasiIso_of_map_quasiIsoₓ'. -/
 theorem CategoryTheory.Functor.quasiIso_of_map_quasiIso {C D : HomologicalComplex A c} (f : C ⟶ D)
     (hf : QuasiIso ((F.mapHomologicalComplex _).map f)) : QuasiIso f :=

50251fd6

bump to nightly-2023-05-19-03

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

9a2fedb8

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Joël Riou
 
 ! This file was ported from Lean 3 source module algebra.homology.quasi_iso
-! leanprover-community/mathlib commit 956af7c76589f444f2e1313911bad16366ea476d
+! leanprover-community/mathlib commit 50251fd6309cca5ca2e747882ffecd2729f38c5d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.CategoryTheory.Abelian.Homology
 /-!
 # Quasi-isomorphisms
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A chain map is a quasi-isomorphism if it induces isomorphisms on homology.
 
 ## Future work

956af7c7

bump to nightly-2023-05-17-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/f8c79b0a623404854a2902b836eac32156fd7712

63fc1745

Diff

@@ -36,6 +36,12 @@ variable [HasEqualizers V] [HasImages V] [HasImageMaps V] [HasCokernels V]
 
 variable {c : ComplexShape ι} {C D E : HomologicalComplex V c}
 
+/- warning: quasi_iso -> QuasiIso is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u3}} {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} V _inst_1] [_inst_3 : CategoryTheory.Limits.HasZeroObject.{u1, u2} V _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} V _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} V _inst_1] [_inst_6 : CategoryTheory.Limits.HasImageMaps.{u1, u2} V _inst_1 _inst_5] [_inst_7 : CategoryTheory.Limits.HasCokernels.{u1, u2} V _inst_1 _inst_2] {c : ComplexShape.{u3} ι} {C : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c} {D : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c}, (Quiver.Hom.{succ (max u3 u1), max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c) (HomologicalComplex.CategoryTheory.category.{u1, u2, u3} ι V _inst_1 _inst_2 c))) C D) -> Prop
+but is expected to have type
+  forall {ι : Type.{u3}} {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} V _inst_1] [_inst_3 : CategoryTheory.Limits.HasEqualizers.{u1, u2} V _inst_1] [_inst_4 : CategoryTheory.Limits.HasImages.{u1, u2} V _inst_1] [_inst_5 : CategoryTheory.Limits.HasImageMaps.{u1, u2} V _inst_1 _inst_4] [_inst_6 : CategoryTheory.Limits.HasCokernels.{u1, u2} V _inst_1 _inst_2] {_inst_7 : ComplexShape.{u3} ι} {c : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7} {C : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7}, (Quiver.Hom.{max (succ u1) (succ u3), max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7))) c C) -> Prop
+Case conversion may be inaccurate. Consider using '#align quasi_iso QuasiIsoₓ'. -/
 /-- A chain map is a quasi-isomorphism if it induces isomorphisms on homology.
 -/
 class QuasiIso (f : C ⟶ D) : Prop where
@@ -44,6 +50,12 @@ class QuasiIso (f : C ⟶ D) : Prop where
 
 attribute [instance] QuasiIso.isIso
 
+/- warning: quasi_iso_of_iso -> quasiIso_of_iso is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u3}} {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} V _inst_1] [_inst_3 : CategoryTheory.Limits.HasZeroObject.{u1, u2} V _inst_1] [_inst_4 : CategoryTheory.Limits.HasEqualizers.{u1, u2} V _inst_1] [_inst_5 : CategoryTheory.Limits.HasImages.{u1, u2} V _inst_1] [_inst_6 : CategoryTheory.Limits.HasImageMaps.{u1, u2} V _inst_1 _inst_5] [_inst_7 : CategoryTheory.Limits.HasCokernels.{u1, u2} V _inst_1 _inst_2] {c : ComplexShape.{u3} ι} {C : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c} {D : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c} (f : Quiver.Hom.{succ (max u3 u1), max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c) (CategoryTheory.CategoryStruct.toQuiver.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c) (HomologicalComplex.CategoryTheory.category.{u1, u2, u3} ι V _inst_1 _inst_2 c))) C D) [_inst_8 : CategoryTheory.IsIso.{max u3 u1, max u2 u3 u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 c) (HomologicalComplex.CategoryTheory.category.{u1, u2, u3} ι V _inst_1 _inst_2 c) C D f], QuasiIso.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 c C D f
+but is expected to have type
+  forall {ι : Type.{u3}} {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} V _inst_1] [_inst_3 : CategoryTheory.Limits.HasEqualizers.{u1, u2} V _inst_1] [_inst_4 : CategoryTheory.Limits.HasImages.{u1, u2} V _inst_1] [_inst_5 : CategoryTheory.Limits.HasImageMaps.{u1, u2} V _inst_1 _inst_4] [_inst_6 : CategoryTheory.Limits.HasCokernels.{u1, u2} V _inst_1 _inst_2] {_inst_7 : ComplexShape.{u3} ι} {c : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7} {C : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7} (D : Quiver.Hom.{max (succ u1) (succ u3), max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7))) c C) [f : CategoryTheory.IsIso.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) c C D], QuasiIso.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 c C D
+Case conversion may be inaccurate. Consider using '#align quasi_iso_of_iso quasiIso_of_isoₓ'. -/
 instance (priority := 100) quasiIso_of_iso (f : C ⟶ D) [IsIso f] : QuasiIso f
     where IsIso i :=
     by
@@ -51,17 +63,35 @@ instance (priority := 100) quasiIso_of_iso (f : C ⟶ D) [IsIso f] : QuasiIso f
     infer_instance
 #align quasi_iso_of_iso quasiIso_of_iso
 
+/- warning: quasi_iso_comp -> quasiIso_comp is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {ι : Type.{u3}} {V : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} V] [_inst_2 : CategoryTheory.Limits.HasZeroMorphisms.{u1, u2} V _inst_1] [_inst_3 : CategoryTheory.Limits.HasEqualizers.{u1, u2} V _inst_1] [_inst_4 : CategoryTheory.Limits.HasImages.{u1, u2} V _inst_1] [_inst_5 : CategoryTheory.Limits.HasImageMaps.{u1, u2} V _inst_1 _inst_4] [_inst_6 : CategoryTheory.Limits.HasCokernels.{u1, u2} V _inst_1 _inst_2] {_inst_7 : ComplexShape.{u3} ι} {c : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7} {C : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7} {D : HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7} (E : Quiver.Hom.{max (succ u1) (succ u3), max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7))) c C) [f : QuasiIso.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 c C E] (_inst_8 : Quiver.Hom.{max (succ u1) (succ u3), max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max (max u2 u1) u3} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7))) C D) [g : QuasiIso.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 C D _inst_8], QuasiIso.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_3 _inst_4 _inst_5 _inst_6 _inst_7 c D (CategoryTheory.CategoryStruct.comp.{max u3 u1, max (max u3 u2) u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (CategoryTheory.Category.toCategoryStruct.{max u3 u1, max (max u3 u2) u1} (HomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, u3} ι V _inst_1 _inst_2 _inst_7)) c C D E _inst_8)
+Case conversion may be inaccurate. Consider using '#align quasi_iso_comp quasiIso_compₓ'. -/
 instance quasiIso_comp (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso g] : QuasiIso (f ≫ g)
     where IsIso i := by
     rw [functor.map_comp]
     infer_instance
 #align quasi_iso_comp quasiIso_comp
 
+/- warning: quasi_iso_of_comp_left -> quasiIso_of_comp_left is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quasi_iso_of_comp_left quasiIso_of_comp_leftₓ'. -/
 theorem quasiIso_of_comp_left (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso (f ≫ g)] :
     QuasiIso g :=
   { IsIso := fun i => IsIso.of_isIso_fac_left ((homologyFunctor V c i).map_comp f g).symm }
 #align quasi_iso_of_comp_left quasiIso_of_comp_left
 
+/- warning: quasi_iso_of_comp_right -> quasiIso_of_comp_right is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align quasi_iso_of_comp_right quasiIso_of_comp_rightₓ'. -/
 theorem quasiIso_of_comp_right (f : C ⟶ D) (g : D ⟶ E) [QuasiIso g] [QuasiIso (f ≫ g)] :
     QuasiIso f :=
   { IsIso := fun i => IsIso.of_isIso_fac_right ((homologyFunctor V c i).map_comp f g).symm }
@@ -74,22 +104,34 @@ section
 variable {W : Type _} [Category W] [Preadditive W] [HasCokernels W] [HasImages W] [HasEqualizers W]
   [HasZeroObject W] [HasImageMaps W]
 
+/- warning: homotopy_equiv.to_quasi_iso -> HomotopyEquiv.toQuasiIso is a dubious translation:
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align homotopy_equiv.to_quasi_iso HomotopyEquiv.toQuasiIsoₓ'. -/
 /-- An homotopy equivalence is a quasi-isomorphism. -/
-theorem to_quasiIso {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) : QuasiIso e.Hom :=
+theorem toQuasiIso {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) : QuasiIso e.Hom :=
   ⟨fun i => by
     refine' ⟨⟨(homologyFunctor W c i).map e.inv, _⟩⟩
     simp only [← functor.map_comp, ← (homologyFunctor W c i).map_id]
     constructor <;> apply homology_map_eq_of_homotopy
     exacts[e.homotopy_hom_inv_id, e.homotopy_inv_hom_id]⟩
-#align homotopy_equiv.to_quasi_iso HomotopyEquiv.to_quasiIso
-
-theorem to_quasiIso_inv {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) (i : ι) :
-    (@asIso _ _ _ _ _ (e.to_quasiIso.1 i)).inv = (homologyFunctor W c i).map e.inv :=
+#align homotopy_equiv.to_quasi_iso HomotopyEquiv.toQuasiIso
+
+/- warning: homotopy_equiv.to_quasi_iso_inv -> HomotopyEquiv.toQuasiIso_inv is a dubious translation:
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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c) (HomologicalComplex.CategoryTheory.category.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c) W _inst_8 (homologyFunctor.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c _inst_12 _inst_11 _inst_14 _inst_10 i) D) (CategoryTheory.Functor.map.{max u1 u3, u3, max u2 u1 u3, u2} (HomologicalComplex.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c) (HomologicalComplex.CategoryTheory.category.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c) W _inst_8 (homologyFunctor.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c _inst_12 _inst_11 _inst_14 _inst_10 i) C D (HomotopyEquiv.hom.{u3, u2, u1} ι W _inst_8 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+but is expected to have type
+  forall {ι : Type.{u1}} {c : ComplexShape.{u1} ι} {W : Type.{u2}} [_inst_8 : CategoryTheory.Category.{u3, u2} W] [_inst_9 : CategoryTheory.Preadditive.{u3, u2} W _inst_8] [_inst_10 : CategoryTheory.Limits.HasCokernels.{u3, u2} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9)] [_inst_11 : CategoryTheory.Limits.HasImages.{u3, u2} W _inst_8] [_inst_12 : CategoryTheory.Limits.HasEqualizers.{u3, u2} W _inst_8] [_inst_13 : CategoryTheory.Limits.HasImageMaps.{u3, u2} W _inst_8 _inst_11] {_inst_14 : HomologicalComplex.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c} {C : HomologicalComplex.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c} (D : HomotopyEquiv.{u3, u2, u1} ι W _inst_8 _inst_9 c _inst_14 C) (e : ι), Eq.{succ u3} (Quiver.Hom.{succ u3, u2} W (CategoryTheory.CategoryStruct.toQuiver.{u3, u2} W 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c) (HomologicalComplex.instCategoryHomologicalComplex.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c) W _inst_8 (homologyFunctor.{u3, u2, u1} ι W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} W _inst_8 _inst_9) c _inst_12 _inst_11 _inst_13 _inst_10 e)) C _inst_14 (HomotopyEquiv.inv.{u3, u2, u1} ι W _inst_8 _inst_9 c _inst_14 C D))
+Case conversion may be inaccurate. Consider using '#align homotopy_equiv.to_quasi_iso_inv HomotopyEquiv.toQuasiIso_invₓ'. -/
+theorem toQuasiIso_inv {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) (i : ι) :
+    (@asIso _ _ _ _ _ (e.toQuasiIso.1 i)).inv = (homologyFunctor W c i).map e.inv :=
   by
   symm
   simp only [← iso.hom_comp_eq_id, as_iso_hom, ← functor.map_comp, ← (homologyFunctor W c i).map_id,
     homology_map_eq_of_homotopy e.homotopy_hom_inv_id _]
-#align homotopy_equiv.to_quasi_iso_inv HomotopyEquiv.to_quasiIso_inv
+#align homotopy_equiv.to_quasi_iso_inv HomotopyEquiv.toQuasiIso_inv
 
 end
 
@@ -105,6 +147,12 @@ section
 
 variable {X : ChainComplex W ℕ} {Y : W} (f : X ⟶ (ChainComplex.single₀ _).obj Y) [hf : QuasiIso f]
 
+/- warning: homological_complex.hom.to_single₀_cokernel_at_zero_iso -> HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso is a dubious translation:
+lean 3 declaration is
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne} {Y : W} (f : Quiver.Hom.{succ u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9)) Y) f], CategoryTheory.Iso.{u2, u1} W _inst_8 (CategoryTheory.Limits.cokernel.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (HomologicalComplex.x.{u2, u1, 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+but is expected to have type
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_inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasCoequalizers.{u2, u1} W _inst_8 _inst_9)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} 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Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) Y
+Case conversion may be inaccurate. Consider using '#align homological_complex.hom.to_single₀_cokernel_at_zero_iso HomologicalComplex.Hom.toSingle₀CokernelAtZeroIsoₓ'. -/
 /-- If a chain map `f : X ⟶ Y[0]` is a quasi-isomorphism, then the cokernel of the differential
 `d : X₁ → X₀` is isomorphic to `Y.` -/
 noncomputable def toSingle₀CokernelAtZeroIso : cokernel (X.d 1 0) ≅ Y :=
@@ -112,6 +160,12 @@ noncomputable def toSingle₀CokernelAtZeroIso : cokernel (X.d 1 0) ≅ Y :=
     ((@asIso _ _ _ _ _ (hf.1 0)).trans ((ChainComplex.homologyFunctor0Single₀ W).app Y))
 #align homological_complex.hom.to_single₀_cokernel_at_zero_iso HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso
 
+/- warning: homological_complex.hom.to_single₀_cokernel_at_zero_iso_hom_eq -> HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso_hom_eq is a dubious translation:
+lean 3 declaration is
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(CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9)) Y) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))))))
+but is expected to have type
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)} {Y : W} (f : Quiver.Hom.{succ u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) X (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y)) [hf : QuasiIso.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasPullbacks.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9))) (CategoryTheory.Limits.hasCokernels_of_hasCoequalizers.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasCoequalizers.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) f], Eq.{succ u2} (Quiver.Hom.{succ u2, u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CategoryTheory.Limits.cokernel.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat 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Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))))) (id.{0} (Eq.{1} Prop (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat 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(CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 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(CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) => Eq.{1} Prop (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (CategoryTheory.CategoryStruct.comp.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.d.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat W _inst_8 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Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))) (Eq.refl.{1} Prop (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (CategoryTheory.CategoryStruct.comp.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.d.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W 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+Case conversion may be inaccurate. Consider using '#align homological_complex.hom.to_single₀_cokernel_at_zero_iso_hom_eq HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso_hom_eqₓ'. -/
 theorem toSingle₀CokernelAtZeroIso_hom_eq [hf : QuasiIso f] :
     f.toSingle₀CokernelAtZeroIso.Hom =
       cokernel.desc (X.d 1 0) (f.f 0) (by rw [← f.2 1 0 rfl] <;> exact comp_zero) :=
@@ -124,6 +178,12 @@ theorem toSingle₀CokernelAtZeroIso_hom_eq [hf : QuasiIso f] :
   simp [homology.desc, iso.refl_inv (X.X 0)]
 #align homological_complex.hom.to_single₀_cokernel_at_zero_iso_hom_eq HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso_hom_eq
 
+/- warning: homological_complex.hom.to_single₀_epi_at_zero -> HomologicalComplex.Hom.to_single₀_epi_at_zero is a dubious translation:
+lean 3 declaration is
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne} {Y : W} (f : Quiver.Hom.{succ u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) X (CategoryTheory.Functor.obj.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9)) Y)) [hf : QuasiIso.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasPullbacks.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9))) (CategoryTheory.Abelian.hasCokernels.{u2, u1} W _inst_8 _inst_9) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) X (CategoryTheory.Functor.obj.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9)) Y) f], CategoryTheory.Epi.{u2, u1} W _inst_8 (HomologicalComplex.x.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) X (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HomologicalComplex.x.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Functor.obj.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9)) Y) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) X (CategoryTheory.Functor.obj.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9)) Y) f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))
+but is expected to have type
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)} {Y : W} (f : Quiver.Hom.{succ u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) X (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y)) [hf : QuasiIso.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, 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(CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (ChainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) f], CategoryTheory.Epi.{u2, u1} W _inst_8 (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) f (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
+Case conversion may be inaccurate. Consider using '#align homological_complex.hom.to_single₀_epi_at_zero HomologicalComplex.Hom.to_single₀_epi_at_zeroₓ'. -/
 theorem to_single₀_epi_at_zero [hf : QuasiIso f] : Epi (f.f 0) :=
   by
   constructor
@@ -133,6 +193,12 @@ theorem to_single₀_epi_at_zero [hf : QuasiIso f] : Epi (f.f 0) :=
   rw [(@cancel_epi _ _ _ _ _ _ (epi_comp _ _) _ _).1 Hgh]
 #align homological_complex.hom.to_single₀_epi_at_zero HomologicalComplex.Hom.to_single₀_epi_at_zero
 
+/- warning: homological_complex.hom.to_single₀_exact_d_f_at_zero -> HomologicalComplex.Hom.to_single₀_exact_d_f_at_zero is a dubious translation:
+lean 3 declaration is
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne} {Y : W} (f : Quiver.Hom.{succ u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9)) Y)) [hf : QuasiIso.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasPullbacks.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9))) (CategoryTheory.Abelian.hasCokernels.{u2, u1} W _inst_8 _inst_9) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) X (CategoryTheory.Functor.obj.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9)) Y) f], CategoryTheory.Exact.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasKernels.{u2, u1} W _inst_8 _inst_9) (HomologicalComplex.x.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat 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(HomologicalComplex.x.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Functor.obj.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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(HomologicalComplex.d.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) X (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) X (CategoryTheory.Functor.obj.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9)) Y) f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))
+but is expected to have type
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)} {Y : W} (f : Quiver.Hom.{succ u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) X (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y)) [hf : QuasiIso.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, 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+Case conversion may be inaccurate. Consider using '#align homological_complex.hom.to_single₀_exact_d_f_at_zero HomologicalComplex.Hom.to_single₀_exact_d_f_at_zeroₓ'. -/
 theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f 0) :=
   by
   rw [preadditive.exact_iff_homology_zero]
@@ -146,6 +212,12 @@ theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f
     infer_instance
 #align homological_complex.hom.to_single₀_exact_d_f_at_zero HomologicalComplex.Hom.to_single₀_exact_d_f_at_zero
 
+/- warning: homological_complex.hom.to_single₀_exact_at_succ -> HomologicalComplex.Hom.to_single₀_exact_at_succ is a dubious translation:
+lean 3 declaration is
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne} {Y : W} (f : Quiver.Hom.{succ u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) X (CategoryTheory.Functor.obj.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9)) Y)) [hf : QuasiIso.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasPullbacks.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9))) (CategoryTheory.Abelian.hasCokernels.{u2, u1} W _inst_8 _inst_9) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) X (CategoryTheory.Functor.obj.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9)) Y) f] (n : Nat), CategoryTheory.Exact.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasKernels.{u2, u1} W _inst_8 _inst_9) (HomologicalComplex.x.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))))) (HomologicalComplex.x.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HomologicalComplex.x.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) X n) (HomologicalComplex.d.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))) (HomologicalComplex.d.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) n (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))) n)
+but is expected to have type
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)} {Y : W} (f : Quiver.Hom.{succ u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) X (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (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.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y)) [hf : QuasiIso.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasPullbacks.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9))) (CategoryTheory.Limits.hasCokernels_of_hasCoequalizers.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasCoequalizers.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (ChainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) 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u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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_inst_9)) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X n) (HomologicalComplex.d.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.d.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.down.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) n)
+Case conversion may be inaccurate. Consider using '#align homological_complex.hom.to_single₀_exact_at_succ HomologicalComplex.Hom.to_single₀_exact_at_succₓ'. -/
 theorem to_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
     Exact (X.d (n + 2) (n + 1)) (X.d (n + 1) n) :=
   (Preadditive.exact_iff_homology_zero _ _).2
@@ -160,6 +232,12 @@ section
 
 variable {X : CochainComplex W ℕ} {Y : W} (f : (CochainComplex.single₀ _).obj Y ⟶ X)
 
+/- warning: homological_complex.hom.from_single₀_kernel_at_zero_iso -> HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso is a dubious translation:
+lean 3 declaration is
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne} {Y : W} (f : Quiver.Hom.{succ u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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+but is expected to have type
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)} {Y : W} (f : Quiver.Hom.{succ u2, max u2 u1} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) X) [hf : QuasiIso.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasPullbacks.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9))) (CategoryTheory.Limits.hasCokernels_of_hasCoequalizers.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasCoequalizers.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) X f], CategoryTheory.Iso.{u2, u1} W _inst_8 (CategoryTheory.Limits.kernel.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.d.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (CategoryTheory.Limits.HasKernels.has_limit.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasKernels_of_hasEqualizers.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.d.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) Y
+Case conversion may be inaccurate. Consider using '#align homological_complex.hom.from_single₀_kernel_at_zero_iso HomologicalComplex.Hom.fromSingle₀KernelAtZeroIsoₓ'. -/
 /-- If a cochain map `f : Y[0] ⟶ X` is a quasi-isomorphism, then the kernel of the differential
 `d : X₀ → X₁` is isomorphic to `Y.` -/
 noncomputable def fromSingle₀KernelAtZeroIso [hf : QuasiIso f] : kernel (X.d 0 1) ≅ Y :=
@@ -167,6 +245,12 @@ noncomputable def fromSingle₀KernelAtZeroIso [hf : QuasiIso f] : kernel (X.d 0
     ((@asIso _ _ _ _ _ (hf.1 0)).symm.trans ((CochainComplex.homologyFunctor0Single₀ W).app Y))
 #align homological_complex.hom.from_single₀_kernel_at_zero_iso HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso
 
+/- warning: homological_complex.hom.from_single₀_kernel_at_zero_iso_inv_eq -> HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso_inv_eq is a dubious translation:
+lean 3 declaration is
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne} {Y : W} (f : Quiver.Hom.{succ u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)))) (CategoryTheory.Functor.obj.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9)) Y) X) [hf : QuasiIso.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 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_inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Functor.obj.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (HomologicalComplex.CategoryTheory.category.{u2, u1, 0} Nat W _inst_8 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9)) Y) X f (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))
+but is expected to have type
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)} {Y : W} (f : Quiver.Hom.{succ u2, max u2 u1} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max 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(OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) => Eq.{1} Prop (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (CategoryTheory.CategoryStruct.comp.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) 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(AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{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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Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))) (Eq.refl.{1} Prop (Eq.{succ u2} (Quiver.Hom.{succ u2, u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (CategoryTheory.CategoryStruct.comp.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) 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(StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) X f (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))
+Case conversion may be inaccurate. Consider using '#align homological_complex.hom.from_single₀_kernel_at_zero_iso_inv_eq HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso_inv_eqₓ'. -/
 theorem fromSingle₀KernelAtZeroIso_inv_eq [hf : QuasiIso f] :
     f.fromSingle₀KernelAtZeroIso.inv =
       kernel.lift (X.d 0 1) (f.f 0) (by rw [f.2 0 1 rfl] <;> exact zero_comp) :=
@@ -183,6 +267,12 @@ theorem fromSingle₀KernelAtZeroIso_inv_eq [hf : QuasiIso f] :
   simp [homology.π, kernel_subobject_map_comp, iso.refl_hom (X.X 0), category.comp_id]
 #align homological_complex.hom.from_single₀_kernel_at_zero_iso_inv_eq HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso_inv_eq
 
+/- warning: homological_complex.hom.from_single₀_mono_at_zero -> HomologicalComplex.Hom.from_single₀_mono_at_zero is a dubious translation:
+lean 3 declaration is
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne} {Y : W} (f : Quiver.Hom.{succ u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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+but is expected to have type
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)} {Y : W} (f : Quiver.Hom.{succ u2, max u2 u1} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) X) [hf : QuasiIso.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasPullbacks.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9))) (CategoryTheory.Limits.hasCokernels_of_hasCoequalizers.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasCoequalizers.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) X f], CategoryTheory.Mono.{u2, u1} W _inst_8 (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) X f (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
+Case conversion may be inaccurate. Consider using '#align homological_complex.hom.from_single₀_mono_at_zero HomologicalComplex.Hom.from_single₀_mono_at_zeroₓ'. -/
 theorem from_single₀_mono_at_zero [hf : QuasiIso f] : Mono (f.f 0) :=
   by
   constructor
@@ -192,6 +282,12 @@ theorem from_single₀_mono_at_zero [hf : QuasiIso f] : Mono (f.f 0) :=
   rw [(@cancel_mono _ _ _ _ _ _ (mono_comp _ _) _ _).1 Hgh]
 #align homological_complex.hom.from_single₀_mono_at_zero HomologicalComplex.Hom.from_single₀_mono_at_zero
 
+/- warning: homological_complex.hom.from_single₀_exact_f_d_at_zero -> HomologicalComplex.Hom.from_single₀_exact_f_d_at_zero is a dubious translation:
+lean 3 declaration is
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne} {Y : W} (f : Quiver.Hom.{succ u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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+but is expected to have type
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)} {Y : W} (f : Quiver.Hom.{succ u2, max u2 u1} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) X) [hf : QuasiIso.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasPullbacks.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9))) (CategoryTheory.Limits.hasCokernels_of_hasCoequalizers.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasCoequalizers.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) X f], CategoryTheory.Exact.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasKernels_of_hasEqualizers.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (HomologicalComplex.X.{u2, u1, 0} Nat 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(OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HomologicalComplex.Hom.f.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W 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+Case conversion may be inaccurate. Consider using '#align homological_complex.hom.from_single₀_exact_f_d_at_zero HomologicalComplex.Hom.from_single₀_exact_f_d_at_zeroₓ'. -/
 theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso f] : Exact (f.f 0) (X.d 0 1) :=
   by
   rw [preadditive.exact_iff_homology_zero]
@@ -206,6 +302,12 @@ theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso f] : Exact (f.f 0) (X.d
     infer_instance
 #align homological_complex.hom.from_single₀_exact_f_d_at_zero HomologicalComplex.Hom.from_single₀_exact_f_d_at_zero
 
+/- warning: homological_complex.hom.from_single₀_exact_at_succ -> HomologicalComplex.Hom.from_single₀_exact_at_succ is a dubious translation:
+lean 3 declaration is
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne} {Y : W} (f : Quiver.Hom.{succ u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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+but is expected to have type
+  forall {W : Type.{u1}} [_inst_8 : CategoryTheory.Category.{u2, u1} W] [_inst_9 : CategoryTheory.Abelian.{u2, u1} W _inst_8] {X : CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)} {Y : W} (f : Quiver.Hom.{succ u2, max u2 u1} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) X) [hf : QuasiIso.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasPullbacks.{u2, u1} W _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9))) (CategoryTheory.Limits.hasCokernels_of_hasCoequalizers.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasCoequalizers.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u2, succ u2, u1, max u2 u1} W (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} W (CategoryTheory.Category.toCategoryStruct.{u2, u1} W _inst_8)) (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u2, max u1 u2} (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u2, u2, u1, max u1 u2} W _inst_8 (CochainComplex.{u2, u1, 0} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasZeroObject.{u2, u1} W _inst_8 _inst_9))) Y) X f] (n : Nat), CategoryTheory.Exact.{u2, u1} W _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Limits.hasKernels_of_hasEqualizers.{u2, u1} W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} W _inst_8 _inst_9)) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X n) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.X.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)))) (HomologicalComplex.d.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X n (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))) (HomologicalComplex.d.{u2, u1, 0} Nat W _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} W _inst_8 (CategoryTheory.Abelian.toPreadditive.{u2, u1} W _inst_8 _inst_9)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) X (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))) (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2))))
+Case conversion may be inaccurate. Consider using '#align homological_complex.hom.from_single₀_exact_at_succ HomologicalComplex.Hom.from_single₀_exact_at_succₓ'. -/
 theorem from_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
     Exact (X.d n (n + 1)) (X.d (n + 1) (n + 2)) :=
   (Preadditive.exact_iff_homology_zero _ _).2
@@ -223,6 +325,12 @@ end HomologicalComplex.Hom
 variable {A : Type _} [Category A] [Abelian A] {B : Type _} [Category B] [Abelian B] (F : A ⥤ B)
   [Functor.Additive F] [PreservesFiniteLimits F] [PreservesFiniteColimits F] [Faithful F]
 
+/- warning: category_theory.functor.quasi_iso_of_map_quasi_iso -> CategoryTheory.Functor.quasiIso_of_map_quasiIso is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {c : ComplexShape.{u1} ι} {A : Type.{u2}} [_inst_8 : CategoryTheory.Category.{u3, u2} A] [_inst_9 : CategoryTheory.Abelian.{u3, u2} A _inst_8] {B : Type.{u4}} [_inst_10 : CategoryTheory.Category.{u5, u4} B] [_inst_11 : CategoryTheory.Abelian.{u5, u4} B _inst_10] (F : CategoryTheory.Functor.{u3, u5, u2, u4} A _inst_8 B _inst_10) [_inst_12 : CategoryTheory.Functor.Additive.{u2, u4, u3, u5} A B _inst_8 _inst_10 (CategoryTheory.Abelian.toPreadditive.{u3, u2} A _inst_8 _inst_9) (CategoryTheory.Abelian.toPreadditive.{u5, u4} B _inst_10 _inst_11) F] [_inst_13 : CategoryTheory.Limits.PreservesFiniteLimits.{u3, u5, u2, u4} A _inst_8 B _inst_10 F] [_inst_14 : CategoryTheory.Limits.PreservesFiniteColimits.{u3, u5, u2, u4} A _inst_8 B _inst_10 F] [_inst_15 : CategoryTheory.Faithful.{u3, u5, u2, u4} A _inst_8 B _inst_10 F] {C : HomologicalComplex.{u3, u2, u1} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u3, u2} A _inst_8 _inst_9)) c} {D : HomologicalComplex.{u3, u2, u1} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u3, u2} A _inst_8 _inst_9)) c} (f : Quiver.Hom.{succ (max u1 u3), max u2 u1 u3} (HomologicalComplex.{u3, u2, u1} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u3, u2} A _inst_8 _inst_9)) c) (CategoryTheory.CategoryStruct.toQuiver.{max u1 u3, max u2 u1 u3} (HomologicalComplex.{u3, u2, u1} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u3, u2} A _inst_8 _inst_9)) c) (CategoryTheory.Category.toCategoryStruct.{max u1 u3, max u2 u1 u3} (HomologicalComplex.{u3, u2, u1} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u2} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u3, u2} A 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+but is expected to have type
+  forall {ι : Type.{u3}} {c : ComplexShape.{u3} ι} {A : Type.{u4}} [_inst_8 : CategoryTheory.Category.{u5, u4} A] [_inst_9 : CategoryTheory.Abelian.{u5, u4} A _inst_8] {B : Type.{u1}} [_inst_10 : CategoryTheory.Category.{u2, u1} B] [_inst_11 : CategoryTheory.Abelian.{u2, u1} B _inst_10] (F : CategoryTheory.Functor.{u5, u2, u4, u1} A _inst_8 B _inst_10) [_inst_12 : CategoryTheory.Functor.Additive.{u4, u1, u5, u2} A B _inst_8 _inst_10 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9) (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11) F] [_inst_13 : CategoryTheory.Limits.PreservesFiniteLimits.{u5, u2, u4, u1} A _inst_8 B _inst_10 F] [_inst_14 : CategoryTheory.Limits.PreservesFiniteColimits.{u5, u2, u4, u1} A _inst_8 B _inst_10 F] [_inst_15 : CategoryTheory.Faithful.{u5, u2, u4, u1} A _inst_8 B _inst_10 F] {C : HomologicalComplex.{u5, u4, u3} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} A _inst_8 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max (max u1 u2) u3} (HomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max (max u1 u2) u3} (HomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c))) (CategoryTheory.Functor.toPrefunctor.{max u5 u3, max u2 u3, max (max u4 u5) u3, max (max u1 u2) u3} (HomologicalComplex.{u5, u4, u3} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9)) c) (HomologicalComplex.instCategoryHomologicalComplex.{u5, u4, u3} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9)) c) (HomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c) (CategoryTheory.Functor.mapHomologicalComplex.{u5, u4, u3, u1, u2} ι A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9) B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11) F _inst_12 c)) D) (Prefunctor.map.{max (succ u5) (succ u3), max (succ u2) (succ u3), max (max u4 u5) u3, max (max u1 u2) u3} (HomologicalComplex.{u5, u4, u3} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9)) c) (CategoryTheory.CategoryStruct.toQuiver.{max u5 u3, max (max u4 u5) u3} (HomologicalComplex.{u5, u4, u3} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9)) c) (CategoryTheory.Category.toCategoryStruct.{max u5 u3, max (max u4 u5) u3} (HomologicalComplex.{u5, u4, u3} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9)) c) (HomologicalComplex.instCategoryHomologicalComplex.{u5, u4, u3} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9)) c))) (HomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u3, max (max u1 u2) u3} (HomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c) (CategoryTheory.Category.toCategoryStruct.{max u2 u3, max (max u1 u2) u3} (HomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c))) (CategoryTheory.Functor.toPrefunctor.{max u5 u3, max u2 u3, max (max u4 u5) u3, max (max u1 u2) u3} (HomologicalComplex.{u5, u4, u3} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9)) c) (HomologicalComplex.instCategoryHomologicalComplex.{u5, u4, u3} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9)) c) (HomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c) (HomologicalComplex.instCategoryHomologicalComplex.{u2, u1, u3} ι B _inst_10 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11)) c) (CategoryTheory.Functor.mapHomologicalComplex.{u5, u4, u3, u1, u2} ι A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9) B _inst_10 (CategoryTheory.Abelian.toPreadditive.{u2, u1} B _inst_10 _inst_11) F _inst_12 c)) C D f)) -> (QuasiIso.{u5, u4, u3} ι A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9)) (CategoryTheory.Abelian.hasEqualizers.{u5, u4} A _inst_8 _inst_9) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u5, u4} A _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u5, u4} A _inst_8 _inst_9)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u5, u4} A _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u5, u4} A _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u5, u4} A _inst_8 _inst_9)) (CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers.{u5, u4} A _inst_8 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u5, u4} A _inst_8 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u5, u4} A _inst_8 _inst_9)) (CategoryTheory.Abelian.hasPullbacks.{u5, u4} A _inst_8 _inst_9) (CategoryTheory.Abelian.hasEqualizers.{u5, u4} A _inst_8 _inst_9))) (CategoryTheory.Limits.hasCokernels_of_hasCoequalizers.{u5, u4} A _inst_8 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u5, u4} A _inst_8 (CategoryTheory.Abelian.toPreadditive.{u5, u4} A _inst_8 _inst_9)) (CategoryTheory.Abelian.hasCoequalizers.{u5, u4} A _inst_8 _inst_9)) c C D f)
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.quasi_iso_of_map_quasi_iso CategoryTheory.Functor.quasiIso_of_map_quasiIsoₓ'. -/
 theorem CategoryTheory.Functor.quasiIso_of_map_quasiIso {C D : HomologicalComplex A c} (f : C ⟶ D)
     (hf : QuasiIso ((F.mapHomologicalComplex _).map f)) : QuasiIso f :=
   ⟨fun i =>

956af7c7

bump to nightly-2023-04-20-00

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

d6678ca6

Diff

@@ -133,26 +133,26 @@ theorem to_single₀_epi_at_zero [hf : QuasiIso f] : Epi (f.f 0) :=
   rw [(@cancel_epi _ _ _ _ _ _ (epi_comp _ _) _ _).1 Hgh]
 #align homological_complex.hom.to_single₀_epi_at_zero HomologicalComplex.Hom.to_single₀_epi_at_zero
 
-theorem toSingle₀ExactDFAtZero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f 0) :=
+theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f 0) :=
   by
   rw [preadditive.exact_iff_homology_zero]
   have h : X.d 1 0 ≫ f.f 0 = 0 := by
-    simp only [← f.2 1 0 rfl, ChainComplex.single₀_obj_x_d, comp_zero]
+    simp only [← f.2 1 0 rfl, ChainComplex.single₀_obj_X_d, comp_zero]
   refine' ⟨h, Nonempty.intro (homologyIsoKernelDesc _ _ _ ≪≫ _)⟩
   · suffices is_iso (cokernel.desc _ _ h) by
       haveI := this
       apply kernel.of_mono
     rw [← to_single₀_cokernel_at_zero_iso_hom_eq]
     infer_instance
-#align homological_complex.hom.to_single₀_exact_d_f_at_zero HomologicalComplex.Hom.toSingle₀ExactDFAtZero
+#align homological_complex.hom.to_single₀_exact_d_f_at_zero HomologicalComplex.Hom.to_single₀_exact_d_f_at_zero
 
-theorem toSingle₀ExactAtSucc [hf : QuasiIso f] (n : ℕ) :
+theorem to_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
     Exact (X.d (n + 2) (n + 1)) (X.d (n + 1) n) :=
   (Preadditive.exact_iff_homology_zero _ _).2
     ⟨X.d_comp_d _ _ _,
       ⟨(ChainComplex.homologySuccIso _ _).symm.trans
           ((@asIso _ _ _ _ _ (hf.1 (n + 1))).trans homologyZeroZero)⟩⟩
-#align homological_complex.hom.to_single₀_exact_at_succ HomologicalComplex.Hom.toSingle₀ExactAtSucc
+#align homological_complex.hom.to_single₀_exact_at_succ HomologicalComplex.Hom.to_single₀_exact_at_succ
 
 end
 
@@ -192,11 +192,11 @@ theorem from_single₀_mono_at_zero [hf : QuasiIso f] : Mono (f.f 0) :=
   rw [(@cancel_mono _ _ _ _ _ _ (mono_comp _ _) _ _).1 Hgh]
 #align homological_complex.hom.from_single₀_mono_at_zero HomologicalComplex.Hom.from_single₀_mono_at_zero
 
-theorem fromSingle₀ExactFDAtZero [hf : QuasiIso f] : Exact (f.f 0) (X.d 0 1) :=
+theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso f] : Exact (f.f 0) (X.d 0 1) :=
   by
   rw [preadditive.exact_iff_homology_zero]
   have h : f.f 0 ≫ X.d 0 1 = 0 := by
-    simp only [HomologicalComplex.Hom.comm, CochainComplex.single₀_obj_x_d, zero_comp]
+    simp only [HomologicalComplex.Hom.comm, CochainComplex.single₀_obj_X_d, zero_comp]
   refine' ⟨h, Nonempty.intro (homologyIsoCokernelLift _ _ _ ≪≫ _)⟩
   · suffices is_iso (kernel.lift (X.d 0 1) (f.f 0) h)
       by
@@ -204,15 +204,15 @@ theorem fromSingle₀ExactFDAtZero [hf : QuasiIso f] : Exact (f.f 0) (X.d 0 1) :
       apply cokernel.of_epi
     rw [← from_single₀_kernel_at_zero_iso_inv_eq f]
     infer_instance
-#align homological_complex.hom.from_single₀_exact_f_d_at_zero HomologicalComplex.Hom.fromSingle₀ExactFDAtZero
+#align homological_complex.hom.from_single₀_exact_f_d_at_zero HomologicalComplex.Hom.from_single₀_exact_f_d_at_zero
 
-theorem fromSingle₀ExactAtSucc [hf : QuasiIso f] (n : ℕ) :
+theorem from_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
     Exact (X.d n (n + 1)) (X.d (n + 1) (n + 2)) :=
   (Preadditive.exact_iff_homology_zero _ _).2
     ⟨X.d_comp_d _ _ _,
       ⟨(CochainComplex.homologySuccIso _ _).symm.trans
           ((@asIso _ _ _ _ _ (hf.1 (n + 1))).symm.trans homologyZeroZero)⟩⟩
-#align homological_complex.hom.from_single₀_exact_at_succ HomologicalComplex.Hom.fromSingle₀ExactAtSucc
+#align homological_complex.hom.from_single₀_exact_at_succ HomologicalComplex.Hom.from_single₀_exact_at_succ
 
 end

956af7c7

bump to nightly-2023-04-18-00

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

7809aa1d

Diff

@@ -133,7 +133,7 @@ theorem to_single₀_epi_at_zero [hf : QuasiIso f] : Epi (f.f 0) :=
   rw [(@cancel_epi _ _ _ _ _ _ (epi_comp _ _) _ _).1 Hgh]
 #align homological_complex.hom.to_single₀_epi_at_zero HomologicalComplex.Hom.to_single₀_epi_at_zero
 
-theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f 0) :=
+theorem toSingle₀ExactDFAtZero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f 0) :=
   by
   rw [preadditive.exact_iff_homology_zero]
   have h : X.d 1 0 ≫ f.f 0 = 0 := by
@@ -144,15 +144,15 @@ theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f
       apply kernel.of_mono
     rw [← to_single₀_cokernel_at_zero_iso_hom_eq]
     infer_instance
-#align homological_complex.hom.to_single₀_exact_d_f_at_zero HomologicalComplex.Hom.to_single₀_exact_d_f_at_zero
+#align homological_complex.hom.to_single₀_exact_d_f_at_zero HomologicalComplex.Hom.toSingle₀ExactDFAtZero
 
-theorem to_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
+theorem toSingle₀ExactAtSucc [hf : QuasiIso f] (n : ℕ) :
     Exact (X.d (n + 2) (n + 1)) (X.d (n + 1) n) :=
   (Preadditive.exact_iff_homology_zero _ _).2
     ⟨X.d_comp_d _ _ _,
       ⟨(ChainComplex.homologySuccIso _ _).symm.trans
           ((@asIso _ _ _ _ _ (hf.1 (n + 1))).trans homologyZeroZero)⟩⟩
-#align homological_complex.hom.to_single₀_exact_at_succ HomologicalComplex.Hom.to_single₀_exact_at_succ
+#align homological_complex.hom.to_single₀_exact_at_succ HomologicalComplex.Hom.toSingle₀ExactAtSucc
 
 end
 
@@ -192,7 +192,7 @@ theorem from_single₀_mono_at_zero [hf : QuasiIso f] : Mono (f.f 0) :=
   rw [(@cancel_mono _ _ _ _ _ _ (mono_comp _ _) _ _).1 Hgh]
 #align homological_complex.hom.from_single₀_mono_at_zero HomologicalComplex.Hom.from_single₀_mono_at_zero
 
-theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso f] : Exact (f.f 0) (X.d 0 1) :=
+theorem fromSingle₀ExactFDAtZero [hf : QuasiIso f] : Exact (f.f 0) (X.d 0 1) :=
   by
   rw [preadditive.exact_iff_homology_zero]
   have h : f.f 0 ≫ X.d 0 1 = 0 := by
@@ -204,15 +204,15 @@ theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso f] : Exact (f.f 0) (X.d
       apply cokernel.of_epi
     rw [← from_single₀_kernel_at_zero_iso_inv_eq f]
     infer_instance
-#align homological_complex.hom.from_single₀_exact_f_d_at_zero HomologicalComplex.Hom.from_single₀_exact_f_d_at_zero
+#align homological_complex.hom.from_single₀_exact_f_d_at_zero HomologicalComplex.Hom.fromSingle₀ExactFDAtZero
 
-theorem from_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
+theorem fromSingle₀ExactAtSucc [hf : QuasiIso f] (n : ℕ) :
     Exact (X.d n (n + 1)) (X.d (n + 1) (n + 2)) :=
   (Preadditive.exact_iff_homology_zero _ _).2
     ⟨X.d_comp_d _ _ _,
       ⟨(CochainComplex.homologySuccIso _ _).symm.trans
           ((@asIso _ _ _ _ _ (hf.1 (n + 1))).symm.trans homologyZeroZero)⟩⟩
-#align homological_complex.hom.from_single₀_exact_at_succ HomologicalComplex.Hom.from_single₀_exact_at_succ
+#align homological_complex.hom.from_single₀_exact_at_succ HomologicalComplex.Hom.fromSingle₀ExactAtSucc
 
 end

956af7c7

bump to nightly-2023-03-07-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/3b267e70a936eebb21ab546f49a8df34dd300b25

c0bba963

Diff

@@ -44,26 +44,28 @@ class QuasiIso (f : C ⟶ D) : Prop where
 
 attribute [instance] QuasiIso.isIso
 
-instance (priority := 100) quasiIsoOfIso (f : C ⟶ D) [IsIso f] : QuasiIso f
+instance (priority := 100) quasiIso_of_iso (f : C ⟶ D) [IsIso f] : QuasiIso f
     where IsIso i :=
     by
     change is_iso ((homologyFunctor V c i).mapIso (as_iso f)).Hom
     infer_instance
-#align quasi_iso_of_iso quasiIsoOfIso
+#align quasi_iso_of_iso quasiIso_of_iso
 
-instance quasiIsoComp (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso g] : QuasiIso (f ≫ g)
+instance quasiIso_comp (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso g] : QuasiIso (f ≫ g)
     where IsIso i := by
     rw [functor.map_comp]
     infer_instance
-#align quasi_iso_comp quasiIsoComp
+#align quasi_iso_comp quasiIso_comp
 
-theorem quasiIsoOfCompLeft (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso (f ≫ g)] : QuasiIso g :=
+theorem quasiIso_of_comp_left (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso (f ≫ g)] :
+    QuasiIso g :=
   { IsIso := fun i => IsIso.of_isIso_fac_left ((homologyFunctor V c i).map_comp f g).symm }
-#align quasi_iso_of_comp_left quasiIsoOfCompLeft
+#align quasi_iso_of_comp_left quasiIso_of_comp_left
 
-theorem quasiIsoOfCompRight (f : C ⟶ D) (g : D ⟶ E) [QuasiIso g] [QuasiIso (f ≫ g)] : QuasiIso f :=
+theorem quasiIso_of_comp_right (f : C ⟶ D) (g : D ⟶ E) [QuasiIso g] [QuasiIso (f ≫ g)] :
+    QuasiIso f :=
   { IsIso := fun i => IsIso.of_isIso_fac_right ((homologyFunctor V c i).map_comp f g).symm }
-#align quasi_iso_of_comp_right quasiIsoOfCompRight
+#align quasi_iso_of_comp_right quasiIso_of_comp_right
 
 namespace HomotopyEquiv
 
@@ -73,21 +75,21 @@ variable {W : Type _} [Category W] [Preadditive W] [HasCokernels W] [HasImages W
   [HasZeroObject W] [HasImageMaps W]
 
 /-- An homotopy equivalence is a quasi-isomorphism. -/
-theorem toQuasiIso {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) : QuasiIso e.Hom :=
+theorem to_quasiIso {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) : QuasiIso e.Hom :=
   ⟨fun i => by
     refine' ⟨⟨(homologyFunctor W c i).map e.inv, _⟩⟩
     simp only [← functor.map_comp, ← (homologyFunctor W c i).map_id]
     constructor <;> apply homology_map_eq_of_homotopy
     exacts[e.homotopy_hom_inv_id, e.homotopy_inv_hom_id]⟩
-#align homotopy_equiv.to_quasi_iso HomotopyEquiv.toQuasiIso
+#align homotopy_equiv.to_quasi_iso HomotopyEquiv.to_quasiIso
 
-theorem toQuasiIso_inv {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) (i : ι) :
-    (@asIso _ _ _ _ _ (e.toQuasiIso.1 i)).inv = (homologyFunctor W c i).map e.inv :=
+theorem to_quasiIso_inv {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) (i : ι) :
+    (@asIso _ _ _ _ _ (e.to_quasiIso.1 i)).inv = (homologyFunctor W c i).map e.inv :=
   by
   symm
   simp only [← iso.hom_comp_eq_id, as_iso_hom, ← functor.map_comp, ← (homologyFunctor W c i).map_id,
     homology_map_eq_of_homotopy e.homotopy_hom_inv_id _]
-#align homotopy_equiv.to_quasi_iso_inv HomotopyEquiv.toQuasiIso_inv
+#align homotopy_equiv.to_quasi_iso_inv HomotopyEquiv.to_quasiIso_inv
 
 end
 
@@ -221,7 +223,7 @@ end HomologicalComplex.Hom
 variable {A : Type _} [Category A] [Abelian A] {B : Type _} [Category B] [Abelian B] (F : A ⥤ B)
   [Functor.Additive F] [PreservesFiniteLimits F] [PreservesFiniteColimits F] [Faithful F]
 
-theorem CategoryTheory.Functor.quasiIsoOfMapQuasiIso {C D : HomologicalComplex A c} (f : C ⟶ D)
+theorem CategoryTheory.Functor.quasiIso_of_map_quasiIso {C D : HomologicalComplex A c} (f : C ⟶ D)
     (hf : QuasiIso ((F.mapHomologicalComplex _).map f)) : QuasiIso f :=
   ⟨fun i =>
     haveI : is_iso (F.map ((homologyFunctor A c i).map f)) :=
@@ -229,5 +231,5 @@ theorem CategoryTheory.Functor.quasiIsoOfMapQuasiIso {C D : HomologicalComplex A
       rw [← functor.comp_map, ← nat_iso.naturality_2 (F.homology_functor_iso i) f, functor.comp_map]
       infer_instance
     is_iso_of_reflects_iso _ F⟩
-#align category_theory.functor.quasi_iso_of_map_quasi_iso CategoryTheory.Functor.quasiIsoOfMapQuasiIso
+#align category_theory.functor.quasi_iso_of_map_quasi_iso CategoryTheory.Functor.quasiIso_of_map_quasiIso

956af7c7

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

956af7c7

chore(CategoryTheory): move Full, Faithful, EssSurj, IsEquivalence and ReflectsIsomorphisms to the Functor namespace (#11985)

These notions on functors are now Functor.Full, Functor.Faithful, Functor.EssSurj, Functor.IsEquivalence, Functor.ReflectsIsomorphisms. Deprecated aliases are introduced for the previous names.

65b7affc

Diff

@@ -203,7 +203,7 @@ end ToSingle₀
 end HomologicalComplex.Hom
 
 variable {A : Type*} [Category A] [Abelian A] {B : Type*} [Category B] [Abelian B] (F : A ⥤ B)
-  [Functor.Additive F] [PreservesFiniteLimits F] [PreservesFiniteColimits F] [Faithful F]
+  [Functor.Additive F] [PreservesFiniteLimits F] [PreservesFiniteColimits F] [F.Faithful]
 
 theorem CategoryTheory.Functor.quasiIso'_of_map_quasiIso' {C D : HomologicalComplex A c}
     (f : C ⟶ D) (hf : QuasiIso' ((F.mapHomologicalComplex _).map f)) : QuasiIso' f :=
@@ -438,7 +438,7 @@ instance quasiIsoAt_map_of_preservesHomology [hφ : QuasiIsoAt φ i] :
   exact ShortComplex.quasiIso_map_of_preservesLeftHomology F
     ((shortComplexFunctor C₁ c i).map φ)
 
-lemma quasiIsoAt_map_iff_of_preservesHomology [ReflectsIsomorphisms F] :
+lemma quasiIsoAt_map_iff_of_preservesHomology [F.ReflectsIsomorphisms] :
     QuasiIsoAt ((F.mapHomologicalComplex c).map φ) i ↔ QuasiIsoAt φ i := by
   simp only [quasiIsoAt_iff]
   exact ShortComplex.quasiIso_map_iff_of_preservesLeftHomology F
@@ -455,7 +455,7 @@ variable [∀ i, K.HasHomology i] [∀ i, L.HasHomology i]
 instance quasiIso_map_of_preservesHomology [hφ : QuasiIso φ] :
     QuasiIso ((F.mapHomologicalComplex c).map φ) where
 
-lemma quasiIso_map_iff_of_preservesHomology [ReflectsIsomorphisms F] :
+lemma quasiIso_map_iff_of_preservesHomology [F.ReflectsIsomorphisms] :
     QuasiIso ((F.mapHomologicalComplex c).map φ) ↔ QuasiIso φ := by
   simp only [quasiIso_iff, quasiIsoAt_map_iff_of_preservesHomology φ F]

956af7c7

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

Empty lines were removed by executing the following Python script twice

import os
import re


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

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

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

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

75c86f04

Diff

@@ -29,9 +29,7 @@ variable {ι : Type*}
 section
 
 variable {V : Type u} [Category.{v} V] [HasZeroMorphisms V] [HasZeroObject V]
-
 variable [HasEqualizers V] [HasImages V] [HasImageMaps V] [HasCokernels V]
-
 variable {c : ComplexShape ι} {C D E : HomologicalComplex V c}
 
 /-- A chain map is a quasi-isomorphism if it induces isomorphisms on homology.

956af7c7

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

@@ -468,13 +468,13 @@ end PreservesHomology
 variable (C c)
 
 /-- The morphism property on `HomologicalComplex C c` given by quasi-isomorphisms. -/
-def qis [CategoryWithHomology C] :
+def quasiIso [CategoryWithHomology C] :
     MorphismProperty (HomologicalComplex C c) := fun _ _ f => QuasiIso f
 
 variable {C c}
 
 @[simp]
-lemma qis_iff [CategoryWithHomology C] (f : K ⟶ L) : qis C c f ↔ QuasiIso f := by rfl
+lemma mem_quasiIso_iff [CategoryWithHomology C] (f : K ⟶ L) : quasiIso C c f ↔ QuasiIso f := by rfl
 
 end HomologicalComplex
 
@@ -497,8 +497,10 @@ instance : QuasiIso e.hom where
 
 instance : QuasiIso e.inv := (inferInstance : QuasiIso e.symm.hom)
 
-lemma homotopyEquivalences_subset_qis [CategoryWithHomology C] :
-    homotopyEquivalences C c ⊆ qis C c := by
+variable (C c)
+
+lemma homotopyEquivalences_subset_quasiIso [CategoryWithHomology C] :
+    homotopyEquivalences C c ⊆ quasiIso C c := by
   rintro K L _ ⟨e, rfl⟩
-  simp only [qis_iff]
+  simp only [HomologicalComplex.mem_quasiIso_iff]
   infer_instance

956af7c7

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

@@ -422,6 +422,49 @@ lemma quasiIso_of_arrow_mk_iso (φ : K ⟶ L) (φ' : K' ⟶ L') (e : Arrow.mk φ
 
 namespace HomologicalComplex
 
+section PreservesHomology
+
+variable {C₁ C₂ : Type*} [Category C₁] [Category C₂] [Preadditive C₁] [Preadditive C₂]
+  {K L : HomologicalComplex C₁ c} (φ : K ⟶ L) (F : C₁ ⥤ C₂) [F.Additive]
+  [F.PreservesHomology]
+
+section
+
+variable (i : ι) [K.HasHomology i] [L.HasHomology i]
+  [((F.mapHomologicalComplex c).obj K).HasHomology i]
+  [((F.mapHomologicalComplex c).obj L).HasHomology i]
+
+instance quasiIsoAt_map_of_preservesHomology [hφ : QuasiIsoAt φ i] :
+    QuasiIsoAt ((F.mapHomologicalComplex c).map φ) i := by
+  rw [quasiIsoAt_iff] at hφ ⊢
+  exact ShortComplex.quasiIso_map_of_preservesLeftHomology F
+    ((shortComplexFunctor C₁ c i).map φ)
+
+lemma quasiIsoAt_map_iff_of_preservesHomology [ReflectsIsomorphisms F] :
+    QuasiIsoAt ((F.mapHomologicalComplex c).map φ) i ↔ QuasiIsoAt φ i := by
+  simp only [quasiIsoAt_iff]
+  exact ShortComplex.quasiIso_map_iff_of_preservesLeftHomology F
+    ((shortComplexFunctor C₁ c i).map φ)
+
+end
+
+section
+
+variable [∀ i, K.HasHomology i] [∀ i, L.HasHomology i]
+  [∀ i, ((F.mapHomologicalComplex c).obj K).HasHomology i]
+  [∀ i, ((F.mapHomologicalComplex c).obj L).HasHomology i]
+
+instance quasiIso_map_of_preservesHomology [hφ : QuasiIso φ] :
+    QuasiIso ((F.mapHomologicalComplex c).map φ) where
+
+lemma quasiIso_map_iff_of_preservesHomology [ReflectsIsomorphisms F] :
+    QuasiIso ((F.mapHomologicalComplex c).map φ) ↔ QuasiIso φ := by
+  simp only [quasiIso_iff, quasiIsoAt_map_iff_of_preservesHomology φ F]
+
+end
+
+end PreservesHomology
+
 variable (C c)
 
 /-- The morphism property on `HomologicalComplex C c` given by quasi-isomorphisms. -/

956af7c7

feat: the homology functor on the homotopy category for the new API (#8595)

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

b112cb6b

Diff

@@ -220,6 +220,8 @@ end
 
 open HomologicalComplex
 
+section
+
 variable {ι : Type*} {C : Type u} [Category.{v} C] [HasZeroMorphisms C]
   {c : ComplexShape ι} {K L M K' L' : HomologicalComplex C c}
 
@@ -417,3 +419,43 @@ lemma quasiIso_of_arrow_mk_iso (φ : K ⟶ L) (φ' : K' ⟶ L') (e : Arrow.mk φ
     [∀ i, K'.HasHomology i] [∀ i, L'.HasHomology i]
     [hφ : QuasiIso φ] : QuasiIso φ' := by
   simpa only [← quasiIso_iff_of_arrow_mk_iso φ φ' e]
+
+namespace HomologicalComplex
+
+variable (C c)
+
+/-- The morphism property on `HomologicalComplex C c` given by quasi-isomorphisms. -/
+def qis [CategoryWithHomology C] :
+    MorphismProperty (HomologicalComplex C c) := fun _ _ f => QuasiIso f
+
+variable {C c}
+
+@[simp]
+lemma qis_iff [CategoryWithHomology C] (f : K ⟶ L) : qis C c f ↔ QuasiIso f := by rfl
+
+end HomologicalComplex
+
+end
+
+section
+
+variable {ι : Type*} {C : Type u} [Category.{v} C] [Preadditive C]
+  {c : ComplexShape ι} {K L : HomologicalComplex C c}
+
+section
+
+variable (e : HomotopyEquiv K L) [∀ i, K.HasHomology i] [∀ i, L.HasHomology i]
+
+instance : QuasiIso e.hom where
+  quasiIsoAt n := by
+    classical
+    rw [quasiIsoAt_iff_isIso_homologyMap]
+    exact IsIso.of_iso (e.toHomologyIso n)
+
+instance : QuasiIso e.inv := (inferInstance : QuasiIso e.symm.hom)
+
+lemma homotopyEquivalences_subset_qis [CategoryWithHomology C] :
+    homotopyEquivalences C c ⊆ qis C c := by
+  rintro K L _ ⟨e, rfl⟩
+  simp only [qis_iff]
+  infer_instance

956af7c7

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Joël Riou
 -/
 import Mathlib.Algebra.Homology.Homotopy
-import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
+import Mathlib.Algebra.Homology.SingleHomology
 import Mathlib.CategoryTheory.Abelian.Homology
 
 #align_import algebra.homology.quasi_iso from "leanprover-community/mathlib"@"956af7c76589f444f2e1313911bad16366ea476d"
@@ -20,9 +20,7 @@ Define the derived category as the localization at quasi-isomorphisms? (TODO @jo
 -/
 
 
-open CategoryTheory
-
-open CategoryTheory.Limits
+open CategoryTheory Limits
 
 universe v u
 
@@ -133,8 +131,7 @@ theorem to_single₀_epi_at_zero [hf : QuasiIso' f] : Epi (f.f 0) := by
 
 theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso' f] : Exact (X.d 1 0) (f.f 0) := by
   rw [Preadditive.exact_iff_homology'_zero]
-  have h : X.d 1 0 ≫ f.f 0 = 0 := by
-    simp only [← f.2 1 0 rfl, ChainComplex.single₀_obj_X_d, comp_zero]
+  have h : X.d 1 0 ≫ f.f 0 = 0 := by simp only [← f.comm 1 0, single_obj_d, comp_zero]
   refine' ⟨h, Nonempty.intro (homology'IsoKernelDesc _ _ _ ≪≫ _)⟩
   suffices IsIso (cokernel.desc _ _ h) by apply kernel.ofMono
   rw [← toSingle₀CokernelAtZeroIso_hom_eq]
@@ -186,8 +183,7 @@ theorem from_single₀_mono_at_zero [hf : QuasiIso' f] : Mono (f.f 0) := by
 
 theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso' f] : Exact (f.f 0) (X.d 0 1) := by
   rw [Preadditive.exact_iff_homology'_zero]
-  have h : f.f 0 ≫ X.d 0 1 = 0 := by
-    simp only [HomologicalComplex.Hom.comm, CochainComplex.single₀_obj_X_d, zero_comp]
+  have h : f.f 0 ≫ X.d 0 1 = 0 := by simp
   refine' ⟨h, Nonempty.intro (homology'IsoCokernelLift _ _ _ ≪≫ _)⟩
   suffices IsIso (kernel.lift (X.d 0 1) (f.f 0) h) by apply cokernel.ofEpi
   rw [← fromSingle₀KernelAtZeroIso_inv_eq f]

956af7c7

feat: quasi-isomorphisms of homological complexes (#8206)

This PR defines the typeclass QuasiIso which corresponds to quasi-isomorphisms of homological complexes for the new homology API.

a189a128

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Joël Riou
 -/
 import Mathlib.Algebra.Homology.Homotopy
+import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex
 import Mathlib.CategoryTheory.Abelian.Homology
 
 #align_import algebra.homology.quasi_iso from "leanprover-community/mathlib"@"956af7c76589f444f2e1313911bad16366ea476d"
@@ -15,7 +16,7 @@ A chain map is a quasi-isomorphism if it induces isomorphisms on homology.
 
 ## Future work
 
-Define the derived category as the localization at quasi-isomorphisms?
+Define the derived category as the localization at quasi-isomorphisms? (TODO @joelriou)
 -/
 
 
@@ -27,6 +28,8 @@ universe v u
 
 variable {ι : Type*}
 
+section
+
 variable {V : Type u} [Category.{v} V] [HasZeroMorphisms V] [HasZeroObject V]
 
 variable [HasEqualizers V] [HasImages V] [HasImageMaps V] [HasCokernels V]
@@ -216,3 +219,205 @@ theorem CategoryTheory.Functor.quasiIso'_of_map_quasiIso' {C D : HomologicalComp
       infer_instance
     isIso_of_reflects_iso _ F⟩
 #align category_theory.functor.quasi_iso_of_map_quasi_iso CategoryTheory.Functor.quasiIso'_of_map_quasiIso'
+
+end
+
+open HomologicalComplex
+
+variable {ι : Type*} {C : Type u} [Category.{v} C] [HasZeroMorphisms C]
+  {c : ComplexShape ι} {K L M K' L' : HomologicalComplex C c}
+
+/-- A morphism of homological complexes `f : K ⟶ L` is a quasi-isomorphism in degree `i`
+when it induces a quasi-isomorphism of short complexes `K.sc i ⟶ L.sc i`. -/
+class QuasiIsoAt (f : K ⟶ L) (i : ι) [K.HasHomology i] [L.HasHomology i] : Prop where
+  quasiIso : ShortComplex.QuasiIso ((shortComplexFunctor C c i).map f)
+
+lemma quasiIsoAt_iff (f : K ⟶ L) (i : ι) [K.HasHomology i] [L.HasHomology i] :
+    QuasiIsoAt f i ↔
+      ShortComplex.QuasiIso ((shortComplexFunctor C c i).map f) := by
+  constructor
+  · intro h
+    exact h.quasiIso
+  · intro h
+    exact ⟨h⟩
+
+instance quasiIsoAt_of_isIso (f : K ⟶ L) [IsIso f] (i : ι) [K.HasHomology i] [L.HasHomology i] :
+    QuasiIsoAt f i := by
+  rw [quasiIsoAt_iff]
+  infer_instance
+
+lemma quasiIsoAt_iff' (f : K ⟶ L) (i j k : ι) (hi : c.prev j = i) (hk : c.next j = k)
+    [K.HasHomology j] [L.HasHomology j] [(K.sc' i j k).HasHomology] [(L.sc' i j k).HasHomology] :
+    QuasiIsoAt f j ↔
+      ShortComplex.QuasiIso ((shortComplexFunctor' C c i j k).map f) := by
+  rw [quasiIsoAt_iff]
+  exact ShortComplex.quasiIso_iff_of_arrow_mk_iso _ _
+    (Arrow.isoOfNatIso (natIsoSc' C c i j k hi hk) (Arrow.mk f))
+
+lemma quasiIsoAt_iff_isIso_homologyMap (f : K ⟶ L) (i : ι)
+    [K.HasHomology i] [L.HasHomology i] :
+    QuasiIsoAt f i ↔ IsIso (homologyMap f i) := by
+  rw [quasiIsoAt_iff, ShortComplex.quasiIso_iff]
+  rfl
+
+lemma quasiIsoAt_iff_exactAt (f : K ⟶ L) (i : ι) [K.HasHomology i] [L.HasHomology i]
+    (hK : K.ExactAt i) :
+    QuasiIsoAt f i ↔ L.ExactAt i := by
+  simp only [quasiIsoAt_iff, ShortComplex.quasiIso_iff, exactAt_iff,
+    ShortComplex.exact_iff_isZero_homology] at hK ⊢
+  constructor
+  · intro h
+    exact IsZero.of_iso hK (@asIso _ _ _ _ _ h).symm
+  · intro hL
+    exact ⟨⟨0, IsZero.eq_of_src hK _ _, IsZero.eq_of_tgt hL _ _⟩⟩
+
+lemma quasiIsoAt_iff_exactAt' (f : K ⟶ L) (i : ι) [K.HasHomology i] [L.HasHomology i]
+    (hL : L.ExactAt i) :
+    QuasiIsoAt f i ↔ K.ExactAt i := by
+  simp only [quasiIsoAt_iff, ShortComplex.quasiIso_iff, exactAt_iff,
+    ShortComplex.exact_iff_isZero_homology] at hL ⊢
+  constructor
+  · intro h
+    exact IsZero.of_iso hL (@asIso _ _ _ _ _ h)
+  · intro hK
+    exact ⟨⟨0, IsZero.eq_of_src hK _ _, IsZero.eq_of_tgt hL _ _⟩⟩
+
+instance (f : K ⟶ L) (i : ι) [K.HasHomology i] [L.HasHomology i] [hf : QuasiIsoAt f i] :
+    IsIso (homologyMap f i) := by
+  simpa only [quasiIsoAt_iff, ShortComplex.quasiIso_iff] using hf
+
+/-- The isomorphism `K.homology i ≅ L.homology i` induced by a morphism `f : K ⟶ L` such
+that `[QuasiIsoAt f i]` holds. -/
+@[simps! hom]
+noncomputable def isoOfQuasiIsoAt (f : K ⟶ L) (i : ι) [K.HasHomology i] [L.HasHomology i]
+    [QuasiIsoAt f i] : K.homology i ≅ L.homology i :=
+  asIso (homologyMap f i)
+
+@[reassoc (attr := simp)]
+lemma isoOfQuasiIsoAt_hom_inv_id (f : K ⟶ L) (i : ι) [K.HasHomology i] [L.HasHomology i]
+    [QuasiIsoAt f i] :
+    homologyMap f i ≫ (isoOfQuasiIsoAt f i).inv = 𝟙 _ :=
+  (isoOfQuasiIsoAt f i).hom_inv_id
+
+@[reassoc (attr := simp)]
+lemma isoOfQuasiIsoAt_inv_hom_id (f : K ⟶ L) (i : ι) [K.HasHomology i] [L.HasHomology i]
+    [QuasiIsoAt f i] :
+    (isoOfQuasiIsoAt f i).inv ≫ homologyMap f i = 𝟙 _ :=
+  (isoOfQuasiIsoAt f i).inv_hom_id
+
+lemma CochainComplex.quasiIsoAt₀_iff {K L : CochainComplex C ℕ} (f : K ⟶ L)
+    [K.HasHomology 0] [L.HasHomology 0] [(K.sc' 0 0 1).HasHomology] [(L.sc' 0 0 1).HasHomology] :
+    QuasiIsoAt f 0 ↔
+      ShortComplex.QuasiIso ((HomologicalComplex.shortComplexFunctor' C _ 0 0 1).map f) :=
+  quasiIsoAt_iff' _ _ _ _ (by simp) (by simp)
+
+lemma ChainComplex.quasiIsoAt₀_iff {K L : ChainComplex C ℕ} (f : K ⟶ L)
+    [K.HasHomology 0] [L.HasHomology 0] [(K.sc' 1 0 0).HasHomology] [(L.sc' 1 0 0).HasHomology] :
+    QuasiIsoAt f 0 ↔
+      ShortComplex.QuasiIso ((HomologicalComplex.shortComplexFunctor' C _ 1 0 0).map f) :=
+  quasiIsoAt_iff' _ _ _ _ (by simp) (by simp)
+
+/-- A morphism of homological complexes `f : K ⟶ L` is a quasi-isomorphism when it
+is so in every degree, i.e. when the induced maps `homologyMap f i : K.homology i ⟶ L.homology i`
+are all isomorphisms (see `quasiIso_iff` and `quasiIsoAt_iff_isIso_homologyMap`). -/
+class QuasiIso (f : K ⟶ L) [∀ i, K.HasHomology i] [∀ i, L.HasHomology i] : Prop where
+  quasiIsoAt : ∀ i, QuasiIsoAt f i := by infer_instance
+
+lemma quasiIso_iff (f : K ⟶ L) [∀ i, K.HasHomology i] [∀ i, L.HasHomology i] :
+    QuasiIso f ↔ ∀ i, QuasiIsoAt f i :=
+  ⟨fun h => h.quasiIsoAt, fun h => ⟨h⟩⟩
+
+attribute [instance] QuasiIso.quasiIsoAt
+
+instance quasiIso_of_isIso (f : K ⟶ L) [IsIso f] [∀ i, K.HasHomology i] [∀ i, L.HasHomology i] :
+    QuasiIso f where
+
+instance quasiIsoAt_comp (φ : K ⟶ L) (φ' : L ⟶ M) (i : ι) [K.HasHomology i]
+    [L.HasHomology i] [M.HasHomology i]
+    [hφ : QuasiIsoAt φ i] [hφ' : QuasiIsoAt φ' i] :
+    QuasiIsoAt (φ ≫ φ') i := by
+  rw [quasiIsoAt_iff] at hφ hφ' ⊢
+  rw [Functor.map_comp]
+  exact ShortComplex.quasiIso_comp _ _
+
+instance quasiIso_comp (φ : K ⟶ L) (φ' : L ⟶ M) [∀ i, K.HasHomology i]
+    [∀ i, L.HasHomology i] [∀ i, M.HasHomology i]
+    [hφ : QuasiIso φ] [hφ' : QuasiIso φ'] :
+    QuasiIso (φ ≫ φ') where
+
+lemma quasiIsoAt_of_comp_left (φ : K ⟶ L) (φ' : L ⟶ M) (i : ι) [K.HasHomology i]
+    [L.HasHomology i] [M.HasHomology i]
+    [hφ : QuasiIsoAt φ i] [hφφ' : QuasiIsoAt (φ ≫ φ') i] :
+    QuasiIsoAt φ' i := by
+  rw [quasiIsoAt_iff_isIso_homologyMap] at hφ hφφ' ⊢
+  rw [homologyMap_comp] at hφφ'
+  exact IsIso.of_isIso_comp_left (homologyMap φ i) (homologyMap φ' i)
+
+lemma quasiIsoAt_iff_comp_left (φ : K ⟶ L) (φ' : L ⟶ M) (i : ι) [K.HasHomology i]
+    [L.HasHomology i] [M.HasHomology i]
+    [hφ : QuasiIsoAt φ i] :
+    QuasiIsoAt (φ ≫ φ') i ↔ QuasiIsoAt φ' i := by
+  constructor
+  · intro
+    exact quasiIsoAt_of_comp_left φ φ' i
+  · intro
+    infer_instance
+
+lemma quasiIso_iff_comp_left (φ : K ⟶ L) (φ' : L ⟶ M) [∀ i, K.HasHomology i]
+    [∀ i, L.HasHomology i] [∀ i, M.HasHomology i]
+    [hφ : QuasiIso φ] :
+    QuasiIso (φ ≫ φ') ↔ QuasiIso φ' := by
+  simp only [quasiIso_iff, quasiIsoAt_iff_comp_left φ φ']
+
+lemma quasiIso_of_comp_left (φ : K ⟶ L) (φ' : L ⟶ M) [∀ i, K.HasHomology i]
+    [∀ i, L.HasHomology i] [∀ i, M.HasHomology i]
+    [hφ : QuasiIso φ] [hφφ' : QuasiIso (φ ≫ φ')] :
+    QuasiIso φ' := by
+  rw [← quasiIso_iff_comp_left φ φ']
+  infer_instance
+
+lemma quasiIsoAt_of_comp_right (φ : K ⟶ L) (φ' : L ⟶ M) (i : ι) [K.HasHomology i]
+    [L.HasHomology i] [M.HasHomology i]
+    [hφ' : QuasiIsoAt φ' i] [hφφ' : QuasiIsoAt (φ ≫ φ') i] :
+    QuasiIsoAt φ i := by
+  rw [quasiIsoAt_iff_isIso_homologyMap] at hφ' hφφ' ⊢
+  rw [homologyMap_comp] at hφφ'
+  exact IsIso.of_isIso_comp_right (homologyMap φ i) (homologyMap φ' i)
+
+lemma quasiIsoAt_iff_comp_right (φ : K ⟶ L) (φ' : L ⟶ M) (i : ι) [K.HasHomology i]
+    [L.HasHomology i] [M.HasHomology i]
+    [hφ' : QuasiIsoAt φ' i] :
+    QuasiIsoAt (φ ≫ φ') i ↔ QuasiIsoAt φ i := by
+  constructor
+  · intro
+    exact quasiIsoAt_of_comp_right φ φ' i
+  · intro
+    infer_instance
+
+lemma quasiIso_iff_comp_right (φ : K ⟶ L) (φ' : L ⟶ M) [∀ i, K.HasHomology i]
+    [∀ i, L.HasHomology i] [∀ i, M.HasHomology i]
+    [hφ' : QuasiIso φ'] :
+    QuasiIso (φ ≫ φ') ↔ QuasiIso φ := by
+  simp only [quasiIso_iff, quasiIsoAt_iff_comp_right φ φ']
+
+lemma quasiIso_of_comp_right (φ : K ⟶ L) (φ' : L ⟶ M) [∀ i, K.HasHomology i]
+    [∀ i, L.HasHomology i] [∀ i, M.HasHomology i]
+    [hφ : QuasiIso φ'] [hφφ' : QuasiIso (φ ≫ φ')] :
+    QuasiIso φ := by
+  rw [← quasiIso_iff_comp_right φ φ']
+  infer_instance
+
+lemma quasiIso_iff_of_arrow_mk_iso (φ : K ⟶ L) (φ' : K' ⟶ L') (e : Arrow.mk φ ≅ Arrow.mk φ')
+    [∀ i, K.HasHomology i] [∀ i, L.HasHomology i]
+    [∀ i, K'.HasHomology i] [∀ i, L'.HasHomology i] :
+    QuasiIso φ ↔ QuasiIso φ' := by
+  rw [← quasiIso_iff_comp_left (show K' ⟶ K from e.inv.left) φ,
+    ← quasiIso_iff_comp_right φ' (show L' ⟶ L from e.inv.right)]
+  erw [Arrow.w e.inv]
+  rfl
+
+lemma quasiIso_of_arrow_mk_iso (φ : K ⟶ L) (φ' : K' ⟶ L') (e : Arrow.mk φ ≅ Arrow.mk φ')
+    [∀ i, K.HasHomology i] [∀ i, L.HasHomology i]
+    [∀ i, K'.HasHomology i] [∀ i, L'.HasHomology i]
+    [hφ : QuasiIso φ] : QuasiIso φ' := by
+  simpa only [← quasiIso_iff_of_arrow_mk_iso φ φ' e]

956af7c7

refactor: introduce the new homology API for homological complex and rename the old one (#7954)

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

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

c5fe4511

Diff

@@ -35,33 +35,34 @@ variable {c : ComplexShape ι} {C D E : HomologicalComplex V c}
 
 /-- A chain map is a quasi-isomorphism if it induces isomorphisms on homology.
 -/
-class QuasiIso (f : C ⟶ D) : Prop where
-  isIso : ∀ i, IsIso ((homologyFunctor V c i).map f)
-#align quasi_iso QuasiIso
+class QuasiIso' (f : C ⟶ D) : Prop where
+  isIso : ∀ i, IsIso ((homology'Functor V c i).map f)
+#align quasi_iso QuasiIso'
 
-attribute [instance] QuasiIso.isIso
+attribute [instance] QuasiIso'.isIso
 
-instance (priority := 100) quasiIso_of_iso (f : C ⟶ D) [IsIso f] : QuasiIso f where
+instance (priority := 100) quasiIso'_of_iso (f : C ⟶ D) [IsIso f] : QuasiIso' f where
   isIso i := by
-    change IsIso ((homologyFunctor V c i).mapIso (asIso f)).hom
+    change IsIso ((homology'Functor V c i).mapIso (asIso f)).hom
     infer_instance
-#align quasi_iso_of_iso quasiIso_of_iso
+#align quasi_iso_of_iso quasiIso'_of_iso
 
-instance quasiIso_comp (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso g] : QuasiIso (f ≫ g) where
+instance quasiIso'_comp (f : C ⟶ D) [QuasiIso' f] (g : D ⟶ E) [QuasiIso' g] :
+    QuasiIso' (f ≫ g) where
   isIso i := by
     rw [Functor.map_comp]
     infer_instance
-#align quasi_iso_comp quasiIso_comp
+#align quasi_iso_comp quasiIso'_comp
 
-theorem quasiIso_of_comp_left (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso (f ≫ g)] :
-    QuasiIso g :=
-  { isIso := fun i => IsIso.of_isIso_fac_left ((homologyFunctor V c i).map_comp f g).symm }
-#align quasi_iso_of_comp_left quasiIso_of_comp_left
+theorem quasiIso'_of_comp_left (f : C ⟶ D) [QuasiIso' f] (g : D ⟶ E) [QuasiIso' (f ≫ g)] :
+    QuasiIso' g :=
+  { isIso := fun i => IsIso.of_isIso_fac_left ((homology'Functor V c i).map_comp f g).symm }
+#align quasi_iso_of_comp_left quasiIso'_of_comp_left
 
-theorem quasiIso_of_comp_right (f : C ⟶ D) (g : D ⟶ E) [QuasiIso g] [QuasiIso (f ≫ g)] :
-    QuasiIso f :=
-  { isIso := fun i => IsIso.of_isIso_fac_right ((homologyFunctor V c i).map_comp f g).symm }
-#align quasi_iso_of_comp_right quasiIso_of_comp_right
+theorem quasiIso'_of_comp_right (f : C ⟶ D) (g : D ⟶ E) [QuasiIso' g] [QuasiIso' (f ≫ g)] :
+    QuasiIso' f :=
+  { isIso := fun i => IsIso.of_isIso_fac_right ((homology'Functor V c i).map_comp f g).symm }
+#align quasi_iso_of_comp_right quasiIso'_of_comp_right
 
 namespace HomotopyEquiv
 
@@ -71,21 +72,21 @@ variable {W : Type*} [Category W] [Preadditive W] [HasCokernels W] [HasImages W]
   [HasZeroObject W] [HasImageMaps W]
 
 /-- A homotopy equivalence is a quasi-isomorphism. -/
-theorem toQuasiIso {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) : QuasiIso e.hom :=
+theorem toQuasiIso' {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) : QuasiIso' e.hom :=
   ⟨fun i => by
-    refine' ⟨⟨(homologyFunctor W c i).map e.inv, _⟩⟩
-    simp only [← Functor.map_comp, ← (homologyFunctor W c i).map_id]
-    constructor <;> apply homology_map_eq_of_homotopy
+    refine' ⟨⟨(homology'Functor W c i).map e.inv, _⟩⟩
+    simp only [← Functor.map_comp, ← (homology'Functor W c i).map_id]
+    constructor <;> apply homology'_map_eq_of_homotopy
     exacts [e.homotopyHomInvId, e.homotopyInvHomId]⟩
-#align homotopy_equiv.to_quasi_iso HomotopyEquiv.toQuasiIso
+#align homotopy_equiv.to_quasi_iso HomotopyEquiv.toQuasiIso'
 
-theorem toQuasiIso_inv {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) (i : ι) :
-    (@asIso _ _ _ _ _ (e.toQuasiIso.1 i)).inv = (homologyFunctor W c i).map e.inv := by
+theorem toQuasiIso'_inv {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) (i : ι) :
+    (@asIso _ _ _ _ _ (e.toQuasiIso'.1 i)).inv = (homology'Functor W c i).map e.inv := by
   symm
-  haveI := e.toQuasiIso.1 i -- Porting note: Added this to get `asIso_hom` to work.
-  simp only [← Iso.hom_comp_eq_id, asIso_hom, ← Functor.map_comp, ← (homologyFunctor W c i).map_id,
-    homology_map_eq_of_homotopy e.homotopyHomInvId _]
-#align homotopy_equiv.to_quasi_iso_inv HomotopyEquiv.toQuasiIso_inv
+  haveI := e.toQuasiIso'.1 i -- Porting note: Added this to get `asIso_hom` to work.
+  simp only [← Iso.hom_comp_eq_id, asIso_hom, ← Functor.map_comp,
+    ← (homology'Functor W c i).map_id, homology'_map_eq_of_homotopy e.homotopyHomInvId _]
+#align homotopy_equiv.to_quasi_iso_inv HomotopyEquiv.toQuasiIso'_inv
 
 end
 
@@ -99,27 +100,27 @@ variable {W : Type*} [Category W] [Abelian W]
 
 section
 
-variable {X : ChainComplex W ℕ} {Y : W} (f : X ⟶ (ChainComplex.single₀ _).obj Y) [hf : QuasiIso f]
+variable {X : ChainComplex W ℕ} {Y : W} (f : X ⟶ (ChainComplex.single₀ _).obj Y) [hf : QuasiIso' f]
 
 /-- If a chain map `f : X ⟶ Y[0]` is a quasi-isomorphism, then the cokernel of the differential
 `d : X₁ → X₀` is isomorphic to `Y`. -/
 noncomputable def toSingle₀CokernelAtZeroIso : cokernel (X.d 1 0) ≅ Y :=
-  X.homologyZeroIso.symm.trans
-    ((@asIso _ _ _ _ _ (hf.1 0)).trans ((ChainComplex.homologyFunctor0Single₀ W).app Y))
+  X.homology'ZeroIso.symm.trans
+    ((@asIso _ _ _ _ _ (hf.1 0)).trans ((ChainComplex.homology'Functor0Single₀ W).app Y))
 #align homological_complex.hom.to_single₀_cokernel_at_zero_iso HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso
 
-theorem toSingle₀CokernelAtZeroIso_hom_eq [hf : QuasiIso f] :
+theorem toSingle₀CokernelAtZeroIso_hom_eq [hf : QuasiIso' f] :
     f.toSingle₀CokernelAtZeroIso.hom =
       cokernel.desc (X.d 1 0) (f.f 0) (by rw [← f.2 1 0 rfl]; exact comp_zero) := by
   ext
-  dsimp only [toSingle₀CokernelAtZeroIso, ChainComplex.homologyZeroIso, homologyOfZeroRight,
-    homology.mapIso, ChainComplex.homologyFunctor0Single₀, cokernel.map]
+  dsimp only [toSingle₀CokernelAtZeroIso, ChainComplex.homology'ZeroIso, homology'OfZeroRight,
+    homology'.mapIso, ChainComplex.homology'Functor0Single₀, cokernel.map]
   dsimp [asIso]
-  simp only [cokernel.π_desc, Category.assoc, homology.map_desc, cokernel.π_desc_assoc]
-  simp [homology.desc, Iso.refl_inv (X.X 0)]
+  simp only [cokernel.π_desc, Category.assoc, homology'.map_desc, cokernel.π_desc_assoc]
+  simp [homology'.desc, Iso.refl_inv (X.X 0)]
 #align homological_complex.hom.to_single₀_cokernel_at_zero_iso_hom_eq HomologicalComplex.Hom.toSingle₀CokernelAtZeroIso_hom_eq
 
-theorem to_single₀_epi_at_zero [hf : QuasiIso f] : Epi (f.f 0) := by
+theorem to_single₀_epi_at_zero [hf : QuasiIso' f] : Epi (f.f 0) := by
   constructor
   intro Z g h Hgh
   rw [← cokernel.π_desc (X.d 1 0) (f.f 0) (by rw [← f.2 1 0 rfl]; exact comp_zero),
@@ -127,22 +128,22 @@ theorem to_single₀_epi_at_zero [hf : QuasiIso f] : Epi (f.f 0) := by
   rw [(@cancel_epi _ _ _ _ _ _ (epi_comp _ _) _ _).1 Hgh]
 #align homological_complex.hom.to_single₀_epi_at_zero HomologicalComplex.Hom.to_single₀_epi_at_zero
 
-theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso f] : Exact (X.d 1 0) (f.f 0) := by
-  rw [Preadditive.exact_iff_homology_zero]
+theorem to_single₀_exact_d_f_at_zero [hf : QuasiIso' f] : Exact (X.d 1 0) (f.f 0) := by
+  rw [Preadditive.exact_iff_homology'_zero]
   have h : X.d 1 0 ≫ f.f 0 = 0 := by
     simp only [← f.2 1 0 rfl, ChainComplex.single₀_obj_X_d, comp_zero]
-  refine' ⟨h, Nonempty.intro (homologyIsoKernelDesc _ _ _ ≪≫ _)⟩
+  refine' ⟨h, Nonempty.intro (homology'IsoKernelDesc _ _ _ ≪≫ _)⟩
   suffices IsIso (cokernel.desc _ _ h) by apply kernel.ofMono
   rw [← toSingle₀CokernelAtZeroIso_hom_eq]
   infer_instance
 #align homological_complex.hom.to_single₀_exact_d_f_at_zero HomologicalComplex.Hom.to_single₀_exact_d_f_at_zero
 
-theorem to_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
+theorem to_single₀_exact_at_succ [hf : QuasiIso' f] (n : ℕ) :
     Exact (X.d (n + 2) (n + 1)) (X.d (n + 1) n) :=
-  (Preadditive.exact_iff_homology_zero _ _).2
+  (Preadditive.exact_iff_homology'_zero _ _).2
     ⟨X.d_comp_d _ _ _,
-      ⟨(ChainComplex.homologySuccIso _ _).symm.trans
-          ((@asIso _ _ _ _ _ (hf.1 (n + 1))).trans homologyZeroZero)⟩⟩
+      ⟨(ChainComplex.homology'SuccIso _ _).symm.trans
+          ((@asIso _ _ _ _ _ (hf.1 (n + 1))).trans homology'ZeroZero)⟩⟩
 #align homological_complex.hom.to_single₀_exact_at_succ HomologicalComplex.Hom.to_single₀_exact_at_succ
 
 end
@@ -153,26 +154,26 @@ variable {X : CochainComplex W ℕ} {Y : W} (f : (CochainComplex.single₀ _).ob
 
 /-- If a cochain map `f : Y[0] ⟶ X` is a quasi-isomorphism, then the kernel of the differential
 `d : X₀ → X₁` is isomorphic to `Y`. -/
-noncomputable def fromSingle₀KernelAtZeroIso [hf : QuasiIso f] : kernel (X.d 0 1) ≅ Y :=
-  X.homologyZeroIso.symm.trans
+noncomputable def fromSingle₀KernelAtZeroIso [hf : QuasiIso' f] : kernel (X.d 0 1) ≅ Y :=
+  X.homology'ZeroIso.symm.trans
     ((@asIso _ _ _ _ _ (hf.1 0)).symm.trans ((CochainComplex.homologyFunctor0Single₀ W).app Y))
 #align homological_complex.hom.from_single₀_kernel_at_zero_iso HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso
 
-theorem fromSingle₀KernelAtZeroIso_inv_eq [hf : QuasiIso f] :
+theorem fromSingle₀KernelAtZeroIso_inv_eq [hf : QuasiIso' f] :
     f.fromSingle₀KernelAtZeroIso.inv =
       kernel.lift (X.d 0 1) (f.f 0) (by rw [f.2 0 1 rfl]; exact zero_comp) := by
   ext
-  dsimp only [fromSingle₀KernelAtZeroIso, CochainComplex.homologyZeroIso, homologyOfZeroLeft,
-    homology.mapIso, CochainComplex.homologyFunctor0Single₀, kernel.map]
+  dsimp only [fromSingle₀KernelAtZeroIso, CochainComplex.homology'ZeroIso, homology'OfZeroLeft,
+    homology'.mapIso, CochainComplex.homologyFunctor0Single₀, kernel.map]
   simp only [Iso.trans_inv, Iso.app_inv, Iso.symm_inv, Category.assoc, equalizer_as_kernel,
     kernel.lift_ι]
   dsimp [asIso]
-  simp only [Category.assoc, homology.π_map, cokernelZeroIsoTarget_hom,
-    cokernelIsoOfEq_hom_comp_desc, kernelSubobject_arrow, homology.π_map_assoc, IsIso.inv_comp_eq]
-  simp [homology.π, kernelSubobjectMap_comp, Iso.refl_hom (X.X 0), Category.comp_id]
+  simp only [Category.assoc, homology'.π_map, cokernelZeroIsoTarget_hom,
+    cokernelIsoOfEq_hom_comp_desc, kernelSubobject_arrow, homology'.π_map_assoc, IsIso.inv_comp_eq]
+  simp [homology'.π, kernelSubobjectMap_comp, Iso.refl_hom (X.X 0), Category.comp_id]
 #align homological_complex.hom.from_single₀_kernel_at_zero_iso_inv_eq HomologicalComplex.Hom.fromSingle₀KernelAtZeroIso_inv_eq
 
-theorem from_single₀_mono_at_zero [hf : QuasiIso f] : Mono (f.f 0) := by
+theorem from_single₀_mono_at_zero [hf : QuasiIso' f] : Mono (f.f 0) := by
   constructor
   intro Z g h Hgh
   rw [← kernel.lift_ι (X.d 0 1) (f.f 0) (by rw [f.2 0 1 rfl]; exact zero_comp),
@@ -180,22 +181,22 @@ theorem from_single₀_mono_at_zero [hf : QuasiIso f] : Mono (f.f 0) := by
   rw [(@cancel_mono _ _ _ _ _ _ (mono_comp _ _) _ _).1 Hgh]
 #align homological_complex.hom.from_single₀_mono_at_zero HomologicalComplex.Hom.from_single₀_mono_at_zero
 
-theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso f] : Exact (f.f 0) (X.d 0 1) := by
-  rw [Preadditive.exact_iff_homology_zero]
+theorem from_single₀_exact_f_d_at_zero [hf : QuasiIso' f] : Exact (f.f 0) (X.d 0 1) := by
+  rw [Preadditive.exact_iff_homology'_zero]
   have h : f.f 0 ≫ X.d 0 1 = 0 := by
     simp only [HomologicalComplex.Hom.comm, CochainComplex.single₀_obj_X_d, zero_comp]
-  refine' ⟨h, Nonempty.intro (homologyIsoCokernelLift _ _ _ ≪≫ _)⟩
+  refine' ⟨h, Nonempty.intro (homology'IsoCokernelLift _ _ _ ≪≫ _)⟩
   suffices IsIso (kernel.lift (X.d 0 1) (f.f 0) h) by apply cokernel.ofEpi
   rw [← fromSingle₀KernelAtZeroIso_inv_eq f]
   infer_instance
 #align homological_complex.hom.from_single₀_exact_f_d_at_zero HomologicalComplex.Hom.from_single₀_exact_f_d_at_zero
 
-theorem from_single₀_exact_at_succ [hf : QuasiIso f] (n : ℕ) :
+theorem from_single₀_exact_at_succ [hf : QuasiIso' f] (n : ℕ) :
     Exact (X.d n (n + 1)) (X.d (n + 1) (n + 2)) :=
-  (Preadditive.exact_iff_homology_zero _ _).2
+  (Preadditive.exact_iff_homology'_zero _ _).2
     ⟨X.d_comp_d _ _ _,
-      ⟨(CochainComplex.homologySuccIso _ _).symm.trans
-          ((@asIso _ _ _ _ _ (hf.1 (n + 1))).symm.trans homologyZeroZero)⟩⟩
+      ⟨(CochainComplex.homology'SuccIso _ _).symm.trans
+          ((@asIso _ _ _ _ _ (hf.1 (n + 1))).symm.trans homology'ZeroZero)⟩⟩
 #align homological_complex.hom.from_single₀_exact_at_succ HomologicalComplex.Hom.from_single₀_exact_at_succ
 
 end
@@ -207,11 +208,11 @@ end HomologicalComplex.Hom
 variable {A : Type*} [Category A] [Abelian A] {B : Type*} [Category B] [Abelian B] (F : A ⥤ B)
   [Functor.Additive F] [PreservesFiniteLimits F] [PreservesFiniteColimits F] [Faithful F]
 
-theorem CategoryTheory.Functor.quasiIso_of_map_quasiIso {C D : HomologicalComplex A c} (f : C ⟶ D)
-    (hf : QuasiIso ((F.mapHomologicalComplex _).map f)) : QuasiIso f :=
+theorem CategoryTheory.Functor.quasiIso'_of_map_quasiIso' {C D : HomologicalComplex A c}
+    (f : C ⟶ D) (hf : QuasiIso' ((F.mapHomologicalComplex _).map f)) : QuasiIso' f :=
   ⟨fun i =>
-    haveI : IsIso (F.map ((homologyFunctor A c i).map f)) := by
-      rw [← Functor.comp_map, ← NatIso.naturality_2 (F.homologyFunctorIso i) f, Functor.comp_map]
+    haveI : IsIso (F.map ((homology'Functor A c i).map f)) := by
+      rw [← Functor.comp_map, ← NatIso.naturality_2 (F.homology'FunctorIso i) f, Functor.comp_map]
       infer_instance
     isIso_of_reflects_iso _ F⟩
-#align category_theory.functor.quasi_iso_of_map_quasi_iso CategoryTheory.Functor.quasiIso_of_map_quasiIso
+#align category_theory.functor.quasi_iso_of_map_quasi_iso CategoryTheory.Functor.quasiIso'_of_map_quasiIso'

956af7c7

chore: tidy various files (#7035)

d04897a6

Diff

@@ -36,31 +36,31 @@ variable {c : ComplexShape ι} {C D E : HomologicalComplex V c}
 /-- A chain map is a quasi-isomorphism if it induces isomorphisms on homology.
 -/
 class QuasiIso (f : C ⟶ D) : Prop where
-  IsIso : ∀ i, IsIso ((homologyFunctor V c i).map f)
+  isIso : ∀ i, IsIso ((homologyFunctor V c i).map f)
 #align quasi_iso QuasiIso
 
-attribute [instance] QuasiIso.IsIso
+attribute [instance] QuasiIso.isIso
 
 instance (priority := 100) quasiIso_of_iso (f : C ⟶ D) [IsIso f] : QuasiIso f where
-  IsIso i := by
+  isIso i := by
     change IsIso ((homologyFunctor V c i).mapIso (asIso f)).hom
     infer_instance
 #align quasi_iso_of_iso quasiIso_of_iso
 
 instance quasiIso_comp (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso g] : QuasiIso (f ≫ g) where
-  IsIso i := by
+  isIso i := by
     rw [Functor.map_comp]
     infer_instance
 #align quasi_iso_comp quasiIso_comp
 
 theorem quasiIso_of_comp_left (f : C ⟶ D) [QuasiIso f] (g : D ⟶ E) [QuasiIso (f ≫ g)] :
     QuasiIso g :=
-  { IsIso := fun i => IsIso.of_isIso_fac_left ((homologyFunctor V c i).map_comp f g).symm }
+  { isIso := fun i => IsIso.of_isIso_fac_left ((homologyFunctor V c i).map_comp f g).symm }
 #align quasi_iso_of_comp_left quasiIso_of_comp_left
 
 theorem quasiIso_of_comp_right (f : C ⟶ D) (g : D ⟶ E) [QuasiIso g] [QuasiIso (f ≫ g)] :
     QuasiIso f :=
-  { IsIso := fun i => IsIso.of_isIso_fac_right ((homologyFunctor V c i).map_comp f g).symm }
+  { isIso := fun i => IsIso.of_isIso_fac_right ((homologyFunctor V c i).map_comp f g).symm }
 #align quasi_iso_of_comp_right quasiIso_of_comp_right
 
 namespace HomotopyEquiv

956af7c7

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -25,7 +25,7 @@ open CategoryTheory.Limits
 
 universe v u
 
-variable {ι : Type _}
+variable {ι : Type*}
 
 variable {V : Type u} [Category.{v} V] [HasZeroMorphisms V] [HasZeroObject V]
 
@@ -67,7 +67,7 @@ namespace HomotopyEquiv
 
 section
 
-variable {W : Type _} [Category W] [Preadditive W] [HasCokernels W] [HasImages W] [HasEqualizers W]
+variable {W : Type*} [Category W] [Preadditive W] [HasCokernels W] [HasImages W] [HasEqualizers W]
   [HasZeroObject W] [HasImageMaps W]
 
 /-- A homotopy equivalence is a quasi-isomorphism. -/
@@ -95,7 +95,7 @@ namespace HomologicalComplex.Hom
 
 section ToSingle₀
 
-variable {W : Type _} [Category W] [Abelian W]
+variable {W : Type*} [Category W] [Abelian W]
 
 section
 
@@ -204,7 +204,7 @@ end ToSingle₀
 
 end HomologicalComplex.Hom
 
-variable {A : Type _} [Category A] [Abelian A] {B : Type _} [Category B] [Abelian B] (F : A ⥤ B)
+variable {A : Type*} [Category A] [Abelian A] {B : Type*} [Category B] [Abelian B] (F : A ⥤ B)
   [Functor.Additive F] [PreservesFiniteLimits F] [PreservesFiniteColimits F] [Faithful F]
 
 theorem CategoryTheory.Functor.quasiIso_of_map_quasiIso {C D : HomologicalComplex A c} (f : C ⟶ D)

956af7c7

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Joël Riou
-
-! This file was ported from Lean 3 source module algebra.homology.quasi_iso
-! leanprover-community/mathlib commit 956af7c76589f444f2e1313911bad16366ea476d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Homology.Homotopy
 import Mathlib.CategoryTheory.Abelian.Homology
 
+#align_import algebra.homology.quasi_iso from "leanprover-community/mathlib"@"956af7c76589f444f2e1313911bad16366ea476d"
+
 /-!
 # Quasi-isomorphisms

956af7c7

feat: more consistent use of ext, and updating porting notes. (#5242)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

dbae2f17

Diff

@@ -114,7 +114,7 @@ noncomputable def toSingle₀CokernelAtZeroIso : cokernel (X.d 1 0) ≅ Y :=
 theorem toSingle₀CokernelAtZeroIso_hom_eq [hf : QuasiIso f] :
     f.toSingle₀CokernelAtZeroIso.hom =
       cokernel.desc (X.d 1 0) (f.f 0) (by rw [← f.2 1 0 rfl]; exact comp_zero) := by
-  apply coequalizer.hom_ext
+  ext
   dsimp only [toSingle₀CokernelAtZeroIso, ChainComplex.homologyZeroIso, homologyOfZeroRight,
     homology.mapIso, ChainComplex.homologyFunctor0Single₀, cokernel.map]
   dsimp [asIso]
@@ -164,7 +164,7 @@ noncomputable def fromSingle₀KernelAtZeroIso [hf : QuasiIso f] : kernel (X.d 0
 theorem fromSingle₀KernelAtZeroIso_inv_eq [hf : QuasiIso f] :
     f.fromSingle₀KernelAtZeroIso.inv =
       kernel.lift (X.d 0 1) (f.f 0) (by rw [f.2 0 1 rfl]; exact zero_comp) := by
-  apply equalizer.hom_ext
+  ext
   dsimp only [fromSingle₀KernelAtZeroIso, CochainComplex.homologyZeroIso, homologyOfZeroLeft,
     homology.mapIso, CochainComplex.homologyFunctor0Single₀, kernel.map]
   simp only [Iso.trans_inv, Iso.app_inv, Iso.symm_inv, Category.assoc, equalizer_as_kernel,

956af7c7

chore: fix grammar 1/3 (#5001)

All of these are doc fixes

d8caa37d

Diff

@@ -73,7 +73,7 @@ section
 variable {W : Type _} [Category W] [Preadditive W] [HasCokernels W] [HasImages W] [HasEqualizers W]
   [HasZeroObject W] [HasImageMaps W]
 
-/-- An homotopy equivalence is a quasi-isomorphism. -/
+/-- A homotopy equivalence is a quasi-isomorphism. -/
 theorem toQuasiIso {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) : QuasiIso e.hom :=
   ⟨fun i => by
     refine' ⟨⟨(homologyFunctor W c i).map e.inv, _⟩⟩

956af7c7

chore: add space after exacts (#4945)

Too often tempted to change these during other PRs, so doing a mass edit here.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

bf799bb9

Diff

@@ -79,7 +79,7 @@ theorem toQuasiIso {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) : Quas
     refine' ⟨⟨(homologyFunctor W c i).map e.inv, _⟩⟩
     simp only [← Functor.map_comp, ← (homologyFunctor W c i).map_id]
     constructor <;> apply homology_map_eq_of_homotopy
-    exacts[e.homotopyHomInvId, e.homotopyInvHomId]⟩
+    exacts [e.homotopyHomInvId, e.homotopyInvHomId]⟩
 #align homotopy_equiv.to_quasi_iso HomotopyEquiv.toQuasiIso
 
 theorem toQuasiIso_inv {C D : HomologicalComplex W c} (e : HomotopyEquiv C D) (i : ι) :

956af7c7

feat: port Algebra.Homology.QuasiIso (#3969)

Co-authored-by: Matthew Ballard <matt@mrb.email> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

13d2e52d

`algebra.homology.quasi_iso` ⟷ `Mathlib.Algebra.Homology.QuasiIso`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 539

algebra.homology.quasi_iso ⟷ Mathlib.Algebra.Homology.QuasiIso

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 539

`algebra.homology.quasi_iso` ⟷ `Mathlib.Algebra.Homology.QuasiIso`