category_theory.abelian.right_derived | 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

024a4231

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

0b7c740e

bump to nightly-2023-11-29-11

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

049e2cad

Diff

@@ -72,7 +72,6 @@ def Functor.rightDerived (F : C ⥤ D) [F.Additive] (n : ℕ) : C ⥤ D :=
 #align category_theory.functor.right_derived CategoryTheory.Functor.rightDerived
 -/
 
-#print CategoryTheory.Functor.rightDerivedObjIso /-
 /-- We can compute a right derived functor using a chosen injective resolution. -/
 @[simps]
 def Functor.rightDerivedObjIso (F : C ⥤ D) [F.Additive] (n : ℕ) {X : C}
@@ -84,9 +83,7 @@ def Functor.rightDerivedObjIso (F : C ⥤ D) [F.Additive] (n : ℕ) {X : C}
         (F.mapHomotopyEquiv (InjectiveResolution.homotopyEquiv _ P))) ≪≫
     (HomotopyCategory.homology'Factors D _ n).app _
 #align category_theory.functor.right_derived_obj_iso CategoryTheory.Functor.rightDerivedObjIso
--/
 
-#print CategoryTheory.Functor.rightDerivedObjInjectiveZero /-
 /-- The 0-th derived functor of `F` on an injective object `X` is just `F.obj X`. -/
 @[simps]
 def Functor.rightDerivedObjInjectiveZero (F : C ⥤ D) [F.Additive] (X : C) [Injective X] :
@@ -95,11 +92,9 @@ def Functor.rightDerivedObjInjectiveZero (F : C ⥤ D) [F.Additive] (X : C) [Inj
     (homology'Functor _ _ _).mapIso ((CochainComplex.single₀MapHomologicalComplex F).app X) ≪≫
       (CochainComplex.homologyFunctor0Single₀ D).app (F.obj X)
 #align category_theory.functor.right_derived_obj_injective_zero CategoryTheory.Functor.rightDerivedObjInjectiveZero
--/
 
 open scoped ZeroObject
 
-#print CategoryTheory.Functor.rightDerivedObjInjectiveSucc /-
 /-- The higher derived functors vanish on injective objects. -/
 @[simps inv]
 def Functor.rightDerivedObjInjectiveSucc (F : C ⥤ D) [F.Additive] (n : ℕ) (X : C) [Injective X] :
@@ -108,7 +103,6 @@ def Functor.rightDerivedObjInjectiveSucc (F : C ⥤ D) [F.Additive] (n : ℕ) (X
     (homology'Functor _ _ _).mapIso ((CochainComplex.single₀MapHomologicalComplex F).app X) ≪≫
       (CochainComplex.homology'FunctorSuccSingle₀ D n).app (F.obj X) ≪≫ (Functor.zero_obj _).isoZero
 #align category_theory.functor.right_derived_obj_injective_succ CategoryTheory.Functor.rightDerivedObjInjectiveSucc
--/
 
 #print CategoryTheory.Functor.rightDerived_map_eq /-
 /-- We can compute a right derived functor on a morphism using a descent of that morphism
@@ -165,7 +159,6 @@ theorem NatTrans.rightDerived_comp {F G H : C ⥤ D} [F.Additive] [G.Additive] [
 #align category_theory.nat_trans.right_derived_comp CategoryTheory.NatTrans.rightDerived_comp
 -/
 
-#print CategoryTheory.NatTrans.rightDerived_eq /-
 /-- A component of the natural transformation between right-derived functors can be computed
 using a chosen injective resolution.
 -/
@@ -189,7 +182,6 @@ theorem NatTrans.rightDerived_eq {F G : C ⥤ D} [F.Additive] [G.Additive] (α :
   apply functor.map_homotopy
   apply HomotopyEquiv.homotopyHomInvId
 #align category_theory.nat_trans.right_derived_eq CategoryTheory.NatTrans.rightDerived_eq
--/
 
 end CategoryTheory
 
@@ -209,7 +201,6 @@ open CategoryTheory.Preadditive
 
 variable [Abelian C] [Abelian D] [Additive F]
 
-#print CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteLimits_of_mono /-
 /-- If `preserves_finite_limits F` and `mono f`, then `exact (F.map f) (F.map g)` if
 `exact f g`. -/
 theorem preserves_exact_of_preservesFiniteLimits_of_mono [PreservesFiniteLimits F] [Mono f]
@@ -217,10 +208,8 @@ theorem preserves_exact_of_preservesFiniteLimits_of_mono [PreservesFiniteLimits
   Abelian.exact_of_is_kernel _ _ (by simp [← functor.map_comp, ex.w]) <|
     Limits.isLimitForkMapOfIsLimit' _ ex.w (Abelian.isLimitOfExactOfMono _ _ ex)
 #align category_theory.abelian.functor.preserves_exact_of_preserves_finite_limits_of_mono CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteLimits_of_mono
--/
 
-#print CategoryTheory.Abelian.Functor.exact_of_map_injectiveResolution /-
-theorem exact_of_map_injectiveResolution (P : InjectiveResolution X) [PreservesFiniteLimits F] :
+theorem exact_of_map_injective_resolution (P : InjectiveResolution X) [PreservesFiniteLimits F] :
     Exact (F.map (P.ι.f 0))
       (((F.mapHomologicalComplex (ComplexShape.up ℕ)).obj P.cocomplex).dFrom 0) :=
   Preadditive.exact_of_iso_of_exact' (F.map (P.ι.f 0)) (F.map (P.cocomplex.d 0 1)) _ _ (Iso.refl _)
@@ -228,10 +217,8 @@ theorem exact_of_map_injectiveResolution (P : InjectiveResolution X) [PreservesF
     (HomologicalComplex.xNextIso ((F.mapHomologicalComplex _).obj P.cocomplex) rfl).symm (by simp)
     (by rw [iso.refl_hom, category.id_comp, iso.symm_hom, HomologicalComplex.dFrom_eq] <;> congr)
     (preserves_exact_of_preserves_finite_limits_of_mono _ P.exact₀)
-#align category_theory.abelian.functor.exact_of_map_injective_resolution CategoryTheory.Abelian.Functor.exact_of_map_injectiveResolution
--/
+#align category_theory.abelian.functor.exact_of_map_injective_resolution CategoryTheory.Abelian.Functor.exact_of_map_injective_resolution
 
-#print CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp /-
 /-- Given `P : InjectiveResolution X`, a morphism `(F.right_derived 0).obj X ⟶ F.obj X` given
 `preserves_finite_limits F`. -/
 def rightDerivedZeroToSelfApp [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
@@ -241,9 +228,7 @@ def rightDerivedZeroToSelfApp [EnoughInjectives C] [PreservesFiniteLimits F] {X
       kernel.map _ _ (cokernel.desc _ (𝟙 _) (by simp)) (𝟙 _) (by ext; simp) ≫
         (asIso (kernel.lift _ _ (exact_of_map_injective_resolution F P).w)).inv
 #align category_theory.abelian.functor.right_derived_zero_to_self_app CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp
--/
 
-#print CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv /-
 /-- Given `P : InjectiveResolution X`, a morphism `F.obj X ⟶ (F.right_derived 0).obj X`. -/
 def rightDerivedZeroToSelfAppInv [EnoughInjectives C] {X : C} (P : InjectiveResolution X) :
     F.obj X ⟶ (F.rightDerived 0).obj X :=
@@ -255,9 +240,7 @@ def rightDerivedZeroToSelfAppInv [EnoughInjectives C] {X : C} (P : InjectiveReso
         simp only [InjectiveResolution.ι_f_zero_comp_complex_d, functor.map_zero, zero_comp]) ≫
     (rightDerivedObjIso F 0 P).inv
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv
--/
 
-#print CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp_comp_inv /-
 theorem rightDerivedZeroToSelfApp_comp_inv [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
     (P : InjectiveResolution X) :
     right_derived_zero_to_self_app F P ≫ right_derived_zero_to_self_app_inv F P = 𝟙 _ :=
@@ -273,9 +256,7 @@ theorem rightDerivedZeroToSelfApp_comp_inv [EnoughInjectives C] [PreservesFinite
     homology'.π'_ι, category.assoc, ← category.assoc (cokernel.π _), cokernel.π_desc, whisker_eq]
   convert category.id_comp (cokernel.π _)
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_comp_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp_comp_inv
--/
 
-#print CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv_comp /-
 theorem rightDerivedZeroToSelfAppInv_comp [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
     (P : InjectiveResolution X) :
     right_derived_zero_to_self_app_inv F P ≫ right_derived_zero_to_self_app F P = 𝟙 _ :=
@@ -289,9 +270,7 @@ theorem rightDerivedZeroToSelfAppInv_comp [EnoughInjectives C] [PreservesFiniteL
   rw [← category.assoc, ← category.assoc, category.assoc _ _ (homology'IsoKernelDesc _ _ _).Hom]
   simp
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_inv_comp CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv_comp
--/
 
-#print CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppIso /-
 /-- Given `P : InjectiveResolution X`, the isomorphism `(F.right_derived 0).obj X ≅ F.obj X` if
 `preserves_finite_limits F`. -/
 def rightDerivedZeroToSelfAppIso [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
@@ -302,12 +281,10 @@ def rightDerivedZeroToSelfAppIso [EnoughInjectives C] [PreservesFiniteLimits F]
   hom_inv_id' := right_derived_zero_to_self_app_comp_inv _ P
   inv_hom_id' := right_derived_zero_to_self_app_inv_comp _ P
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_iso CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppIso
--/
 
-#print CategoryTheory.Abelian.Functor.rightDerivedZeroToSelf_natural /-
 /-- Given `P : InjectiveResolution X` and `Q : InjectiveResolution Y` and a morphism `f : X ⟶ Y`,
 naturality of the square given by `right_derived_zero_to_self_natural`. -/
-theorem rightDerivedZeroToSelf_natural [EnoughInjectives C] {X : C} {Y : C} (f : X ⟶ Y)
+theorem rightDerived_zero_to_self_natural [EnoughInjectives C] {X : C} {Y : C} (f : X ⟶ Y)
     (P : InjectiveResolution X) (Q : InjectiveResolution Y) :
     F.map f ≫ right_derived_zero_to_self_app_inv F Q =
       right_derived_zero_to_self_app_inv F P ≫ (F.rightDerived 0).map f :=
@@ -326,10 +303,8 @@ theorem rightDerivedZeroToSelf_natural [EnoughInjectives C] {X : C} {Y : C} (f :
     HomologicalComplex.Hom.sqFrom_left, map_homological_complex_map_f, ← functor.map_comp,
     show f ≫ Q.ι.f 0 = P.ι.f 0 ≫ (InjectiveResolution.desc f Q P).f 0 from
       HomologicalComplex.congr_hom (InjectiveResolution.desc_commutes f Q P).symm 0]
-#align category_theory.abelian.functor.right_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.rightDerivedZeroToSelf_natural
--/
+#align category_theory.abelian.functor.right_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.rightDerived_zero_to_self_natural
 
-#print CategoryTheory.Abelian.Functor.rightDerivedZeroIsoSelf /-
 /-- Given `preserves_finite_limits F`, the natural isomorphism `(F.right_derived 0) ≅ F`. -/
 def rightDerivedZeroIsoSelf [EnoughInjectives C] [PreservesFiniteLimits F] : F.rightDerived 0 ≅ F :=
   Iso.symm <|
@@ -337,7 +312,6 @@ def rightDerivedZeroIsoSelf [EnoughInjectives C] [PreservesFiniteLimits F] : F.r
       (fun X => (right_derived_zero_to_self_app_iso _ (InjectiveResolution.of X)).symm) fun X Y f =>
       right_derived_zero_to_self_natural _ _ _ _
 #align category_theory.abelian.functor.right_derived_zero_iso_self CategoryTheory.Abelian.Functor.rightDerivedZeroIsoSelf
--/
 
 end CategoryTheory.Abelian.Functor

0b7c740e

bump to nightly-2023-10-29-06

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

abdd1870

Diff

@@ -68,7 +68,7 @@ variable [Abelian C] [HasInjectiveResolutions C] [Abelian D]
 #print CategoryTheory.Functor.rightDerived /-
 /-- The right derived functors of an additive functor. -/
 def Functor.rightDerived (F : C ⥤ D) [F.Additive] (n : ℕ) : C ⥤ D :=
-  injectiveResolutions C ⋙ F.mapHomotopyCategory _ ⋙ HomotopyCategory.homologyFunctor D _ n
+  injectiveResolutions C ⋙ F.mapHomotopyCategory _ ⋙ HomotopyCategory.homology'Functor D _ n
 #align category_theory.functor.right_derived CategoryTheory.Functor.rightDerived
 -/
 
@@ -78,11 +78,11 @@ def Functor.rightDerived (F : C ⥤ D) [F.Additive] (n : ℕ) : C ⥤ D :=
 def Functor.rightDerivedObjIso (F : C ⥤ D) [F.Additive] (n : ℕ) {X : C}
     (P : InjectiveResolution X) :
     (F.rightDerived n).obj X ≅
-      (homologyFunctor D _ n).obj ((F.mapHomologicalComplex _).obj P.cocomplex) :=
-  (HomotopyCategory.homologyFunctor D _ n).mapIso
+      (homology'Functor D _ n).obj ((F.mapHomologicalComplex _).obj P.cocomplex) :=
+  (HomotopyCategory.homology'Functor D _ n).mapIso
       (HomotopyCategory.isoOfHomotopyEquiv
         (F.mapHomotopyEquiv (InjectiveResolution.homotopyEquiv _ P))) ≪≫
-    (HomotopyCategory.homologyFactors D _ n).app _
+    (HomotopyCategory.homology'Factors D _ n).app _
 #align category_theory.functor.right_derived_obj_iso CategoryTheory.Functor.rightDerivedObjIso
 -/
 
@@ -92,7 +92,7 @@ def Functor.rightDerivedObjIso (F : C ⥤ D) [F.Additive] (n : ℕ) {X : C}
 def Functor.rightDerivedObjInjectiveZero (F : C ⥤ D) [F.Additive] (X : C) [Injective X] :
     (F.rightDerived 0).obj X ≅ F.obj X :=
   F.rightDerivedObjIso 0 (InjectiveResolution.self X) ≪≫
-    (homologyFunctor _ _ _).mapIso ((CochainComplex.single₀MapHomologicalComplex F).app X) ≪≫
+    (homology'Functor _ _ _).mapIso ((CochainComplex.single₀MapHomologicalComplex F).app X) ≪≫
       (CochainComplex.homologyFunctor0Single₀ D).app (F.obj X)
 #align category_theory.functor.right_derived_obj_injective_zero CategoryTheory.Functor.rightDerivedObjInjectiveZero
 -/
@@ -105,8 +105,8 @@ open scoped ZeroObject
 def Functor.rightDerivedObjInjectiveSucc (F : C ⥤ D) [F.Additive] (n : ℕ) (X : C) [Injective X] :
     (F.rightDerived (n + 1)).obj X ≅ 0 :=
   F.rightDerivedObjIso (n + 1) (InjectiveResolution.self X) ≪≫
-    (homologyFunctor _ _ _).mapIso ((CochainComplex.single₀MapHomologicalComplex F).app X) ≪≫
-      (CochainComplex.homologyFunctorSuccSingle₀ D n).app (F.obj X) ≪≫ (Functor.zero_obj _).isoZero
+    (homology'Functor _ _ _).mapIso ((CochainComplex.single₀MapHomologicalComplex F).app X) ≪≫
+      (CochainComplex.homology'FunctorSuccSingle₀ D n).app (F.obj X) ≪≫ (Functor.zero_obj _).isoZero
 #align category_theory.functor.right_derived_obj_injective_succ CategoryTheory.Functor.rightDerivedObjInjectiveSucc
 -/
 
@@ -119,12 +119,12 @@ theorem Functor.rightDerived_map_eq (F : C ⥤ D) [F.Additive] (n : ℕ) {X Y :
     (w : Q.ι ≫ g = (CochainComplex.single₀ C).map f ≫ P.ι) :
     (F.rightDerived n).map f =
       (F.rightDerivedObjIso n Q).Hom ≫
-        (homologyFunctor D _ n).map ((F.mapHomologicalComplex _).map g) ≫
+        (homology'Functor D _ n).map ((F.mapHomologicalComplex _).map g) ≫
           (F.rightDerivedObjIso n P).inv :=
   by
   dsimp only [functor.right_derived, functor.right_derived_obj_iso]
   dsimp; simp only [category.comp_id, category.id_comp]
-  rw [← homologyFunctor_map, HomotopyCategory.homologyFunctor_map_factors]
+  rw [← homology'Functor_map, HomotopyCategory.homology'Functor_map_factors]
   simp only [← functor.map_comp]
   congr 1
   apply HomotopyCategory.eq_of_homotopy
@@ -145,7 +145,7 @@ theorem Functor.rightDerived_map_eq (F : C ⥤ D) [F.Additive] (n : ℕ) {X Y :
 def NatTrans.rightDerived {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶ G) (n : ℕ) :
     F.rightDerived n ⟶ G.rightDerived n :=
   whiskerLeft (injectiveResolutions C)
-    (whiskerRight (NatTrans.mapHomotopyCategory α _) (HomotopyCategory.homologyFunctor D _ n))
+    (whiskerRight (NatTrans.mapHomotopyCategory α _) (HomotopyCategory.homology'Functor D _ n))
 #align category_theory.nat_trans.right_derived CategoryTheory.NatTrans.rightDerived
 -/
 
@@ -173,13 +173,13 @@ theorem NatTrans.rightDerived_eq {F G : C ⥤ D} [F.Additive] [G.Additive] (α :
     (P : InjectiveResolution X) :
     (NatTrans.rightDerived α n).app X =
       (F.rightDerivedObjIso n P).Hom ≫
-        (homologyFunctor D _ n).map ((NatTrans.mapHomologicalComplex α _).app P.cocomplex) ≫
+        (homology'Functor D _ n).map ((NatTrans.mapHomologicalComplex α _).app P.cocomplex) ≫
           (G.rightDerivedObjIso n P).inv :=
   by
   symm
   dsimp [nat_trans.right_derived, functor.right_derived_obj_iso]
   simp only [category.comp_id, category.id_comp]
-  rw [← homologyFunctor_map, HomotopyCategory.homologyFunctor_map_factors]
+  rw [← homology'Functor_map, HomotopyCategory.homology'Functor_map_factors]
   simp only [← functor.map_comp]
   congr 1
   apply HomotopyCategory.eq_of_homotopy
@@ -237,7 +237,7 @@ theorem exact_of_map_injectiveResolution (P : InjectiveResolution X) [PreservesF
 def rightDerivedZeroToSelfApp [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
     (P : InjectiveResolution X) : (F.rightDerived 0).obj X ⟶ F.obj X :=
   (rightDerivedObjIso F 0 P).Hom ≫
-    (homologyIsoKernelDesc _ _ _).Hom ≫
+    (homology'IsoKernelDesc _ _ _).Hom ≫
       kernel.map _ _ (cokernel.desc _ (𝟙 _) (by simp)) (𝟙 _) (by ext; simp) ≫
         (asIso (kernel.lift _ _ (exact_of_map_injective_resolution F P).w)).inv
 #align category_theory.abelian.functor.right_derived_zero_to_self_app CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp
@@ -247,7 +247,7 @@ def rightDerivedZeroToSelfApp [EnoughInjectives C] [PreservesFiniteLimits F] {X
 /-- Given `P : InjectiveResolution X`, a morphism `F.obj X ⟶ (F.right_derived 0).obj X`. -/
 def rightDerivedZeroToSelfAppInv [EnoughInjectives C] {X : C} (P : InjectiveResolution X) :
     F.obj X ⟶ (F.rightDerived 0).obj X :=
-  homology.lift _ _ _ (F.map (P.ι.f 0) ≫ cokernel.π _)
+  homology'.lift _ _ _ (F.map (P.ι.f 0) ≫ cokernel.π _)
       (by
         have : (ComplexShape.up ℕ).Rel 0 1 := rfl
         rw [category.assoc, cokernel.π_desc, HomologicalComplex.dFrom_eq _ this,
@@ -266,11 +266,11 @@ theorem rightDerivedZeroToSelfApp_comp_inv [EnoughInjectives C] [PreservesFinite
   rw [← category.assoc, iso.comp_inv_eq, category.id_comp, category.assoc, category.assoc, ←
     iso.eq_inv_comp, iso.inv_hom_id]
   ext
-  rw [category.assoc, category.assoc, homology.lift_ι, category.id_comp, homology.π'_ι,
+  rw [category.assoc, category.assoc, homology'.lift_ι, category.id_comp, homology'.π'_ι,
     category.assoc, ← category.assoc _ _ (cokernel.π _), abelian.kernel.lift.inv, ← category.assoc,
     ← category.assoc _ (kernel.ι _), limits.kernel.lift_ι, category.assoc, category.assoc, ←
-    category.assoc (homologyIsoKernelDesc _ _ _).Hom _ _, ← homology.ι, ← category.assoc,
-    homology.π'_ι, category.assoc, ← category.assoc (cokernel.π _), cokernel.π_desc, whisker_eq]
+    category.assoc (homology'IsoKernelDesc _ _ _).Hom _ _, ← homology'.ι, ← category.assoc,
+    homology'.π'_ι, category.assoc, ← category.assoc (cokernel.π _), cokernel.π_desc, whisker_eq]
   convert category.id_comp (cokernel.π _)
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_comp_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp_comp_inv
 -/
@@ -285,8 +285,8 @@ theorem rightDerivedZeroToSelfAppInv_comp [EnoughInjectives C] [PreservesFiniteL
     category.assoc _ _ (F.right_derived_obj_iso 0 P).Hom, iso.inv_hom_id, category.comp_id, ←
     category.assoc, ← category.assoc, is_iso.comp_inv_eq, category.id_comp]
   ext
-  simp only [limits.kernel.lift_ι_assoc, category.assoc, limits.kernel.lift_ι, homology.lift]
-  rw [← category.assoc, ← category.assoc, category.assoc _ _ (homologyIsoKernelDesc _ _ _).Hom]
+  simp only [limits.kernel.lift_ι_assoc, category.assoc, limits.kernel.lift_ι, homology'.lift]
+  rw [← category.assoc, ← category.assoc, category.assoc _ _ (homology'IsoKernelDesc _ _ _).Hom]
   simp
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_inv_comp CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv_comp
 -/
@@ -318,12 +318,12 @@ theorem rightDerivedZeroToSelf_natural [EnoughInjectives C] {X : C} {Y : C} (f :
     category.assoc, category.assoc, category.assoc, category.assoc, iso.inv_hom_id,
     category.comp_id, ← category.assoc (F.right_derived_obj_iso 0 P).inv, iso.inv_hom_id,
     category.id_comp]
-  dsimp only [homologyFunctor_map]
+  dsimp only [homology'Functor_map]
   ext
-  rw [category.assoc, homology.lift_ι, category.assoc, homology.map_ι, ←
-    category.assoc (homology.lift _ _ _ _ _) _ _, homology.lift_ι, category.assoc, cokernel.π_desc,
-    ← category.assoc, ← functor.map_comp, ← category.assoc, HomologicalComplex.Hom.sqFrom_left,
-    map_homological_complex_map_f, ← functor.map_comp,
+  rw [category.assoc, homology'.lift_ι, category.assoc, homology'.map_ι, ←
+    category.assoc (homology'.lift _ _ _ _ _) _ _, homology'.lift_ι, category.assoc,
+    cokernel.π_desc, ← category.assoc, ← functor.map_comp, ← category.assoc,
+    HomologicalComplex.Hom.sqFrom_left, map_homological_complex_map_f, ← functor.map_comp,
     show f ≫ Q.ι.f 0 = P.ι.f 0 ≫ (InjectiveResolution.desc f Q P).f 0 from
       HomologicalComplex.congr_hom (InjectiveResolution.desc_commutes f Q P).symm 0]
 #align category_theory.abelian.functor.right_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.rightDerivedZeroToSelf_natural

0b7c740e

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,11 +3,11 @@ Copyright (c) 2022 Jujian Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jujian Zhang, Scott Morrison
 -/
-import Mathbin.CategoryTheory.Abelian.InjectiveResolution
-import Mathbin.Algebra.Homology.Additive
-import Mathbin.CategoryTheory.Limits.Constructions.EpiMono
-import Mathbin.CategoryTheory.Abelian.Homology
-import Mathbin.CategoryTheory.Abelian.Exact
+import CategoryTheory.Abelian.InjectiveResolution
+import Algebra.Homology.Additive
+import CategoryTheory.Limits.Constructions.EpiMono
+import CategoryTheory.Abelian.Homology
+import CategoryTheory.Abelian.Exact
 
 #align_import category_theory.abelian.right_derived from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"

0b7c740e

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Jujian Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jujian Zhang, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.abelian.right_derived
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Abelian.InjectiveResolution
 import Mathbin.Algebra.Homology.Additive
@@ -14,6 +9,8 @@ import Mathbin.CategoryTheory.Limits.Constructions.EpiMono
 import Mathbin.CategoryTheory.Abelian.Homology
 import Mathbin.CategoryTheory.Abelian.Exact
 
+#align_import category_theory.abelian.right_derived from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
 /-!
 # Right-derived functors

0b7c740e

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -75,6 +75,7 @@ def Functor.rightDerived (F : C ⥤ D) [F.Additive] (n : ℕ) : C ⥤ D :=
 #align category_theory.functor.right_derived CategoryTheory.Functor.rightDerived
 -/
 
+#print CategoryTheory.Functor.rightDerivedObjIso /-
 /-- We can compute a right derived functor using a chosen injective resolution. -/
 @[simps]
 def Functor.rightDerivedObjIso (F : C ⥤ D) [F.Additive] (n : ℕ) {X : C}
@@ -86,7 +87,9 @@ def Functor.rightDerivedObjIso (F : C ⥤ D) [F.Additive] (n : ℕ) {X : C}
         (F.mapHomotopyEquiv (InjectiveResolution.homotopyEquiv _ P))) ≪≫
     (HomotopyCategory.homologyFactors D _ n).app _
 #align category_theory.functor.right_derived_obj_iso CategoryTheory.Functor.rightDerivedObjIso
+-/
 
+#print CategoryTheory.Functor.rightDerivedObjInjectiveZero /-
 /-- The 0-th derived functor of `F` on an injective object `X` is just `F.obj X`. -/
 @[simps]
 def Functor.rightDerivedObjInjectiveZero (F : C ⥤ D) [F.Additive] (X : C) [Injective X] :
@@ -95,9 +98,11 @@ def Functor.rightDerivedObjInjectiveZero (F : C ⥤ D) [F.Additive] (X : C) [Inj
     (homologyFunctor _ _ _).mapIso ((CochainComplex.single₀MapHomologicalComplex F).app X) ≪≫
       (CochainComplex.homologyFunctor0Single₀ D).app (F.obj X)
 #align category_theory.functor.right_derived_obj_injective_zero CategoryTheory.Functor.rightDerivedObjInjectiveZero
+-/
 
 open scoped ZeroObject
 
+#print CategoryTheory.Functor.rightDerivedObjInjectiveSucc /-
 /-- The higher derived functors vanish on injective objects. -/
 @[simps inv]
 def Functor.rightDerivedObjInjectiveSucc (F : C ⥤ D) [F.Additive] (n : ℕ) (X : C) [Injective X] :
@@ -106,7 +111,9 @@ def Functor.rightDerivedObjInjectiveSucc (F : C ⥤ D) [F.Additive] (n : ℕ) (X
     (homologyFunctor _ _ _).mapIso ((CochainComplex.single₀MapHomologicalComplex F).app X) ≪≫
       (CochainComplex.homologyFunctorSuccSingle₀ D n).app (F.obj X) ≪≫ (Functor.zero_obj _).isoZero
 #align category_theory.functor.right_derived_obj_injective_succ CategoryTheory.Functor.rightDerivedObjInjectiveSucc
+-/
 
+#print CategoryTheory.Functor.rightDerived_map_eq /-
 /-- We can compute a right derived functor on a morphism using a descent of that morphism
 to a cochain map between chosen injective resolutions.
 -/
@@ -133,6 +140,7 @@ theorem Functor.rightDerived_map_eq (F : C ⥤ D) [F.Additive] (n : ℕ) {X Y :
     rw [← category.assoc, w, category.assoc]
     simp only [InjectiveResolution.homotopy_equiv_inv_ι]
 #align category_theory.functor.right_derived_map_eq CategoryTheory.Functor.rightDerived_map_eq
+-/
 
 #print CategoryTheory.NatTrans.rightDerived /-
 /-- The natural transformation between right-derived functors induced by a natural transformation.-/
@@ -144,18 +152,23 @@ def NatTrans.rightDerived {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶
 #align category_theory.nat_trans.right_derived CategoryTheory.NatTrans.rightDerived
 -/
 
+#print CategoryTheory.NatTrans.rightDerived_id /-
 @[simp]
 theorem NatTrans.rightDerived_id (F : C ⥤ D) [F.Additive] (n : ℕ) :
     NatTrans.rightDerived (𝟙 F) n = 𝟙 (F.rightDerived n) := by simp [nat_trans.right_derived]; rfl
 #align category_theory.nat_trans.right_derived_id CategoryTheory.NatTrans.rightDerived_id
+-/
 
+#print CategoryTheory.NatTrans.rightDerived_comp /-
 @[simp, nolint simp_nf]
 theorem NatTrans.rightDerived_comp {F G H : C ⥤ D} [F.Additive] [G.Additive] [H.Additive]
     (α : F ⟶ G) (β : G ⟶ H) (n : ℕ) :
     NatTrans.rightDerived (α ≫ β) n = NatTrans.rightDerived α n ≫ NatTrans.rightDerived β n := by
   simp [nat_trans.right_derived]
 #align category_theory.nat_trans.right_derived_comp CategoryTheory.NatTrans.rightDerived_comp
+-/
 
+#print CategoryTheory.NatTrans.rightDerived_eq /-
 /-- A component of the natural transformation between right-derived functors can be computed
 using a chosen injective resolution.
 -/
@@ -179,6 +192,7 @@ theorem NatTrans.rightDerived_eq {F G : C ⥤ D} [F.Additive] [G.Additive] (α :
   apply functor.map_homotopy
   apply HomotopyEquiv.homotopyHomInvId
 #align category_theory.nat_trans.right_derived_eq CategoryTheory.NatTrans.rightDerived_eq
+-/
 
 end CategoryTheory
 
@@ -198,6 +212,7 @@ open CategoryTheory.Preadditive
 
 variable [Abelian C] [Abelian D] [Additive F]
 
+#print CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteLimits_of_mono /-
 /-- If `preserves_finite_limits F` and `mono f`, then `exact (F.map f) (F.map g)` if
 `exact f g`. -/
 theorem preserves_exact_of_preservesFiniteLimits_of_mono [PreservesFiniteLimits F] [Mono f]
@@ -205,7 +220,9 @@ theorem preserves_exact_of_preservesFiniteLimits_of_mono [PreservesFiniteLimits
   Abelian.exact_of_is_kernel _ _ (by simp [← functor.map_comp, ex.w]) <|
     Limits.isLimitForkMapOfIsLimit' _ ex.w (Abelian.isLimitOfExactOfMono _ _ ex)
 #align category_theory.abelian.functor.preserves_exact_of_preserves_finite_limits_of_mono CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteLimits_of_mono
+-/
 
+#print CategoryTheory.Abelian.Functor.exact_of_map_injectiveResolution /-
 theorem exact_of_map_injectiveResolution (P : InjectiveResolution X) [PreservesFiniteLimits F] :
     Exact (F.map (P.ι.f 0))
       (((F.mapHomologicalComplex (ComplexShape.up ℕ)).obj P.cocomplex).dFrom 0) :=
@@ -215,7 +232,9 @@ theorem exact_of_map_injectiveResolution (P : InjectiveResolution X) [PreservesF
     (by rw [iso.refl_hom, category.id_comp, iso.symm_hom, HomologicalComplex.dFrom_eq] <;> congr)
     (preserves_exact_of_preserves_finite_limits_of_mono _ P.exact₀)
 #align category_theory.abelian.functor.exact_of_map_injective_resolution CategoryTheory.Abelian.Functor.exact_of_map_injectiveResolution
+-/
 
+#print CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp /-
 /-- Given `P : InjectiveResolution X`, a morphism `(F.right_derived 0).obj X ⟶ F.obj X` given
 `preserves_finite_limits F`. -/
 def rightDerivedZeroToSelfApp [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
@@ -225,7 +244,9 @@ def rightDerivedZeroToSelfApp [EnoughInjectives C] [PreservesFiniteLimits F] {X
       kernel.map _ _ (cokernel.desc _ (𝟙 _) (by simp)) (𝟙 _) (by ext; simp) ≫
         (asIso (kernel.lift _ _ (exact_of_map_injective_resolution F P).w)).inv
 #align category_theory.abelian.functor.right_derived_zero_to_self_app CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp
+-/
 
+#print CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv /-
 /-- Given `P : InjectiveResolution X`, a morphism `F.obj X ⟶ (F.right_derived 0).obj X`. -/
 def rightDerivedZeroToSelfAppInv [EnoughInjectives C] {X : C} (P : InjectiveResolution X) :
     F.obj X ⟶ (F.rightDerived 0).obj X :=
@@ -237,7 +258,9 @@ def rightDerivedZeroToSelfAppInv [EnoughInjectives C] {X : C} (P : InjectiveReso
         simp only [InjectiveResolution.ι_f_zero_comp_complex_d, functor.map_zero, zero_comp]) ≫
     (rightDerivedObjIso F 0 P).inv
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv
+-/
 
+#print CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp_comp_inv /-
 theorem rightDerivedZeroToSelfApp_comp_inv [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
     (P : InjectiveResolution X) :
     right_derived_zero_to_self_app F P ≫ right_derived_zero_to_self_app_inv F P = 𝟙 _ :=
@@ -253,7 +276,9 @@ theorem rightDerivedZeroToSelfApp_comp_inv [EnoughInjectives C] [PreservesFinite
     homology.π'_ι, category.assoc, ← category.assoc (cokernel.π _), cokernel.π_desc, whisker_eq]
   convert category.id_comp (cokernel.π _)
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_comp_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp_comp_inv
+-/
 
+#print CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv_comp /-
 theorem rightDerivedZeroToSelfAppInv_comp [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
     (P : InjectiveResolution X) :
     right_derived_zero_to_self_app_inv F P ≫ right_derived_zero_to_self_app F P = 𝟙 _ :=
@@ -267,7 +292,9 @@ theorem rightDerivedZeroToSelfAppInv_comp [EnoughInjectives C] [PreservesFiniteL
   rw [← category.assoc, ← category.assoc, category.assoc _ _ (homologyIsoKernelDesc _ _ _).Hom]
   simp
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_inv_comp CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv_comp
+-/
 
+#print CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppIso /-
 /-- Given `P : InjectiveResolution X`, the isomorphism `(F.right_derived 0).obj X ≅ F.obj X` if
 `preserves_finite_limits F`. -/
 def rightDerivedZeroToSelfAppIso [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
@@ -278,7 +305,9 @@ def rightDerivedZeroToSelfAppIso [EnoughInjectives C] [PreservesFiniteLimits F]
   hom_inv_id' := right_derived_zero_to_self_app_comp_inv _ P
   inv_hom_id' := right_derived_zero_to_self_app_inv_comp _ P
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_iso CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppIso
+-/
 
+#print CategoryTheory.Abelian.Functor.rightDerivedZeroToSelf_natural /-
 /-- Given `P : InjectiveResolution X` and `Q : InjectiveResolution Y` and a morphism `f : X ⟶ Y`,
 naturality of the square given by `right_derived_zero_to_self_natural`. -/
 theorem rightDerivedZeroToSelf_natural [EnoughInjectives C] {X : C} {Y : C} (f : X ⟶ Y)
@@ -301,6 +330,7 @@ theorem rightDerivedZeroToSelf_natural [EnoughInjectives C] {X : C} {Y : C} (f :
     show f ≫ Q.ι.f 0 = P.ι.f 0 ≫ (InjectiveResolution.desc f Q P).f 0 from
       HomologicalComplex.congr_hom (InjectiveResolution.desc_commutes f Q P).symm 0]
 #align category_theory.abelian.functor.right_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.rightDerivedZeroToSelf_natural
+-/
 
 #print CategoryTheory.Abelian.Functor.rightDerivedZeroIsoSelf /-
 /-- Given `preserves_finite_limits F`, the natural isomorphism `(F.right_derived 0) ≅ F`. -/

0b7c740e

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -212,7 +212,7 @@ theorem exact_of_map_injectiveResolution (P : InjectiveResolution X) [PreservesF
   Preadditive.exact_of_iso_of_exact' (F.map (P.ι.f 0)) (F.map (P.cocomplex.d 0 1)) _ _ (Iso.refl _)
     (Iso.refl _)
     (HomologicalComplex.xNextIso ((F.mapHomologicalComplex _).obj P.cocomplex) rfl).symm (by simp)
-    (by rw [iso.refl_hom, category.id_comp, iso.symm_hom, HomologicalComplex.dFrom_eq] <;> congr )
+    (by rw [iso.refl_hom, category.id_comp, iso.symm_hom, HomologicalComplex.dFrom_eq] <;> congr)
     (preserves_exact_of_preserves_finite_limits_of_mono _ P.exact₀)
 #align category_theory.abelian.functor.exact_of_map_injective_resolution CategoryTheory.Abelian.Functor.exact_of_map_injectiveResolution

0b7c740e

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -96,7 +96,7 @@ def Functor.rightDerivedObjInjectiveZero (F : C ⥤ D) [F.Additive] (X : C) [Inj
       (CochainComplex.homologyFunctor0Single₀ D).app (F.obj X)
 #align category_theory.functor.right_derived_obj_injective_zero CategoryTheory.Functor.rightDerivedObjInjectiveZero
 
-open ZeroObject
+open scoped ZeroObject
 
 /-- The higher derived functors vanish on injective objects. -/
 @[simps inv]

0b7c740e

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -75,9 +75,6 @@ def Functor.rightDerived (F : C ⥤ D) [F.Additive] (n : ℕ) : C ⥤ D :=
 #align category_theory.functor.right_derived CategoryTheory.Functor.rightDerived
 -/
 
-/- warning: category_theory.functor.right_derived_obj_iso -> CategoryTheory.Functor.rightDerivedObjIso is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.functor.right_derived_obj_iso CategoryTheory.Functor.rightDerivedObjIsoₓ'. -/
 /-- We can compute a right derived functor using a chosen injective resolution. -/
 @[simps]
 def Functor.rightDerivedObjIso (F : C ⥤ D) [F.Additive] (n : ℕ) {X : C}
@@ -90,12 +87,6 @@ def Functor.rightDerivedObjIso (F : C ⥤ D) [F.Additive] (n : ℕ) {X : C}
     (HomotopyCategory.homologyFactors D _ n).app _
 #align category_theory.functor.right_derived_obj_iso CategoryTheory.Functor.rightDerivedObjIso
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.functor.right_derived_obj_injective_zero CategoryTheory.Functor.rightDerivedObjInjectiveZeroₓ'. -/
 /-- The 0-th derived functor of `F` on an injective object `X` is just `F.obj X`. -/
 @[simps]
 def Functor.rightDerivedObjInjectiveZero (F : C ⥤ D) [F.Additive] (X : C) [Injective X] :
@@ -107,12 +98,6 @@ def Functor.rightDerivedObjInjectiveZero (F : C ⥤ D) [F.Additive] (X : C) [Inj
 
 open ZeroObject
 
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 /-- The higher derived functors vanish on injective objects. -/
 @[simps inv]
 def Functor.rightDerivedObjInjectiveSucc (F : C ⥤ D) [F.Additive] (n : ℕ) (X : C) [Injective X] :
@@ -122,9 +107,6 @@ def Functor.rightDerivedObjInjectiveSucc (F : C ⥤ D) [F.Additive] (n : ℕ) (X
       (CochainComplex.homologyFunctorSuccSingle₀ D n).app (F.obj X) ≪≫ (Functor.zero_obj _).isoZero
 #align category_theory.functor.right_derived_obj_injective_succ CategoryTheory.Functor.rightDerivedObjInjectiveSucc
 
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 /-- We can compute a right derived functor on a morphism using a descent of that morphism
 to a cochain map between chosen injective resolutions.
 -/
@@ -162,20 +144,11 @@ def NatTrans.rightDerived {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶
 #align category_theory.nat_trans.right_derived CategoryTheory.NatTrans.rightDerived
 -/
 
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 @[simp]
 theorem NatTrans.rightDerived_id (F : C ⥤ D) [F.Additive] (n : ℕ) :
     NatTrans.rightDerived (𝟙 F) n = 𝟙 (F.rightDerived n) := by simp [nat_trans.right_derived]; rfl
 #align category_theory.nat_trans.right_derived_id CategoryTheory.NatTrans.rightDerived_id
 
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 @[simp, nolint simp_nf]
 theorem NatTrans.rightDerived_comp {F G H : C ⥤ D} [F.Additive] [G.Additive] [H.Additive]
     (α : F ⟶ G) (β : G ⟶ H) (n : ℕ) :
@@ -183,9 +156,6 @@ theorem NatTrans.rightDerived_comp {F G H : C ⥤ D} [F.Additive] [G.Additive] [
   simp [nat_trans.right_derived]
 #align category_theory.nat_trans.right_derived_comp CategoryTheory.NatTrans.rightDerived_comp
 
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 /-- A component of the natural transformation between right-derived functors can be computed
 using a chosen injective resolution.
 -/
@@ -228,12 +198,6 @@ open CategoryTheory.Preadditive
 
 variable [Abelian C] [Abelian D] [Additive F]
 
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 /-- If `preserves_finite_limits F` and `mono f`, then `exact (F.map f) (F.map g)` if
 `exact f g`. -/
 theorem preserves_exact_of_preservesFiniteLimits_of_mono [PreservesFiniteLimits F] [Mono f]
@@ -242,9 +206,6 @@ theorem preserves_exact_of_preservesFiniteLimits_of_mono [PreservesFiniteLimits
     Limits.isLimitForkMapOfIsLimit' _ ex.w (Abelian.isLimitOfExactOfMono _ _ ex)
 #align category_theory.abelian.functor.preserves_exact_of_preserves_finite_limits_of_mono CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteLimits_of_mono
 
-/- warning: category_theory.abelian.functor.exact_of_map_injective_resolution -> CategoryTheory.Abelian.Functor.exact_of_map_injectiveResolution is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.exact_of_map_injective_resolution CategoryTheory.Abelian.Functor.exact_of_map_injectiveResolutionₓ'. -/
 theorem exact_of_map_injectiveResolution (P : InjectiveResolution X) [PreservesFiniteLimits F] :
     Exact (F.map (P.ι.f 0))
       (((F.mapHomologicalComplex (ComplexShape.up ℕ)).obj P.cocomplex).dFrom 0) :=
@@ -255,12 +216,6 @@ theorem exact_of_map_injectiveResolution (P : InjectiveResolution X) [PreservesF
     (preserves_exact_of_preserves_finite_limits_of_mono _ P.exact₀)
 #align category_theory.abelian.functor.exact_of_map_injective_resolution CategoryTheory.Abelian.Functor.exact_of_map_injectiveResolution
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.right_derived_zero_to_self_app CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppₓ'. -/
 /-- Given `P : InjectiveResolution X`, a morphism `(F.right_derived 0).obj X ⟶ F.obj X` given
 `preserves_finite_limits F`. -/
 def rightDerivedZeroToSelfApp [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
@@ -271,12 +226,6 @@ def rightDerivedZeroToSelfApp [EnoughInjectives C] [PreservesFiniteLimits F] {X
         (asIso (kernel.lift _ _ (exact_of_map_injective_resolution F P).w)).inv
 #align category_theory.abelian.functor.right_derived_zero_to_self_app CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.right_derived_zero_to_self_app_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInvₓ'. -/
 /-- Given `P : InjectiveResolution X`, a morphism `F.obj X ⟶ (F.right_derived 0).obj X`. -/
 def rightDerivedZeroToSelfAppInv [EnoughInjectives C] {X : C} (P : InjectiveResolution X) :
     F.obj X ⟶ (F.rightDerived 0).obj X :=
@@ -289,9 +238,6 @@ def rightDerivedZeroToSelfAppInv [EnoughInjectives C] {X : C} (P : InjectiveReso
     (rightDerivedObjIso F 0 P).inv
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv
 
-/- warning: category_theory.abelian.functor.right_derived_zero_to_self_app_comp_inv -> CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp_comp_inv is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.right_derived_zero_to_self_app_comp_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp_comp_invₓ'. -/
 theorem rightDerivedZeroToSelfApp_comp_inv [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
     (P : InjectiveResolution X) :
     right_derived_zero_to_self_app F P ≫ right_derived_zero_to_self_app_inv F P = 𝟙 _ :=
@@ -308,9 +254,6 @@ theorem rightDerivedZeroToSelfApp_comp_inv [EnoughInjectives C] [PreservesFinite
   convert category.id_comp (cokernel.π _)
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_comp_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp_comp_inv
 
-/- warning: category_theory.abelian.functor.right_derived_zero_to_self_app_inv_comp -> CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv_comp is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.right_derived_zero_to_self_app_inv_comp CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv_compₓ'. -/
 theorem rightDerivedZeroToSelfAppInv_comp [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
     (P : InjectiveResolution X) :
     right_derived_zero_to_self_app_inv F P ≫ right_derived_zero_to_self_app F P = 𝟙 _ :=
@@ -325,12 +268,6 @@ theorem rightDerivedZeroToSelfAppInv_comp [EnoughInjectives C] [PreservesFiniteL
   simp
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_inv_comp CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv_comp
 
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-Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.right_derived_zero_to_self_app_iso CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppIsoₓ'. -/
 /-- Given `P : InjectiveResolution X`, the isomorphism `(F.right_derived 0).obj X ≅ F.obj X` if
 `preserves_finite_limits F`. -/
 def rightDerivedZeroToSelfAppIso [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
@@ -342,9 +279,6 @@ def rightDerivedZeroToSelfAppIso [EnoughInjectives C] [PreservesFiniteLimits F]
   inv_hom_id' := right_derived_zero_to_self_app_inv_comp _ P
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_iso CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppIso
 
-/- warning: category_theory.abelian.functor.right_derived_zero_to_self_natural -> CategoryTheory.Abelian.Functor.rightDerivedZeroToSelf_natural is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.right_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.rightDerivedZeroToSelf_naturalₓ'. -/
 /-- Given `P : InjectiveResolution X` and `Q : InjectiveResolution Y` and a morphism `f : X ⟶ Y`,
 naturality of the square given by `right_derived_zero_to_self_natural`. -/
 theorem rightDerivedZeroToSelf_natural [EnoughInjectives C] {X : C} {Y : C} (f : X ⟶ Y)

0b7c740e

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -170,10 +170,7 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align category_theory.nat_trans.right_derived_id CategoryTheory.NatTrans.rightDerived_idₓ'. -/
 @[simp]
 theorem NatTrans.rightDerived_id (F : C ⥤ D) [F.Additive] (n : ℕ) :
-    NatTrans.rightDerived (𝟙 F) n = 𝟙 (F.rightDerived n) :=
-  by
-  simp [nat_trans.right_derived]
-  rfl
+    NatTrans.rightDerived (𝟙 F) n = 𝟙 (F.rightDerived n) := by simp [nat_trans.right_derived]; rfl
 #align category_theory.nat_trans.right_derived_id CategoryTheory.NatTrans.rightDerived_id
 
 /- warning: category_theory.nat_trans.right_derived_comp -> CategoryTheory.NatTrans.rightDerived_comp is a dubious translation:
@@ -270,10 +267,7 @@ def rightDerivedZeroToSelfApp [EnoughInjectives C] [PreservesFiniteLimits F] {X
     (P : InjectiveResolution X) : (F.rightDerived 0).obj X ⟶ F.obj X :=
   (rightDerivedObjIso F 0 P).Hom ≫
     (homologyIsoKernelDesc _ _ _).Hom ≫
-      kernel.map _ _ (cokernel.desc _ (𝟙 _) (by simp)) (𝟙 _)
-          (by
-            ext
-            simp) ≫
+      kernel.map _ _ (cokernel.desc _ (𝟙 _) (by simp)) (𝟙 _) (by ext; simp) ≫
         (asIso (kernel.lift _ _ (exact_of_map_injective_resolution F P).w)).inv
 #align category_theory.abelian.functor.right_derived_zero_to_self_app CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp

0b7c740e

bump to nightly-2023-05-28-03

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

6c6011cf

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jujian Zhang, Scott Morrison
 
 ! This file was ported from Lean 3 source module category_theory.abelian.right_derived
-! leanprover-community/mathlib commit 024a4231815538ac739f52d08dd20a55da0d6b23
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.CategoryTheory.Abelian.Exact
 /-!
 # Right-derived functors
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define the right-derived functors `F.right_derived n : C ⥤ D` for any additive functor `F`
 out of a category with injective resolutions.
 
@@ -73,10 +76,7 @@ def Functor.rightDerived (F : C ⥤ D) [F.Additive] (n : ℕ) : C ⥤ D :=
 -/
 
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Nat.canonicallyOrderedCommSemiring))) (HomologicalComplex.instCategoryHomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (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.mapHomologicalComplex.{u1, u2, 0, u3, u4} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) F _inst_6 (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X P)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.functor.right_derived_obj_iso CategoryTheory.Functor.rightDerivedObjIsoₓ'. -/
 /-- We can compute a right derived functor using a chosen injective resolution. -/
 @[simps]
@@ -123,10 +123,7 @@ def Functor.rightDerivedObjInjectiveSucc (F : C ⥤ D) [F.Additive] (n : ℕ) (X
 #align category_theory.functor.right_derived_obj_injective_succ CategoryTheory.Functor.rightDerivedObjInjectiveSucc
 
 /- warning: category_theory.functor.right_derived_map_eq -> CategoryTheory.Functor.rightDerived_map_eq is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u4, u3} D] [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.HasInjectiveResolutions.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3))] [_inst_5 : CategoryTheory.Abelian.{u4, u3} D _inst_2] (F : CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) [_inst_6 : CategoryTheory.Functor.Additive.{u2, u3, u1, u4} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) F] (n : Nat) {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y X) {P : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X} {Q : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 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(CategoryTheory.Abelian.toPreadditive.{u2, u1} D _inst_2 _inst_5) F] (n : Nat) {X : C} {Y : C} (f : Quiver.Hom.{succ u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u4} C (CategoryTheory.Category.toCategoryStruct.{u3, u4} C _inst_1)) Y X) {P : CategoryTheory.InjectiveResolution.{u3, u4} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 _inst_3)) X} {Q : CategoryTheory.InjectiveResolution.{u3, u4} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, 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(HomologicalComplex.{u3, u4, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (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.Category.toCategoryStruct.{u3, max u4 u3} (HomologicalComplex.{u3, u4, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.Functor.mapHomologicalComplex.{u3, u4, 0, u1, u2} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3) D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u2, u1} D _inst_2 _inst_5) F _inst_6 (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.InjectiveResolution.cocomplex.{u3, u4} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 _inst_3)) X P))) (CategoryTheory.Functor.rightDerivedObjIso.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n X P)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.functor.right_derived_map_eq CategoryTheory.Functor.rightDerived_map_eqₓ'. -/
 /-- We can compute a right derived functor on a morphism using a descent of that morphism
 to a cochain map between chosen injective resolutions.
@@ -180,10 +177,7 @@ theorem NatTrans.rightDerived_id (F : C ⥤ D) [F.Additive] (n : ℕ) :
 #align category_theory.nat_trans.right_derived_id CategoryTheory.NatTrans.rightDerived_id
 
 /- warning: category_theory.nat_trans.right_derived_comp -> CategoryTheory.NatTrans.rightDerived_comp is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u4, u3} D] [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.HasInjectiveResolutions.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3))] [_inst_5 : CategoryTheory.Abelian.{u4, u3} D _inst_2] {F : CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2} {G : CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2} {H : CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2} [_inst_6 : CategoryTheory.Functor.Additive.{u2, u3, u1, u4} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) F] [_inst_7 : CategoryTheory.Functor.Additive.{u2, u3, u1, u4} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) G] [_inst_8 : CategoryTheory.Functor.Additive.{u2, u3, u1, u4} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) H] (α : Quiver.Hom.{succ (max u2 u4), max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u1, u4, u2, u3} C _inst_1 D _inst_2))) F G) (β : Quiver.Hom.{succ (max u2 u4), max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u1, u4, u2, u3} C _inst_1 D _inst_2))) G H) (n : Nat), Eq.{succ (max u2 u4)} (Quiver.Hom.{succ (max u2 u4), max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u1, u4, u2, u3} C _inst_1 D _inst_2))) (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n) (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 H _inst_8 n)) (CategoryTheory.NatTrans.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F H _inst_6 _inst_8 (CategoryTheory.CategoryStruct.comp.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u1, u4, u2, u3} C _inst_1 D _inst_2)) F G H α β) n) (CategoryTheory.CategoryStruct.comp.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u1, u4, u2, u3} C _inst_1 D _inst_2)) (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n) (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 G _inst_7 n) (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 H _inst_8 n) (CategoryTheory.NatTrans.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F G _inst_6 _inst_7 α n) (CategoryTheory.NatTrans.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 G H _inst_7 _inst_8 β n))
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.nat_trans.right_derived_comp CategoryTheory.NatTrans.rightDerived_compₓ'. -/
 @[simp, nolint simp_nf]
 theorem NatTrans.rightDerived_comp {F G H : C ⥤ D} [F.Additive] [G.Additive] [H.Additive]
@@ -193,10 +187,7 @@ theorem NatTrans.rightDerived_comp {F G H : C ⥤ D} [F.Additive] [G.Additive] [
 #align category_theory.nat_trans.right_derived_comp CategoryTheory.NatTrans.rightDerived_comp
 
 /- warning: category_theory.nat_trans.right_derived_eq -> CategoryTheory.NatTrans.rightDerived_eq is a dubious translation:
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(CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u2, u1} D _inst_2 _inst_5) F] [_inst_7 : CategoryTheory.Functor.Additive.{u4, u1, u3, u2} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u2, u1} D _inst_2 _inst_5) G] (α : Quiver.Hom.{max (succ u4) (succ u2), max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u3, u2, u4, u1} C _inst_1 D _inst_2))) F G) (n : Nat) {X : C} (P : CategoryTheory.InjectiveResolution.{u3, u4} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u3, u4} C _inst_1 _inst_3) 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Nat.canonicallyOrderedCommSemiring))) D _inst_2 (homologyFunctor.{u2, u1, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u2, u1} D _inst_2 _inst_5)) (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.Abelian.hasEqualizers.{u2, u1} D _inst_2 _inst_5) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} D _inst_2 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} D _inst_2 _inst_5)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u2, u1} D _inst_2 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} D _inst_2 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} D _inst_2 _inst_5)) (CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers.{u2, u1} D _inst_2 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u2, u1} D _inst_2 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u2, u1} D _inst_2 _inst_5)) (CategoryTheory.Abelian.hasPullbacks.{u2, u1} D _inst_2 _inst_5) (CategoryTheory.Abelian.hasEqualizers.{u2, u1} D _inst_2 _inst_5))) (CategoryTheory.Limits.hasCokernels_of_hasCoequalizers.{u2, u1} D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u2, u1} D _inst_2 _inst_5)) (CategoryTheory.Abelian.hasCoequalizers.{u2, u1} D _inst_2 _inst_5)) n)) (Prefunctor.obj.{succ u3, succ u2, max u4 u3, max u1 u2} (HomologicalComplex.{u3, u4, 0} Nat C _inst_1 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (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))))) (HomologicalComplex.{u2, u1, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u2, u1} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u2, u1} D _inst_2 _inst_5)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.nat_trans.right_derived_eq CategoryTheory.NatTrans.rightDerived_eqₓ'. -/
 /-- A component of the natural transformation between right-derived functors can be computed
 using a chosen injective resolution.
@@ -255,10 +246,7 @@ theorem preserves_exact_of_preservesFiniteLimits_of_mono [PreservesFiniteLimits
 #align category_theory.abelian.functor.preserves_exact_of_preserves_finite_limits_of_mono CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteLimits_of_mono
 
 /- warning: category_theory.abelian.functor.exact_of_map_injective_resolution -> CategoryTheory.Abelian.Functor.exact_of_map_injectiveResolution is a dubious translation:
-lean 3 declaration is
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-  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u1, u2} D] (F : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 D _inst_2) {X : C} [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Abelian.{u1, u2} D _inst_2] [_inst_5 : CategoryTheory.Functor.Additive.{u2, u2, u1, u1} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4) F] (P : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X) [_inst_6 : CategoryTheory.Limits.PreservesFiniteLimits.{u1, u1, u2, u2} C _inst_1 D _inst_2 F], CategoryTheory.Exact.{u1, u2} D _inst_2 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} D _inst_2 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} D _inst_2 _inst_4)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (CategoryTheory.Limits.hasKernels_of_hasEqualizers.{u1, u2} D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} D _inst_2 _inst_4)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) (HomologicalComplex.X.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3))) X) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) (HomologicalComplex.X.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X P) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (HomologicalComplex.xNext.{u1, u2, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u1, succ u1, max u2 u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (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.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (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))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (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))))) (HomologicalComplex.{u1, u2, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (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.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (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))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, max u2 u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (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))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (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))) (HomologicalComplex.{u1, u2, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (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))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (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.mapHomologicalComplex.{u1, u2, 0, u2, u1} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4) F _inst_5 (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X P)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (Prefunctor.map.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) (HomologicalComplex.X.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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P)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.exact_of_map_injective_resolution CategoryTheory.Abelian.Functor.exact_of_map_injectiveResolutionₓ'. -/
 theorem exact_of_map_injectiveResolution (P : InjectiveResolution X) [PreservesFiniteLimits F] :
     Exact (F.map (P.ι.f 0))
@@ -308,10 +296,7 @@ def rightDerivedZeroToSelfAppInv [EnoughInjectives C] {X : C} (P : InjectiveReso
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv
 
 /- warning: category_theory.abelian.functor.right_derived_zero_to_self_app_comp_inv -> CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp_comp_inv is a dubious translation:
-lean 3 declaration is
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 Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.right_derived_zero_to_self_app_comp_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp_comp_invₓ'. -/
 theorem rightDerivedZeroToSelfApp_comp_inv [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
     (P : InjectiveResolution X) :
@@ -330,10 +315,7 @@ theorem rightDerivedZeroToSelfApp_comp_inv [EnoughInjectives C] [PreservesFinite
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_comp_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp_comp_inv
 
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 Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.right_derived_zero_to_self_app_inv_comp CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv_compₓ'. -/
 theorem rightDerivedZeroToSelfAppInv_comp [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
     (P : InjectiveResolution X) :
@@ -367,10 +349,7 @@ def rightDerivedZeroToSelfAppIso [EnoughInjectives C] [PreservesFiniteLimits F]
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_iso CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppIso
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.right_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.rightDerivedZeroToSelf_naturalₓ'. -/
 /-- Given `P : InjectiveResolution X` and `Q : InjectiveResolution Y` and a morphism `f : X ⟶ Y`,
 naturality of the square given by `right_derived_zero_to_self_natural`. -/

024a4231

bump to nightly-2023-05-25-16

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

e9a29bbe

Diff

@@ -65,11 +65,19 @@ variable {C : Type u} [Category.{v} C] {D : Type _} [Category D]
 
 variable [Abelian C] [HasInjectiveResolutions C] [Abelian D]
 
+#print CategoryTheory.Functor.rightDerived /-
 /-- The right derived functors of an additive functor. -/
 def Functor.rightDerived (F : C ⥤ D) [F.Additive] (n : ℕ) : C ⥤ D :=
   injectiveResolutions C ⋙ F.mapHomotopyCategory _ ⋙ HomotopyCategory.homologyFunctor D _ n
 #align category_theory.functor.right_derived CategoryTheory.Functor.rightDerived
+-/
 
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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (HomologicalComplex.CategoryTheory.category.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (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.mapHomologicalComplex.{u1, u2, 0, u3, u4} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) F _inst_6 (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Functor.rightDerivedObjIso._proof_6.{u2, u1} C _inst_1 _inst_3) X P)))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u4, u3} D] [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.HasInjectiveResolutions.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3))] [_inst_5 : CategoryTheory.Abelian.{u4, u3} D _inst_2] (F : CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) [_inst_6 : CategoryTheory.Functor.Additive.{u2, u3, u1, u4} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) F] (n : Nat) {X : C} (P : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X), CategoryTheory.Iso.{u4, u3} D _inst_2 (Prefunctor.obj.{succ u1, succ u4, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u4, u3} D (CategoryTheory.Category.toCategoryStruct.{u4, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u4, u2, u3} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n)) X) (Prefunctor.obj.{succ u4, succ u4, max u3 u4, u3} (HomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.CategoryStruct.toQuiver.{u4, max u3 u4} (HomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (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.Category.toCategoryStruct.{u4, max u3 u4} (HomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (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))) (HomologicalComplex.instCategoryHomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (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))))) D (CategoryTheory.CategoryStruct.toQuiver.{u4, u3} D (CategoryTheory.Category.toCategoryStruct.{u4, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u4, u4, max u3 u4, u3} (HomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (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))) (HomologicalComplex.instCategoryHomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (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))) D _inst_2 (homologyFunctor.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (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.Abelian.hasEqualizers.{u4, u3} D _inst_2 _inst_5) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u4, u3} D _inst_2 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u4, u3} D _inst_2 _inst_5)) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u4, u3} D _inst_2 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u4, u3} D _inst_2 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u4, u3} D _inst_2 _inst_5)) (CategoryTheory.Limits.hasStrongEpiImages_of_hasPullbacks_of_hasEqualizers.{u4, u3} D _inst_2 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u4, u3} D _inst_2 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u4, u3} D _inst_2 _inst_5)) (CategoryTheory.Abelian.hasPullbacks.{u4, u3} D _inst_2 _inst_5) (CategoryTheory.Abelian.hasEqualizers.{u4, u3} D _inst_2 _inst_5))) (CategoryTheory.Limits.hasCokernels_of_hasCoequalizers.{u4, u3} D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (CategoryTheory.Abelian.hasCoequalizers.{u4, u3} D _inst_2 _inst_5)) n)) (Prefunctor.obj.{succ u1, succ u4, max u2 u1, max u3 u4} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (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.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (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))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (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))))) (HomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.CategoryStruct.toQuiver.{u4, max u3 u4} (HomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (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.Category.toCategoryStruct.{u4, max u3 u4} (HomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (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))) (HomologicalComplex.instCategoryHomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u4, max u2 u1, max u3 u4} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (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))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (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))) (HomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (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))) (HomologicalComplex.instCategoryHomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (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.mapHomologicalComplex.{u1, u2, 0, u3, u4} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) F _inst_6 (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X P)))
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.right_derived_obj_iso CategoryTheory.Functor.rightDerivedObjIsoₓ'. -/
 /-- We can compute a right derived functor using a chosen injective resolution. -/
 @[simps]
 def Functor.rightDerivedObjIso (F : C ⥤ D) [F.Additive] (n : ℕ) {X : C}
@@ -82,6 +90,12 @@ def Functor.rightDerivedObjIso (F : C ⥤ D) [F.Additive] (n : ℕ) {X : C}
     (HomotopyCategory.homologyFactors D _ n).app _
 #align category_theory.functor.right_derived_obj_iso CategoryTheory.Functor.rightDerivedObjIso
 
+/- warning: category_theory.functor.right_derived_obj_injective_zero -> CategoryTheory.Functor.rightDerivedObjInjectiveZero is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u4, u3} D] [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.HasInjectiveResolutions.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Functor.rightDerivedObjInjectiveZero._proof_1.{u2, u1} C _inst_1 _inst_3)] [_inst_5 : CategoryTheory.Abelian.{u4, u3} D _inst_2] (F : CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) [_inst_6 : CategoryTheory.Functor.Additive.{u2, u3, u1, u4} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) F] (X : C) [_inst_7 : CategoryTheory.Injective.{u1, u2} C _inst_1 X], CategoryTheory.Iso.{u4, u3} D _inst_2 (CategoryTheory.Functor.obj.{u1, u4, u2, u3} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) X) (CategoryTheory.Functor.obj.{u1, u4, u2, u3} C _inst_1 D _inst_2 F X)
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u4, u3} D] [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.HasInjectiveResolutions.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3))] [_inst_5 : CategoryTheory.Abelian.{u4, u3} D _inst_2] (F : CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) [_inst_6 : CategoryTheory.Functor.Additive.{u2, u3, u1, u4} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) F] (X : C) [_inst_7 : CategoryTheory.Injective.{u1, u2} C _inst_1 X], CategoryTheory.Iso.{u4, u3} D _inst_2 (Prefunctor.obj.{succ u1, succ u4, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u4, u3} D (CategoryTheory.Category.toCategoryStruct.{u4, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u4, u2, u3} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) X) (Prefunctor.obj.{succ u1, succ u4, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u4, u3} D (CategoryTheory.Category.toCategoryStruct.{u4, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u4, u2, u3} C _inst_1 D _inst_2 F) X)
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.right_derived_obj_injective_zero CategoryTheory.Functor.rightDerivedObjInjectiveZeroₓ'. -/
 /-- The 0-th derived functor of `F` on an injective object `X` is just `F.obj X`. -/
 @[simps]
 def Functor.rightDerivedObjInjectiveZero (F : C ⥤ D) [F.Additive] (X : C) [Injective X] :
@@ -93,6 +107,12 @@ def Functor.rightDerivedObjInjectiveZero (F : C ⥤ D) [F.Additive] (X : C) [Inj
 
 open ZeroObject
 
+/- warning: category_theory.functor.right_derived_obj_injective_succ -> CategoryTheory.Functor.rightDerivedObjInjectiveSucc is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u4, u3} D] [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.HasInjectiveResolutions.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Functor.rightDerivedObjInjectiveSucc._proof_1.{u2, u1} C _inst_1 _inst_3)] [_inst_5 : CategoryTheory.Abelian.{u4, u3} D _inst_2] (F : CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) [_inst_6 : CategoryTheory.Functor.Additive.{u2, u3, u1, u4} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) F] (n : Nat) (X : C) [_inst_7 : CategoryTheory.Injective.{u1, u2} C _inst_1 X], CategoryTheory.Iso.{u4, u3} D _inst_2 (CategoryTheory.Functor.obj.{u1, u4, u2, u3} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 (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))))) X) (OfNat.ofNat.{u3} D 0 (OfNat.mk.{u3} D 0 (Zero.zero.{u3} D (CategoryTheory.Limits.HasZeroObject.zero'.{u4, u3} D _inst_2 (CategoryTheory.Abelian.hasZeroObject.{u4, u3} D _inst_2 _inst_5)))))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u4, u3} D] [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.HasInjectiveResolutions.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3))] [_inst_5 : CategoryTheory.Abelian.{u4, u3} D _inst_2] (F : CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) [_inst_6 : CategoryTheory.Functor.Additive.{u2, u3, u1, u4} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) F] (n : Nat) (X : C) [_inst_7 : CategoryTheory.Injective.{u1, u2} C _inst_1 X], CategoryTheory.Iso.{u4, u3} D _inst_2 (Prefunctor.obj.{succ u1, succ u4, u2, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u4, u3} D (CategoryTheory.Category.toCategoryStruct.{u4, u3} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u4, u2, u3} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) n (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) X) (OfNat.ofNat.{u3} D 0 (Zero.toOfNat0.{u3} D (CategoryTheory.Limits.HasZeroObject.zero'.{u4, u3} D _inst_2 (CategoryTheory.Abelian.hasZeroObject.{u4, u3} D _inst_2 _inst_5))))
+Case conversion may be inaccurate. Consider using '#align category_theory.functor.right_derived_obj_injective_succ CategoryTheory.Functor.rightDerivedObjInjectiveSuccₓ'. -/
 /-- The higher derived functors vanish on injective objects. -/
 @[simps inv]
 def Functor.rightDerivedObjInjectiveSucc (F : C ⥤ D) [F.Additive] (n : ℕ) (X : C) [Injective X] :
@@ -102,6 +122,12 @@ def Functor.rightDerivedObjInjectiveSucc (F : C ⥤ D) [F.Additive] (n : ℕ) (X
       (CochainComplex.homologyFunctorSuccSingle₀ D n).app (F.obj X) ≪≫ (Functor.zero_obj _).isoZero
 #align category_theory.functor.right_derived_obj_injective_succ CategoryTheory.Functor.rightDerivedObjInjectiveSucc
 
+/- warning: category_theory.functor.right_derived_map_eq -> CategoryTheory.Functor.rightDerived_map_eq is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u4, u3} D] [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.HasInjectiveResolutions.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3))] [_inst_5 : CategoryTheory.Abelian.{u4, u3} D _inst_2] (F : CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) [_inst_6 : CategoryTheory.Functor.Additive.{u2, u3, u1, u4} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) 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(CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u4, u3} D _inst_2 _inst_5)) (CategoryTheory.Abelian.hasPullbacks.{u4, u3} D _inst_2 _inst_5) (CategoryTheory.Abelian.hasEqualizers.{u4, u3} D _inst_2 _inst_5))) (CategoryTheory.Abelian.hasCokernels.{u4, u3} D _inst_2 _inst_5) n) (CategoryTheory.Functor.obj.{u1, u4, max u2 u1, max u3 u4} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (HomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (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))))) 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_inst_3) D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) F _inst_6 (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X P)) (CategoryTheory.Functor.map.{u1, u4, max u2 u1, max u3 u4} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Functor.rightDerivedObjIso._proof_6.{u2, u1} C _inst_1 _inst_3) Y Q) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X P) g)) (CategoryTheory.Iso.inv.{u4, u3} D _inst_2 (CategoryTheory.Functor.obj.{u1, u4, u2, u3} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n) X) (CategoryTheory.Functor.obj.{u4, u4, max u3 u4, u3} (HomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (HomologicalComplex.CategoryTheory.category.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(CategoryTheory.Functor.rightDerivedObjIso._proof_4.{u3, u4} D _inst_2 _inst_5) (CategoryTheory.Functor.rightDerivedObjIso._proof_5.{u3, u4} D _inst_2 _inst_5)) (CategoryTheory.Abelian.hasCokernels.{u4, u3} D _inst_2 _inst_5) n) (CategoryTheory.Functor.obj.{u1, u4, max u2 u1, max u3 u4} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (HomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (HomologicalComplex.CategoryTheory.category.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (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.mapHomologicalComplex.{u1, u2, 0, u3, u4} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) F _inst_6 (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Functor.rightDerivedObjIso._proof_6.{u2, u1} C _inst_1 _inst_3) X P))) (CategoryTheory.Functor.rightDerivedObjIso.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n X P)))))
+but is expected to have type
+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u3, u4} C] {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{u2, u1} D] [_inst_3 : CategoryTheory.Abelian.{u3, u4} C _inst_1] [_inst_4 : CategoryTheory.HasInjectiveResolutions.{u3, u4} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 _inst_3))] [_inst_5 : CategoryTheory.Abelian.{u2, u1} D _inst_2] (F : CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) [_inst_6 : CategoryTheory.Functor.Additive.{u4, u1, u3, u2} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u2, u1} D _inst_2 _inst_5) F] (n : Nat) {X : C} {Y : C} (f : Quiver.Hom.{succ u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u4} C (CategoryTheory.Category.toCategoryStruct.{u3, u4} C _inst_1)) Y X) {P : CategoryTheory.InjectiveResolution.{u3, u4} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 _inst_3)) X} {Q : CategoryTheory.InjectiveResolution.{u3, u4} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 _inst_3)) Y} (g : Quiver.Hom.{succ u3, max u4 u3} (CochainComplex.{u3, u4, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u3, max u4 u3} (CochainComplex.{u3, u4, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u3, max u4 u3} (CochainComplex.{u3, u4, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u3, u4, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.InjectiveResolution.cocomplex.{u3, u4} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 _inst_3)) Y Q) (CategoryTheory.InjectiveResolution.cocomplex.{u3, u4} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 _inst_3)) X P)), (Eq.{succ u3} (Quiver.Hom.{succ u3, max u4 u3} (CochainComplex.{u3, u4, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u3, max u4 u3} (CochainComplex.{u3, u4, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u3, max u4 u3} (CochainComplex.{u3, u4, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u3, u4, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (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 u3, succ u3, u4, max u4 u3} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u4} C (CategoryTheory.Category.toCategoryStruct.{u3, u4} C _inst_1)) (CochainComplex.{u3, u4, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} 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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.{u3, u4, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (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.{u3, u3, u4, max u4 u3} C _inst_1 (CochainComplex.{u3, u4, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u3, u4, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (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.{u3, u4} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasZeroObject.{u3, u4} C _inst_1 _inst_3))) Y) (CategoryTheory.InjectiveResolution.cocomplex.{u3, u4} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 _inst_3)) X P)) (CategoryTheory.CategoryStruct.comp.{u3, max u4 u3} (CochainComplex.{u3, u4, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u3, max u4 u3} (CochainComplex.{u3, u4, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u3, u4, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (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 u3, succ u3, u4, max u4 u3} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u4} C (CategoryTheory.Category.toCategoryStruct.{u3, u4} C _inst_1)) (CochainComplex.{u3, u4, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u3, max u4 u3} (CochainComplex.{u3, u4, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u3, max u4 u3} (CochainComplex.{u3, u4, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u3, u4, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (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.{u3, u3, u4, max u4 u3} C _inst_1 (CochainComplex.{u3, u4, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat 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+Case conversion may be inaccurate. Consider using '#align category_theory.functor.right_derived_map_eq CategoryTheory.Functor.rightDerived_map_eqₓ'. -/
 /-- We can compute a right derived functor on a morphism using a descent of that morphism
 to a cochain map between chosen injective resolutions.
 -/
@@ -129,6 +155,7 @@ theorem Functor.rightDerived_map_eq (F : C ⥤ D) [F.Additive] (n : ℕ) {X Y :
     simp only [InjectiveResolution.homotopy_equiv_inv_ι]
 #align category_theory.functor.right_derived_map_eq CategoryTheory.Functor.rightDerived_map_eq
 
+#print CategoryTheory.NatTrans.rightDerived /-
 /-- The natural transformation between right-derived functors induced by a natural transformation.-/
 @[simps]
 def NatTrans.rightDerived {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶ G) (n : ℕ) :
@@ -136,7 +163,14 @@ def NatTrans.rightDerived {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶
   whiskerLeft (injectiveResolutions C)
     (whiskerRight (NatTrans.mapHomotopyCategory α _) (HomotopyCategory.homologyFunctor D _ n))
 #align category_theory.nat_trans.right_derived CategoryTheory.NatTrans.rightDerived
+-/
 
+/- warning: category_theory.nat_trans.right_derived_id -> CategoryTheory.NatTrans.rightDerived_id is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u4, u3} D] [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.HasInjectiveResolutions.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3))] [_inst_5 : CategoryTheory.Abelian.{u4, u3} D _inst_2] (F : CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) [_inst_6 : CategoryTheory.Functor.Additive.{u2, u3, u1, u4} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) F] (n : Nat), Eq.{succ (max u2 u4)} (Quiver.Hom.{succ (max u2 u4), max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u1, u4, u2, u3} C _inst_1 D _inst_2))) (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n) (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n)) (CategoryTheory.NatTrans.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F F _inst_6 _inst_6 (CategoryTheory.CategoryStruct.id.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u1, u4, u2, u3} C _inst_1 D _inst_2)) F) n) (CategoryTheory.CategoryStruct.id.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u1, u4, u2, u3} C _inst_1 D _inst_2)) (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n))
+but is expected to have type
+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u3, u4} C] {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{u2, u1} D] [_inst_3 : CategoryTheory.Abelian.{u3, u4} C _inst_1] [_inst_4 : CategoryTheory.HasInjectiveResolutions.{u3, u4} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 _inst_3))] [_inst_5 : CategoryTheory.Abelian.{u2, u1} D _inst_2] (F : CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) [_inst_6 : CategoryTheory.Functor.Additive.{u4, u1, u3, u2} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u2, u1} D _inst_2 _inst_5) F] (n : Nat), Eq.{max (succ u4) (succ u2)} (Quiver.Hom.{max (succ u4) (succ u2), max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u3, u2, u4, u1} C _inst_1 D _inst_2))) (CategoryTheory.Functor.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n) (CategoryTheory.Functor.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n)) (CategoryTheory.NatTrans.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F F _inst_6 _inst_6 (CategoryTheory.CategoryStruct.id.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u3, u2, u4, u1} C _inst_1 D _inst_2)) F) n) (CategoryTheory.CategoryStruct.id.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u3, u2, u4, u1} C _inst_1 D _inst_2)) (CategoryTheory.Functor.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n))
+Case conversion may be inaccurate. Consider using '#align category_theory.nat_trans.right_derived_id CategoryTheory.NatTrans.rightDerived_idₓ'. -/
 @[simp]
 theorem NatTrans.rightDerived_id (F : C ⥤ D) [F.Additive] (n : ℕ) :
     NatTrans.rightDerived (𝟙 F) n = 𝟙 (F.rightDerived n) :=
@@ -145,6 +179,12 @@ theorem NatTrans.rightDerived_id (F : C ⥤ D) [F.Additive] (n : ℕ) :
   rfl
 #align category_theory.nat_trans.right_derived_id CategoryTheory.NatTrans.rightDerived_id
 
+/- warning: category_theory.nat_trans.right_derived_comp -> CategoryTheory.NatTrans.rightDerived_comp is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u3, u4} C] {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{u2, u1} D] [_inst_3 : CategoryTheory.Abelian.{u3, u4} C _inst_1] [_inst_4 : CategoryTheory.HasInjectiveResolutions.{u3, u4} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 _inst_3))] [_inst_5 : CategoryTheory.Abelian.{u2, u1} D _inst_2] {F : CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2} {G : CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2} {H : CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2} [_inst_6 : CategoryTheory.Functor.Additive.{u4, u1, u3, u2} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u2, u1} D _inst_2 _inst_5) F] [_inst_7 : CategoryTheory.Functor.Additive.{u4, u1, u3, u2} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u2, u1} D _inst_2 _inst_5) G] [_inst_8 : CategoryTheory.Functor.Additive.{u4, u1, u3, u2} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u2, u1} D _inst_2 _inst_5) H] (α : Quiver.Hom.{max (succ u4) (succ u2), max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u3, u2, u4, u1} C _inst_1 D _inst_2))) F G) (β : Quiver.Hom.{max (succ u4) (succ u2), max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u3, u2, u4, u1} C _inst_1 D _inst_2))) G H) (n : Nat), Eq.{max (succ u4) (succ u2)} (Quiver.Hom.{max (succ u4) (succ u2), max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u3, u2, u4, u1} C _inst_1 D _inst_2))) (CategoryTheory.Functor.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n) (CategoryTheory.Functor.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 H _inst_8 n)) (CategoryTheory.NatTrans.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F H _inst_6 _inst_8 (CategoryTheory.CategoryStruct.comp.{max u2 u4, max (max (max u2 u1) u4) u3} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u4, max (max (max u2 u1) u4) u3} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u3, u2, u4, u1} C _inst_1 D _inst_2)) F G H α β) n) (CategoryTheory.CategoryStruct.comp.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u3, u2, u4, u1} C _inst_1 D _inst_2)) (CategoryTheory.Functor.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n) (CategoryTheory.Functor.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 G _inst_7 n) (CategoryTheory.Functor.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 H _inst_8 n) (CategoryTheory.NatTrans.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F G _inst_6 _inst_7 α n) (CategoryTheory.NatTrans.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 G H _inst_7 _inst_8 β n))
+Case conversion may be inaccurate. Consider using '#align category_theory.nat_trans.right_derived_comp CategoryTheory.NatTrans.rightDerived_compₓ'. -/
 @[simp, nolint simp_nf]
 theorem NatTrans.rightDerived_comp {F G H : C ⥤ D} [F.Additive] [G.Additive] [H.Additive]
     (α : F ⟶ G) (β : G ⟶ H) (n : ℕ) :
@@ -152,6 +192,12 @@ theorem NatTrans.rightDerived_comp {F G H : C ⥤ D} [F.Additive] [G.Additive] [
   simp [nat_trans.right_derived]
 #align category_theory.nat_trans.right_derived_comp CategoryTheory.NatTrans.rightDerived_comp
 
+/- warning: category_theory.nat_trans.right_derived_eq -> CategoryTheory.NatTrans.rightDerived_eq is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u3}} [_inst_2 : CategoryTheory.Category.{u4, u3} D] [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.HasInjectiveResolutions.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3))] [_inst_5 : CategoryTheory.Abelian.{u4, u3} D _inst_2] {F : CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2} {G : CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2} [_inst_6 : CategoryTheory.Functor.Additive.{u2, u3, u1, u4} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) F] [_inst_7 : CategoryTheory.Functor.Additive.{u2, u3, u1, u4} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) G] (α : Quiver.Hom.{succ (max u2 u4), max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u2 u4, max u1 u4 u2 u3} (CategoryTheory.Functor.{u1, u4, u2, u3} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u1, u4, u2, u3} C _inst_1 D _inst_2))) F G) (n : Nat) {X : C} (P : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X), Eq.{succ u4} (Quiver.Hom.{succ u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u4, u3} D (CategoryTheory.Category.toCategoryStruct.{u4, u3} D _inst_2)) (CategoryTheory.Functor.obj.{u1, u4, u2, u3} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n) X) (CategoryTheory.Functor.obj.{u1, u4, u2, u3} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 G _inst_7 n) X)) (CategoryTheory.NatTrans.app.{u1, u4, u2, u3} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n) (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 G _inst_7 n) (CategoryTheory.NatTrans.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F G _inst_6 _inst_7 α n) X) (CategoryTheory.CategoryStruct.comp.{u4, u3} D (CategoryTheory.Category.toCategoryStruct.{u4, u3} D _inst_2) (CategoryTheory.Functor.obj.{u1, u4, u2, u3} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n) X) (CategoryTheory.Functor.obj.{u4, u4, max u3 u4, u3} (HomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat 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_inst_5)) (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.Abelian.hasEqualizers.{u4, u3} D _inst_2 _inst_5) (CategoryTheory.Functor.rightDerivedObjIso._proof_3.{u3, u4} D _inst_2 _inst_5) (CategoryTheory.Limits.hasImageMapsOfHasStrongEpiImages.{u4, u3} D _inst_2 (CategoryTheory.Functor.rightDerivedObjIso._proof_4.{u3, u4} D _inst_2 _inst_5) (CategoryTheory.Functor.rightDerivedObjIso._proof_5.{u3, u4} D _inst_2 _inst_5)) (CategoryTheory.Abelian.hasCokernels.{u4, u3} D _inst_2 _inst_5) n) (CategoryTheory.Functor.obj.{u1, u4, max u2 u1, max u3 u4} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 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_inst_3 _inst_4 _inst_5 F _inst_6 n X P)) (CategoryTheory.CategoryStruct.comp.{u4, u3} D (CategoryTheory.Category.toCategoryStruct.{u4, u3} D _inst_2) (CategoryTheory.Functor.obj.{u4, u4, max u3 u4, u3} (HomologicalComplex.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (HomologicalComplex.CategoryTheory.category.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (ComplexShape.up.{0} Nat 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(CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) G _inst_7 (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.NatTrans.mapHomologicalComplex.{u1, u2, 0, u3, u4} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) F G _inst_6 _inst_7 α (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (HomologicalComplex.CategoryTheory.category.{u4, u3, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u4, u3} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5)) (ComplexShape.up.{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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(AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (CategoryTheory.Functor.mapHomologicalComplex.{u1, u2, 0, u3, u4} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u4, u3} D _inst_2 _inst_5) G _inst_7 (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Functor.rightDerivedObjIso._proof_6.{u2, u1} C _inst_1 _inst_3) X P))) (CategoryTheory.Functor.rightDerivedObjIso.{u1, u2, u3, u4} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 G _inst_7 n X P))))
+but is expected to have type
+  forall {C : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u3, u4} C] {D : Type.{u1}} [_inst_2 : CategoryTheory.Category.{u2, u1} D] [_inst_3 : CategoryTheory.Abelian.{u3, u4} C _inst_1] [_inst_4 : CategoryTheory.HasInjectiveResolutions.{u3, u4} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 _inst_3))] [_inst_5 : CategoryTheory.Abelian.{u2, u1} D _inst_2] {F : CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2} {G : CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2} [_inst_6 : CategoryTheory.Functor.Additive.{u4, u1, u3, u2} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u2, u1} D _inst_2 _inst_5) F] [_inst_7 : CategoryTheory.Functor.Additive.{u4, u1, u3, u2} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u2, u1} D _inst_2 _inst_5) G] (α : Quiver.Hom.{max (succ u4) (succ u2), max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.CategoryStruct.toQuiver.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Category.toCategoryStruct.{max u4 u2, max (max (max u4 u3) u1) u2} (CategoryTheory.Functor.{u3, u2, u4, u1} C _inst_1 D _inst_2) (CategoryTheory.Functor.category.{u3, u2, u4, u1} C _inst_1 D _inst_2))) F G) (n : Nat) {X : C} (P : CategoryTheory.InjectiveResolution.{u3, u4} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 _inst_3)) X), Eq.{succ u2} (Quiver.Hom.{succ u2, u1} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} D (CategoryTheory.Category.toCategoryStruct.{u2, u1} D _inst_2)) (Prefunctor.obj.{succ u3, succ u2, u4, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u4} C (CategoryTheory.Category.toCategoryStruct.{u3, u4} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} D (CategoryTheory.Category.toCategoryStruct.{u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u3, u2, u4, u1} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n)) X) (Prefunctor.obj.{succ u3, succ u2, u4, u1} C (CategoryTheory.CategoryStruct.toQuiver.{u3, u4} C (CategoryTheory.Category.toCategoryStruct.{u3, u4} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u1} D (CategoryTheory.Category.toCategoryStruct.{u2, u1} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u3, u2, u4, u1} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 G _inst_7 n)) X)) (CategoryTheory.NatTrans.app.{u3, u2, u4, u1} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F _inst_6 n) (CategoryTheory.Functor.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 G _inst_7 n) (CategoryTheory.NatTrans.rightDerived.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 F G _inst_6 _inst_7 α n) X) (CategoryTheory.CategoryStruct.comp.{u2, u1} D (CategoryTheory.Category.toCategoryStruct.{u2, u1} D _inst_2) 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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.InjectiveResolution.cocomplex.{u3, u4} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u3, u4} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u3, u4} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u3, u4} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u3, u4} C _inst_1 _inst_3)) X P))) (CategoryTheory.Functor.rightDerivedObjIso.{u3, u4, u1, u2} C _inst_1 D _inst_2 _inst_3 _inst_4 _inst_5 G _inst_7 n X P))))
+Case conversion may be inaccurate. Consider using '#align category_theory.nat_trans.right_derived_eq CategoryTheory.NatTrans.rightDerived_eqₓ'. -/
 /-- A component of the natural transformation between right-derived functors can be computed
 using a chosen injective resolution.
 -/
@@ -194,6 +240,12 @@ open CategoryTheory.Preadditive
 
 variable [Abelian C] [Abelian D] [Additive F]
 
+/- warning: category_theory.abelian.functor.preserves_exact_of_preserves_finite_limits_of_mono -> CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteLimits_of_mono is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u1, u2} D] (F : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 D _inst_2) {X : C} {Y : C} {Z : C} {f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y} {g : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y Z} [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Abelian.{u1, u2} D _inst_2] [_inst_5 : CategoryTheory.Functor.Additive.{u2, u2, u1, u1} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4) F] [_inst_6 : CategoryTheory.Limits.PreservesFiniteLimits.{u1, u1, u2, u2} C _inst_1 D _inst_2 F] [_inst_7 : CategoryTheory.Mono.{u1, u2} C _inst_1 X Y f], (CategoryTheory.Exact.{u1, u2} C _inst_1 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasKernels.{u1, u2} C _inst_1 _inst_3) X Y Z f g) -> (CategoryTheory.Exact.{u1, u2} D _inst_2 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} D _inst_2 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} D _inst_2 _inst_4)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (CategoryTheory.Abelian.hasKernels.{u1, u2} D _inst_2 _inst_4) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 D _inst_2 F X) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 D _inst_2 F Y) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 D _inst_2 F Z) (CategoryTheory.Functor.map.{u1, u1, u2, u2} C _inst_1 D _inst_2 F X Y f) (CategoryTheory.Functor.map.{u1, u1, u2, u2} C _inst_1 D _inst_2 F Y Z g))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u1, u2} D] (F : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 D _inst_2) {X : C} {Y : C} {Z : C} {f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y} {g : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y Z} [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Abelian.{u1, u2} D _inst_2] [_inst_5 : CategoryTheory.Functor.Additive.{u2, u2, u1, u1} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4) F] [_inst_6 : CategoryTheory.Limits.PreservesFiniteLimits.{u1, u1, u2, u2} C _inst_1 D _inst_2 F] [_inst_7 : CategoryTheory.Mono.{u1, u2} C _inst_1 X Y f], (CategoryTheory.Exact.{u1, u2} C _inst_1 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Limits.hasKernels_of_hasEqualizers.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3)) X Y Z f g) -> (CategoryTheory.Exact.{u1, u2} D _inst_2 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} D _inst_2 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} D _inst_2 _inst_4)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (CategoryTheory.Limits.hasKernels_of_hasEqualizers.{u1, u2} D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} D _inst_2 _inst_4)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) X) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) Y) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) Z) (Prefunctor.map.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) X Y f) (Prefunctor.map.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) Y Z g))
+Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.preserves_exact_of_preserves_finite_limits_of_mono CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteLimits_of_monoₓ'. -/
 /-- If `preserves_finite_limits F` and `mono f`, then `exact (F.map f) (F.map g)` if
 `exact f g`. -/
 theorem preserves_exact_of_preservesFiniteLimits_of_mono [PreservesFiniteLimits F] [Mono f]
@@ -202,7 +254,13 @@ theorem preserves_exact_of_preservesFiniteLimits_of_mono [PreservesFiniteLimits
     Limits.isLimitForkMapOfIsLimit' _ ex.w (Abelian.isLimitOfExactOfMono _ _ ex)
 #align category_theory.abelian.functor.preserves_exact_of_preserves_finite_limits_of_mono CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteLimits_of_mono
 
-theorem exact_of_map_injective_resolution (P : InjectiveResolution X) [PreservesFiniteLimits F] :
+/- warning: category_theory.abelian.functor.exact_of_map_injective_resolution -> CategoryTheory.Abelian.Functor.exact_of_map_injectiveResolution is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u1, u2} D] (F : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 D _inst_2) {X : C} [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Abelian.{u1, u2} D _inst_2] [_inst_5 : CategoryTheory.Functor.Additive.{u2, u2, u1, u1} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4) F] (P : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 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(CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3)) X) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X P) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X P) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))) (HomologicalComplex.dFrom.{u1, u2, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne) (CategoryTheory.Functor.obj.{u1, u1, max u2 u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (HomologicalComplex.CategoryTheory.category.{u1, u2, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (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.mapHomologicalComplex.{u1, u2, 0, u2, u1} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4) F _inst_5 (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) Nat.hasOne)) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.CategoryTheory.Limits.hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X P)) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u1, u2} D] (F : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 D _inst_2) {X : C} [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Abelian.{u1, u2} D _inst_2] [_inst_5 : CategoryTheory.Functor.Additive.{u2, u2, u1, u1} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4) F] (P : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X) [_inst_6 : CategoryTheory.Limits.PreservesFiniteLimits.{u1, u1, u2, u2} C _inst_1 D _inst_2 F], CategoryTheory.Exact.{u1, u2} D _inst_2 (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} D _inst_2 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} D _inst_2 _inst_4)) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (CategoryTheory.Limits.hasKernels_of_hasEqualizers.{u1, u2} D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} D _inst_2 _inst_4)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) (HomologicalComplex.X.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u1, succ u1, u2, max u2 u1} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CochainComplex.{u1, u2, 0} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) 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(instOfNatNat 0)))) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) (HomologicalComplex.X.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (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)) 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(CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CochainComplex.single₀.{u1, u2} C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3))) X) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X P) (CategoryTheory.InjectiveResolution.ι.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X P) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) (HomologicalComplex.dFrom.{u1, u2, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)) (Prefunctor.obj.{succ u1, succ u1, max u2 u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring))) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (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.Category.toCategoryStruct.{u1, max u2 u1} (HomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (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))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat C _inst_1 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (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))))) (HomologicalComplex.{u1, u2, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat 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(CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (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))) (HomologicalComplex.{u1, u2, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (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))) (HomologicalComplex.instCategoryHomologicalComplex.{u1, u2, 0} Nat D _inst_2 (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4)) (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.mapHomologicalComplex.{u1, u2, 0, u2, u1} Nat C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) D _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4) F _inst_5 (ComplexShape.up.{0} Nat (AddRightCancelMonoid.toAddRightCancelSemigroup.{0} Nat (AddCancelMonoid.toAddRightCancelMonoid.{0} Nat (AddCancelCommMonoid.toAddCancelMonoid.{0} Nat (OrderedCancelAddCommMonoid.toCancelAddCommMonoid.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))) (CanonicallyOrderedCommSemiring.toOne.{0} Nat Nat.canonicallyOrderedCommSemiring)))) (CategoryTheory.InjectiveResolution.cocomplex.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X P)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))
+Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.exact_of_map_injective_resolution CategoryTheory.Abelian.Functor.exact_of_map_injectiveResolutionₓ'. -/
+theorem exact_of_map_injectiveResolution (P : InjectiveResolution X) [PreservesFiniteLimits F] :
     Exact (F.map (P.ι.f 0))
       (((F.mapHomologicalComplex (ComplexShape.up ℕ)).obj P.cocomplex).dFrom 0) :=
   Preadditive.exact_of_iso_of_exact' (F.map (P.ι.f 0)) (F.map (P.cocomplex.d 0 1)) _ _ (Iso.refl _)
@@ -210,8 +268,14 @@ theorem exact_of_map_injective_resolution (P : InjectiveResolution X) [Preserves
     (HomologicalComplex.xNextIso ((F.mapHomologicalComplex _).obj P.cocomplex) rfl).symm (by simp)
     (by rw [iso.refl_hom, category.id_comp, iso.symm_hom, HomologicalComplex.dFrom_eq] <;> congr )
     (preserves_exact_of_preserves_finite_limits_of_mono _ P.exact₀)
-#align category_theory.abelian.functor.exact_of_map_injective_resolution CategoryTheory.Abelian.Functor.exact_of_map_injective_resolution
-
+#align category_theory.abelian.functor.exact_of_map_injective_resolution CategoryTheory.Abelian.Functor.exact_of_map_injectiveResolution
+
+/- warning: category_theory.abelian.functor.right_derived_zero_to_self_app -> CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp is a dubious translation:
+lean 3 declaration is
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u1, u2} D] (F : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 D _inst_2) [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Abelian.{u1, u2} D _inst_2] [_inst_5 : CategoryTheory.Functor.Additive.{u2, u2, u1, u1} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4) F] [_inst_6 : CategoryTheory.EnoughInjectives.{u1, u2} C _inst_1] [_inst_7 : CategoryTheory.Limits.PreservesFiniteLimits.{u1, u1, u2, u2} C _inst_1 D _inst_2 F] {X : C}, (CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp._proof_1.{u2, u1} C _inst_1 _inst_3) X) -> (Quiver.Hom.{succ u1, u2} D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u2, u1} C _inst_1 D _inst_2 _inst_3 (CategoryTheory.InjectiveResolution.CategoryTheory.hasInjectiveResolutions.{u1, u2} C _inst_1 _inst_3 _inst_6) _inst_4 F _inst_5 (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) X) (CategoryTheory.Functor.obj.{u1, u1, u2, u2} C _inst_1 D _inst_2 F X))
+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u1, u2} D] (F : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 D _inst_2) [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Abelian.{u1, u2} D _inst_2] [_inst_5 : CategoryTheory.Functor.Additive.{u2, u2, u1, u1} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4) F] [_inst_6 : CategoryTheory.EnoughInjectives.{u1, u2} C _inst_1] [_inst_7 : CategoryTheory.Limits.PreservesFiniteLimits.{u1, u1, u2, u2} C _inst_1 D _inst_2 F] {X : C}, (CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X) -> (Quiver.Hom.{succ u1, u2} D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u2, u1} C _inst_1 D _inst_2 _inst_3 (CategoryTheory.InjectiveResolution.instHasInjectiveResolutionsHasZeroObjectPreadditiveHasZeroMorphismsToPreadditiveHasEqualizersHasImages_of_hasStrongEpiMonoFactorisationsInstHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3 _inst_6) _inst_4 F _inst_5 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) X) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) X))
+Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.right_derived_zero_to_self_app CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppₓ'. -/
 /-- Given `P : InjectiveResolution X`, a morphism `(F.right_derived 0).obj X ⟶ F.obj X` given
 `preserves_finite_limits F`. -/
 def rightDerivedZeroToSelfApp [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
@@ -225,6 +289,12 @@ def rightDerivedZeroToSelfApp [EnoughInjectives C] [PreservesFiniteLimits F] {X
         (asIso (kernel.lift _ _ (exact_of_map_injective_resolution F P).w)).inv
 #align category_theory.abelian.functor.right_derived_zero_to_self_app CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp
 
+/- warning: category_theory.abelian.functor.right_derived_zero_to_self_app_inv -> CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u1, u2} D] (F : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 D _inst_2) [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Abelian.{u1, u2} D _inst_2] [_inst_5 : CategoryTheory.Functor.Additive.{u2, u2, u1, u1} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4) F] [_inst_6 : CategoryTheory.EnoughInjectives.{u1, u2} C _inst_1] {X : C}, (CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X) -> (Quiver.Hom.{succ u1, u2} D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) X) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u2, u1} C _inst_1 D _inst_2 _inst_3 (CategoryTheory.InjectiveResolution.instHasInjectiveResolutionsHasZeroObjectPreadditiveHasZeroMorphismsToPreadditiveHasEqualizersHasImages_of_hasStrongEpiMonoFactorisationsInstHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3 _inst_6) _inst_4 F _inst_5 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) X))
+Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.right_derived_zero_to_self_app_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInvₓ'. -/
 /-- Given `P : InjectiveResolution X`, a morphism `F.obj X ⟶ (F.right_derived 0).obj X`. -/
 def rightDerivedZeroToSelfAppInv [EnoughInjectives C] {X : C} (P : InjectiveResolution X) :
     F.obj X ⟶ (F.rightDerived 0).obj X :=
@@ -237,6 +307,12 @@ def rightDerivedZeroToSelfAppInv [EnoughInjectives C] {X : C} (P : InjectiveReso
     (rightDerivedObjIso F 0 P).inv
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv
 
+/- warning: category_theory.abelian.functor.right_derived_zero_to_self_app_comp_inv -> CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp_comp_inv 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 category_theory.abelian.functor.right_derived_zero_to_self_app_comp_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp_comp_invₓ'. -/
 theorem rightDerivedZeroToSelfApp_comp_inv [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
     (P : InjectiveResolution X) :
     right_derived_zero_to_self_app F P ≫ right_derived_zero_to_self_app_inv F P = 𝟙 _ :=
@@ -253,6 +329,12 @@ theorem rightDerivedZeroToSelfApp_comp_inv [EnoughInjectives C] [PreservesFinite
   convert category.id_comp (cokernel.π _)
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_comp_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp_comp_inv
 
+/- warning: category_theory.abelian.functor.right_derived_zero_to_self_app_inv_comp -> CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv_comp 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 category_theory.abelian.functor.right_derived_zero_to_self_app_inv_comp CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv_compₓ'. -/
 theorem rightDerivedZeroToSelfAppInv_comp [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
     (P : InjectiveResolution X) :
     right_derived_zero_to_self_app_inv F P ≫ right_derived_zero_to_self_app F P = 𝟙 _ :=
@@ -267,6 +349,12 @@ theorem rightDerivedZeroToSelfAppInv_comp [EnoughInjectives C] [PreservesFiniteL
   simp
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_inv_comp CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv_comp
 
+/- warning: category_theory.abelian.functor.right_derived_zero_to_self_app_iso -> CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppIso is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u1, u2} D] (F : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 D _inst_2) [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Abelian.{u1, u2} D _inst_2] [_inst_5 : CategoryTheory.Functor.Additive.{u2, u2, u1, u1} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4) F] [_inst_6 : CategoryTheory.EnoughInjectives.{u1, u2} C _inst_1] [_inst_7 : CategoryTheory.Limits.PreservesFiniteLimits.{u1, u1, u2, u2} C _inst_1 D _inst_2 F] {X : C}, (CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X) -> (CategoryTheory.Iso.{u1, u2} D _inst_2 (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u2, u1} C _inst_1 D _inst_2 _inst_3 (CategoryTheory.InjectiveResolution.instHasInjectiveResolutionsHasZeroObjectPreadditiveHasZeroMorphismsToPreadditiveHasEqualizersHasImages_of_hasStrongEpiMonoFactorisationsInstHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3 _inst_6) _inst_4 F _inst_5 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) X) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) X))
+Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.right_derived_zero_to_self_app_iso CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppIsoₓ'. -/
 /-- Given `P : InjectiveResolution X`, the isomorphism `(F.right_derived 0).obj X ≅ F.obj X` if
 `preserves_finite_limits F`. -/
 def rightDerivedZeroToSelfAppIso [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
@@ -278,9 +366,15 @@ def rightDerivedZeroToSelfAppIso [EnoughInjectives C] [PreservesFiniteLimits F]
   inv_hom_id' := right_derived_zero_to_self_app_inv_comp _ P
 #align category_theory.abelian.functor.right_derived_zero_to_self_app_iso CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppIso
 
+/- warning: category_theory.abelian.functor.right_derived_zero_to_self_natural -> CategoryTheory.Abelian.Functor.rightDerivedZeroToSelf_natural is a dubious translation:
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+but is expected to have type
+  forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {D : Type.{u2}} [_inst_2 : CategoryTheory.Category.{u1, u2} D] (F : CategoryTheory.Functor.{u1, u1, u2, u2} C _inst_1 D _inst_2) [_inst_3 : CategoryTheory.Abelian.{u1, u2} C _inst_1] [_inst_4 : CategoryTheory.Abelian.{u1, u2} D _inst_2] [_inst_5 : CategoryTheory.Functor.Additive.{u2, u2, u1, u1} C D _inst_1 _inst_2 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Abelian.toPreadditive.{u1, u2} D _inst_2 _inst_4) F] [_inst_6 : CategoryTheory.EnoughInjectives.{u1, u2} C _inst_1] {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y) (P : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) X) (Q : CategoryTheory.InjectiveResolution.{u1, u2} C _inst_1 (CategoryTheory.Abelian.hasZeroObject.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Preadditive.preadditiveHasZeroMorphisms.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_3)) (CategoryTheory.Abelian.hasEqualizers.{u1, u2} C _inst_1 _inst_3) (CategoryTheory.Limits.hasImages_of_hasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 (CategoryTheory.Abelian.instHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3)) Y), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) X) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u2, u1} C _inst_1 D _inst_2 _inst_3 (CategoryTheory.InjectiveResolution.instHasInjectiveResolutionsHasZeroObjectPreadditiveHasZeroMorphismsToPreadditiveHasEqualizersHasImages_of_hasStrongEpiMonoFactorisationsInstHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3 _inst_6) _inst_4 F _inst_5 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) Y)) (CategoryTheory.CategoryStruct.comp.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) X) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) Y) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u2, u1} C _inst_1 D _inst_2 _inst_3 (CategoryTheory.InjectiveResolution.instHasInjectiveResolutionsHasZeroObjectPreadditiveHasZeroMorphismsToPreadditiveHasEqualizersHasImages_of_hasStrongEpiMonoFactorisationsInstHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3 _inst_6) _inst_4 F _inst_5 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) Y) (Prefunctor.map.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) X Y f) (CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv.{u1, u2} C _inst_1 D _inst_2 F _inst_3 _inst_4 _inst_5 _inst_6 Y Q)) (CategoryTheory.CategoryStruct.comp.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 F) X) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u2, u1} C _inst_1 D _inst_2 _inst_3 (CategoryTheory.InjectiveResolution.instHasInjectiveResolutionsHasZeroObjectPreadditiveHasZeroMorphismsToPreadditiveHasEqualizersHasImages_of_hasStrongEpiMonoFactorisationsInstHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3 _inst_6) _inst_4 F _inst_5 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) X) (Prefunctor.obj.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u2, u1} C _inst_1 D _inst_2 _inst_3 (CategoryTheory.InjectiveResolution.instHasInjectiveResolutionsHasZeroObjectPreadditiveHasZeroMorphismsToPreadditiveHasEqualizersHasImages_of_hasStrongEpiMonoFactorisationsInstHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3 _inst_6) _inst_4 F _inst_5 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) Y) (CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv.{u1, u2} C _inst_1 D _inst_2 F _inst_3 _inst_4 _inst_5 _inst_6 X P) (Prefunctor.map.{succ u1, succ u1, u2, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} D (CategoryTheory.Category.toCategoryStruct.{u1, u2} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, u2} C _inst_1 D _inst_2 (CategoryTheory.Functor.rightDerived.{u1, u2, u2, u1} C _inst_1 D _inst_2 _inst_3 (CategoryTheory.InjectiveResolution.instHasInjectiveResolutionsHasZeroObjectPreadditiveHasZeroMorphismsToPreadditiveHasEqualizersHasImages_of_hasStrongEpiMonoFactorisationsInstHasStrongEpiMonoFactorisations.{u1, u2} C _inst_1 _inst_3 _inst_6) _inst_4 F _inst_5 (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))) X Y f))
+Case conversion may be inaccurate. Consider using '#align category_theory.abelian.functor.right_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.rightDerivedZeroToSelf_naturalₓ'. -/
 /-- Given `P : InjectiveResolution X` and `Q : InjectiveResolution Y` and a morphism `f : X ⟶ Y`,
 naturality of the square given by `right_derived_zero_to_self_natural`. -/
-theorem rightDerived_zero_to_self_natural [EnoughInjectives C] {X : C} {Y : C} (f : X ⟶ Y)
+theorem rightDerivedZeroToSelf_natural [EnoughInjectives C] {X : C} {Y : C} (f : X ⟶ Y)
     (P : InjectiveResolution X) (Q : InjectiveResolution Y) :
     F.map f ≫ right_derived_zero_to_self_app_inv F Q =
       right_derived_zero_to_self_app_inv F P ≫ (F.rightDerived 0).map f :=
@@ -299,8 +393,9 @@ theorem rightDerived_zero_to_self_natural [EnoughInjectives C] {X : C} {Y : C} (
     map_homological_complex_map_f, ← functor.map_comp,
     show f ≫ Q.ι.f 0 = P.ι.f 0 ≫ (InjectiveResolution.desc f Q P).f 0 from
       HomologicalComplex.congr_hom (InjectiveResolution.desc_commutes f Q P).symm 0]
-#align category_theory.abelian.functor.right_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.rightDerived_zero_to_self_natural
+#align category_theory.abelian.functor.right_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.rightDerivedZeroToSelf_natural
 
+#print CategoryTheory.Abelian.Functor.rightDerivedZeroIsoSelf /-
 /-- Given `preserves_finite_limits F`, the natural isomorphism `(F.right_derived 0) ≅ F`. -/
 def rightDerivedZeroIsoSelf [EnoughInjectives C] [PreservesFiniteLimits F] : F.rightDerived 0 ≅ F :=
   Iso.symm <|
@@ -308,6 +403,7 @@ def rightDerivedZeroIsoSelf [EnoughInjectives C] [PreservesFiniteLimits F] : F.r
       (fun X => (right_derived_zero_to_self_app_iso _ (InjectiveResolution.of X)).symm) fun X Y f =>
       right_derived_zero_to_self_natural _ _ _ _
 #align category_theory.abelian.functor.right_derived_zero_iso_self CategoryTheory.Abelian.Functor.rightDerivedZeroIsoSelf
+-/
 
 end CategoryTheory.Abelian.Functor

024a4231

bump to nightly-2023-04-20-00

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

d6678ca6

Diff

@@ -196,21 +196,21 @@ variable [Abelian C] [Abelian D] [Additive F]
 
 /-- If `preserves_finite_limits F` and `mono f`, then `exact (F.map f) (F.map g)` if
 `exact f g`. -/
-theorem preservesExactOfPreservesFiniteLimitsOfMono [PreservesFiniteLimits F] [Mono f]
+theorem preserves_exact_of_preservesFiniteLimits_of_mono [PreservesFiniteLimits F] [Mono f]
     (ex : Exact f g) : Exact (F.map f) (F.map g) :=
-  Abelian.exactOfIsKernel _ _ (by simp [← functor.map_comp, ex.w]) <|
+  Abelian.exact_of_is_kernel _ _ (by simp [← functor.map_comp, ex.w]) <|
     Limits.isLimitForkMapOfIsLimit' _ ex.w (Abelian.isLimitOfExactOfMono _ _ ex)
-#align category_theory.abelian.functor.preserves_exact_of_preserves_finite_limits_of_mono CategoryTheory.Abelian.Functor.preservesExactOfPreservesFiniteLimitsOfMono
+#align category_theory.abelian.functor.preserves_exact_of_preserves_finite_limits_of_mono CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteLimits_of_mono
 
-theorem exactOfMapInjectiveResolution (P : InjectiveResolution X) [PreservesFiniteLimits F] :
+theorem exact_of_map_injective_resolution (P : InjectiveResolution X) [PreservesFiniteLimits F] :
     Exact (F.map (P.ι.f 0))
       (((F.mapHomologicalComplex (ComplexShape.up ℕ)).obj P.cocomplex).dFrom 0) :=
-  Preadditive.exactOfIsoOfExact' (F.map (P.ι.f 0)) (F.map (P.cocomplex.d 0 1)) _ _ (Iso.refl _)
+  Preadditive.exact_of_iso_of_exact' (F.map (P.ι.f 0)) (F.map (P.cocomplex.d 0 1)) _ _ (Iso.refl _)
     (Iso.refl _)
     (HomologicalComplex.xNextIso ((F.mapHomologicalComplex _).obj P.cocomplex) rfl).symm (by simp)
     (by rw [iso.refl_hom, category.id_comp, iso.symm_hom, HomologicalComplex.dFrom_eq] <;> congr )
     (preserves_exact_of_preserves_finite_limits_of_mono _ P.exact₀)
-#align category_theory.abelian.functor.exact_of_map_injective_resolution CategoryTheory.Abelian.Functor.exactOfMapInjectiveResolution
+#align category_theory.abelian.functor.exact_of_map_injective_resolution CategoryTheory.Abelian.Functor.exact_of_map_injective_resolution
 
 /-- Given `P : InjectiveResolution X`, a morphism `(F.right_derived 0).obj X ⟶ F.obj X` given
 `preserves_finite_limits F`. -/

024a4231

bump to nightly-2023-04-18-00

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

7809aa1d

Diff

@@ -196,21 +196,21 @@ variable [Abelian C] [Abelian D] [Additive F]
 
 /-- If `preserves_finite_limits F` and `mono f`, then `exact (F.map f) (F.map g)` if
 `exact f g`. -/
-theorem preserves_exact_of_preservesFiniteLimits_of_mono [PreservesFiniteLimits F] [Mono f]
+theorem preservesExactOfPreservesFiniteLimitsOfMono [PreservesFiniteLimits F] [Mono f]
     (ex : Exact f g) : Exact (F.map f) (F.map g) :=
-  Abelian.exact_of_is_kernel _ _ (by simp [← functor.map_comp, ex.w]) <|
+  Abelian.exactOfIsKernel _ _ (by simp [← functor.map_comp, ex.w]) <|
     Limits.isLimitForkMapOfIsLimit' _ ex.w (Abelian.isLimitOfExactOfMono _ _ ex)
-#align category_theory.abelian.functor.preserves_exact_of_preserves_finite_limits_of_mono CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteLimits_of_mono
+#align category_theory.abelian.functor.preserves_exact_of_preserves_finite_limits_of_mono CategoryTheory.Abelian.Functor.preservesExactOfPreservesFiniteLimitsOfMono
 
-theorem exact_of_map_injective_resolution (P : InjectiveResolution X) [PreservesFiniteLimits F] :
+theorem exactOfMapInjectiveResolution (P : InjectiveResolution X) [PreservesFiniteLimits F] :
     Exact (F.map (P.ι.f 0))
       (((F.mapHomologicalComplex (ComplexShape.up ℕ)).obj P.cocomplex).dFrom 0) :=
-  Preadditive.exact_of_iso_of_exact' (F.map (P.ι.f 0)) (F.map (P.cocomplex.d 0 1)) _ _ (Iso.refl _)
+  Preadditive.exactOfIsoOfExact' (F.map (P.ι.f 0)) (F.map (P.cocomplex.d 0 1)) _ _ (Iso.refl _)
     (Iso.refl _)
     (HomologicalComplex.xNextIso ((F.mapHomologicalComplex _).obj P.cocomplex) rfl).symm (by simp)
     (by rw [iso.refl_hom, category.id_comp, iso.symm_hom, HomologicalComplex.dFrom_eq] <;> congr )
     (preserves_exact_of_preserves_finite_limits_of_mono _ P.exact₀)
-#align category_theory.abelian.functor.exact_of_map_injective_resolution CategoryTheory.Abelian.Functor.exact_of_map_injective_resolution
+#align category_theory.abelian.functor.exact_of_map_injective_resolution CategoryTheory.Abelian.Functor.exactOfMapInjectiveResolution
 
 /-- Given `P : InjectiveResolution X`, a morphism `(F.right_derived 0).obj X ⟶ F.obj X` given
 `preserves_finite_limits F`. -/

024a4231

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

024a4231

style: replace '.-/' by '. -/' (#11938)

Purely automatic replacement. If this is in any way controversial; I'm happy to just close this PR.

3556ded2

Diff

@@ -197,7 +197,8 @@ lemma NatTrans.rightDerivedToHomotopyCategory_comp {F G H : C ⥤ D} (α : F ⟶
       NatTrans.rightDerivedToHomotopyCategory α ≫
         NatTrans.rightDerivedToHomotopyCategory β := rfl
 
-/-- The natural transformation between right-derived functors induced by a natural transformation.-/
+/-- The natural transformation between right-derived functors
+induced by a natural transformation. -/
 noncomputable def NatTrans.rightDerived
     {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶ G) (n : ℕ) :
     F.rightDerived n ⟶ G.rightDerived n :=

024a4231

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

@@ -30,8 +30,6 @@ natural transformations between the original additive functors,
 and show how to compute the components.
 
 ## Main results
-* `Functor.rightDerivedObj_injective_zero`: the `0`-th derived functor of `F` on
-  an injective object `X` is isomorphic to `F.obj X`.
 * `Functor.isZero_rightDerived_obj_injective_succ`: injective objects have no higher
   right derived functor.
 * `NatTrans.rightDerived`: the natural isomorphism between right derived functors
@@ -336,7 +334,7 @@ instance (X : C) : IsIso (F.toRightDerivedZero.app X) := by
   dsimp [Functor.toRightDerivedZero]
   infer_instance
 
-instance [PreservesFiniteLimits F] : IsIso F.toRightDerivedZero :=
+instance : IsIso F.toRightDerivedZero :=
   NatIso.isIso_of_isIso_app _
 
 namespace Functor

024a4231

refactor: use the new homology API for right derived functors (#8593)

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

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

547a8415

Diff

@@ -1,13 +1,11 @@
 /-
 Copyright (c) 2022 Jujian Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Jujian Zhang, Scott Morrison
+Authors: Jujian Zhang, Scott Morrison, Joël Riou
 -/
 import Mathlib.CategoryTheory.Abelian.InjectiveResolution
 import Mathlib.Algebra.Homology.Additive
-import Mathlib.CategoryTheory.Limits.Constructions.EpiMono
 import Mathlib.CategoryTheory.Abelian.Homology
-import Mathlib.CategoryTheory.Abelian.Exact
 
 #align_import category_theory.abelian.right_derived from "leanprover-community/mathlib"@"024a4231815538ac739f52d08dd20a55da0d6b23"
 
@@ -17,315 +15,360 @@ import Mathlib.CategoryTheory.Abelian.Exact
 We define the right-derived functors `F.rightDerived n : C ⥤ D` for any additive functor `F`
 out of a category with injective resolutions.
 
-The definition is
-```
-injectiveResolutions C ⋙ F.mapHomotopyCategory _ ⋙ HomotopyCategory.homologyFunctor D _ n
-```
-that is, we pick an injective resolution (thought of as an object of the homotopy category),
-we apply `F` objectwise, and compute `n`-th homology.
+We first define a functor
+`F.rightDerivedToHomotopyCategory : C ⥤ HomotopyCategory D (ComplexShape.up ℕ)` which is
+`injectiveResolutions C ⋙ F.mapHomotopyCategory _`. We show that if `X : C` and
+`I : InjectiveResolution X`, then `F.rightDerivedToHomotopyCategory.obj X` identifies
+to the image in the homotopy category of the functor `F` applied objectwise to `I.cocomplex`
+(this isomorphism is `I.isoRightDerivedToHomotopyCategoryObj F`).
 
-We show that these right-derived functors can be calculated
-on objects using any choice of injective resolution,
-and on morphisms by any choice of lift to a cochain map between chosen injective resolutions.
+Then, the right-derived functors `F.rightDerived n : C ⥤ D` are obtained by composing
+`F.rightDerivedToHomotopyCategory` with the homology functors on the homotopy category.
 
 Similarly we define natural transformations between right-derived functors coming from
 natural transformations between the original additive functors,
 and show how to compute the components.
 
 ## Main results
-* `CategoryTheory.Functor.rightDerivedObj_injective_zero`: the `0`-th derived functor of `F` on
+* `Functor.rightDerivedObj_injective_zero`: the `0`-th derived functor of `F` on
   an injective object `X` is isomorphic to `F.obj X`.
-* `CategoryTheory.Functor.rightDerivedObj_injective_succ`: injective objects have no higher
+* `Functor.isZero_rightDerived_obj_injective_succ`: injective objects have no higher
   right derived functor.
-* `CategoryTheory.NatTrans.rightDerived`: the natural isomorphism between right derived functors
+* `NatTrans.rightDerived`: the natural isomorphism between right derived functors
   induced by natural transformation.
-
-Now, we assume `PreservesFiniteLimits F`, then
-* `CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteLimits_of_mono`: if `f` is
-  mono and `Exact f g`, then `Exact (F.map f) (F.map g)`.
-* `CategoryTheory.Abelian.Functor.rightDerivedZeroIsoSelf`: if there are enough injectives,
-  then there is a natural isomorphism `(F.rightDerived 0) ≅ F`.
+* `Functor.toRightDerivedZero`: the natural transformation `F ⟶ F.rightDerived 0`,
+  which is an isomorphism when `F` is left exact (i.e. preserves finite limits),
+  see also `Functor.rightDerivedZeroIsoSelf`.
 -/
 
-
-noncomputable section
-
-open CategoryTheory
-
-open CategoryTheory.Limits
+universe v u
 
 namespace CategoryTheory
 
-universe v u
+open Category Limits
 
 variable {C : Type u} [Category.{v} C] {D : Type*} [Category D]
+  [Abelian C] [HasInjectiveResolutions C] [Abelian D]
+
+/-- When `F : C ⥤ D` is an additive functor, this is
+the functor `C ⥤ HomotopyCategory D (ComplexShape.up ℕ)` which
+sends `X : C` to `F` applied to an injective resolution of `X`. -/
+noncomputable def Functor.rightDerivedToHomotopyCategory (F : C ⥤ D) [F.Additive] :
+    C ⥤ HomotopyCategory D (ComplexShape.up ℕ) :=
+  injectiveResolutions C ⋙ F.mapHomotopyCategory _
+
+/-- If `I : InjectiveResolution Z` and `F : C ⥤ D` is an additive functor, this is
+an isomorphism between `F.rightDerivedToHomotopyCategory.obj X` and the complex
+obtained by applying `F` to `I.cocomplex`. -/
+noncomputable def InjectiveResolution.isoRightDerivedToHomotopyCategoryObj {X : C}
+    (I : InjectiveResolution X) (F : C ⥤ D) [F.Additive] :
+    F.rightDerivedToHomotopyCategory.obj X ≅
+      (F.mapHomologicalComplex _ ⋙ HomotopyCategory.quotient _ _).obj I.cocomplex :=
+  (F.mapHomotopyCategory _).mapIso I.iso ≪≫
+    (F.mapHomotopyCategoryFactors _).app I.cocomplex
+
+@[reassoc]
+lemma InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_hom_naturality
+    {X Y : C} (f : X ⟶ Y) (I : InjectiveResolution X) (J : InjectiveResolution Y)
+    (φ : I.cocomplex ⟶ J.cocomplex) (comm : I.ι.f 0 ≫ φ.f 0 = f ≫ J.ι.f 0)
+    (F : C ⥤ D) [F.Additive] :
+    F.rightDerivedToHomotopyCategory.map f ≫ (J.isoRightDerivedToHomotopyCategoryObj F).hom =
+      (I.isoRightDerivedToHomotopyCategoryObj F).hom ≫
+        (F.mapHomologicalComplex _ ⋙ HomotopyCategory.quotient _ _).map φ := by
+  dsimp [Functor.rightDerivedToHomotopyCategory, isoRightDerivedToHomotopyCategoryObj]
+  rw [← Functor.map_comp_assoc, iso_hom_naturality f I J φ comm, Functor.map_comp,
+    assoc, assoc]
+  erw [(F.mapHomotopyCategoryFactors (ComplexShape.up ℕ)).hom.naturality]
+  rfl
 
-variable [Abelian C] [HasInjectiveResolutions C] [Abelian D]
+@[reassoc]
+lemma InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_inv_naturality
+    {X Y : C} (f : X ⟶ Y) (I : InjectiveResolution X) (J : InjectiveResolution Y)
+    (φ : I.cocomplex ⟶ J.cocomplex) (comm : I.ι.f 0 ≫ φ.f 0 = f ≫ J.ι.f 0)
+    (F : C ⥤ D) [F.Additive] :
+    (I.isoRightDerivedToHomotopyCategoryObj F).inv ≫ F.rightDerivedToHomotopyCategory.map f =
+      (F.mapHomologicalComplex _ ⋙ HomotopyCategory.quotient _ _).map φ ≫
+        (J.isoRightDerivedToHomotopyCategoryObj F).inv := by
+    rw [← cancel_epi (I.isoRightDerivedToHomotopyCategoryObj F).hom, Iso.hom_inv_id_assoc]
+    dsimp
+    rw [← isoRightDerivedToHomotopyCategoryObj_hom_naturality_assoc f I J φ comm F,
+      Iso.hom_inv_id, comp_id]
 
 /-- The right derived functors of an additive functor. -/
-def Functor.rightDerived (F : C ⥤ D) [F.Additive] (n : ℕ) : C ⥤ D :=
-  injectiveResolutions C ⋙ F.mapHomotopyCategory _ ⋙ HomotopyCategory.homology'Functor D _ n
+noncomputable def Functor.rightDerived (F : C ⥤ D) [F.Additive] (n : ℕ) : C ⥤ D :=
+  F.rightDerivedToHomotopyCategory ⋙ HomotopyCategory.homologyFunctor D _ n
 #align category_theory.functor.right_derived CategoryTheory.Functor.rightDerived
 
 /-- We can compute a right derived functor using a chosen injective resolution. -/
-@[simps!]
-def Functor.rightDerivedObjIso (F : C ⥤ D) [F.Additive] (n : ℕ) {X : C}
-    (P : InjectiveResolution X) :
+noncomputable def InjectiveResolution.isoRightDerivedObj {X : C} (I : InjectiveResolution X)
+    (F : C ⥤ D) [F.Additive] (n : ℕ) :
     (F.rightDerived n).obj X ≅
-      (homology'Functor D _ n).obj ((F.mapHomologicalComplex _).obj P.cocomplex) :=
-  (HomotopyCategory.homology'Functor D _ n).mapIso
-      (HomotopyCategory.isoOfHomotopyEquiv
-        (F.mapHomotopyEquiv (InjectiveResolution.homotopyEquiv _ P))) ≪≫
-    (HomotopyCategory.homology'Factors D _ n).app _
-#align category_theory.functor.right_derived_obj_iso CategoryTheory.Functor.rightDerivedObjIso
-
-/-- The 0-th derived functor of `F` on an injective object `X` is just `F.obj X`. -/
-@[simps!]
-def Functor.rightDerivedObjInjectiveZero (F : C ⥤ D) [F.Additive] (X : C) [Injective X] :
-    (F.rightDerived 0).obj X ≅ F.obj X :=
-  F.rightDerivedObjIso 0 (InjectiveResolution.self X) ≪≫
-    (homology'Functor _ _ _).mapIso
-      ((HomologicalComplex.singleMapHomologicalComplex F (ComplexShape.up ℕ) 0).app X) ≪≫
-      (CochainComplex.homologyFunctor0Single₀ D).app (F.obj X)
-#align category_theory.functor.right_derived_obj_injective_zero CategoryTheory.Functor.rightDerivedObjInjectiveZero
-
-open ZeroObject
+      (HomologicalComplex.homologyFunctor D _ n).obj
+        ((F.mapHomologicalComplex _).obj I.cocomplex) :=
+  (HomotopyCategory.homologyFunctor D _ n).mapIso
+    (I.isoRightDerivedToHomotopyCategoryObj F) ≪≫
+    (HomotopyCategory.homologyFunctorFactors D (ComplexShape.up ℕ) n).app _
+
+@[reassoc]
+lemma InjectiveResolution.isoRightDerivedObj_hom_naturality
+    {X Y : C} (f : X ⟶ Y) (I : InjectiveResolution X) (J : InjectiveResolution Y)
+    (φ : I.cocomplex ⟶ J.cocomplex) (comm : I.ι.f 0 ≫ φ.f 0 = f ≫ J.ι.f 0)
+    (F : C ⥤ D) [F.Additive] (n : ℕ) :
+    (F.rightDerived n).map f ≫ (J.isoRightDerivedObj F n).hom =
+      (I.isoRightDerivedObj F n).hom ≫
+        (F.mapHomologicalComplex _ ⋙ HomologicalComplex.homologyFunctor _ _ n).map φ := by
+  dsimp [isoRightDerivedObj, Functor.rightDerived]
+  rw [assoc, ← Functor.map_comp_assoc,
+    InjectiveResolution.isoRightDerivedToHomotopyCategoryObj_hom_naturality f I J φ comm F,
+    Functor.map_comp, assoc]
+  erw [(HomotopyCategory.homologyFunctorFactors D (ComplexShape.up ℕ) n).hom.naturality]
+  rfl
+
+@[reassoc]
+lemma InjectiveResolution.isoRightDerivedObj_inv_naturality
+    {X Y : C} (f : X ⟶ Y) (I : InjectiveResolution X) (J : InjectiveResolution Y)
+    (φ : I.cocomplex ⟶ J.cocomplex) (comm : I.ι.f 0 ≫ φ.f 0 = f ≫ J.ι.f 0)
+    (F : C ⥤ D) [F.Additive] (n : ℕ) :
+    (I.isoRightDerivedObj F n).inv ≫ (F.rightDerived n).map f =
+        (F.mapHomologicalComplex _ ⋙ HomologicalComplex.homologyFunctor _ _ n).map φ ≫
+          (J.isoRightDerivedObj F n).inv := by
+  rw [← cancel_mono (J.isoRightDerivedObj F n).hom, assoc, assoc,
+    InjectiveResolution.isoRightDerivedObj_hom_naturality f I J φ comm F n,
+    Iso.inv_hom_id_assoc, Iso.inv_hom_id, comp_id]
 
 /-- The higher derived functors vanish on injective objects. -/
-@[simps! inv]
-def Functor.rightDerivedObjInjectiveSucc (F : C ⥤ D) [F.Additive] (n : ℕ) (X : C) [Injective X] :
-    (F.rightDerived (n + 1)).obj X ≅ 0 :=
-  F.rightDerivedObjIso (n + 1) (InjectiveResolution.self X) ≪≫
-    (homology'Functor _ _ _).mapIso
-      ((HomologicalComplex.singleMapHomologicalComplex F (ComplexShape.up ℕ) _).app X) ≪≫
-      (CochainComplex.homology'FunctorSuccSingle₀ D n).app (F.obj X) ≪≫ (Functor.zero_obj _).isoZero
-#align category_theory.functor.right_derived_obj_injective_succ CategoryTheory.Functor.rightDerivedObjInjectiveSucc
+lemma Functor.isZero_rightDerived_obj_injective_succ
+    (F : C ⥤ D) [F.Additive] (n : ℕ) (X : C) [Injective X] :
+    IsZero ((F.rightDerived (n+1)).obj X) := by
+  refine IsZero.of_iso ?_ ((InjectiveResolution.self X).isoRightDerivedObj F (n + 1))
+  erw [← HomologicalComplex.exactAt_iff_isZero_homology]
+  exact ShortComplex.exact_of_isZero_X₂ _ (F.map_isZero (by apply isZero_zero))
 
 /-- We can compute a right derived functor on a morphism using a descent of that morphism
 to a cochain map between chosen injective resolutions.
 -/
-theorem Functor.rightDerived_map_eq (F : C ⥤ D) [F.Additive] (n : ℕ) {X Y : C} (f : Y ⟶ X)
-    {P : InjectiveResolution X} {Q : InjectiveResolution Y} (g : Q.cocomplex ⟶ P.cocomplex)
-    (w : Q.ι ≫ g = (CochainComplex.single₀ C).map f ≫ P.ι) :
+theorem Functor.rightDerived_map_eq (F : C ⥤ D) [F.Additive] (n : ℕ) {X Y : C} (f : X ⟶ Y)
+    {P : InjectiveResolution X} {Q : InjectiveResolution Y} (g : P.cocomplex ⟶ Q.cocomplex)
+    (w : P.ι ≫ g = (CochainComplex.single₀ C).map f ≫ Q.ι) :
     (F.rightDerived n).map f =
-      (F.rightDerivedObjIso n Q).hom ≫
-        (homology'Functor D _ n).map ((F.mapHomologicalComplex _).map g) ≫
-          (F.rightDerivedObjIso n P).inv := by
-  dsimp only [Functor.rightDerived, Functor.rightDerivedObjIso]
-  dsimp
-  simp only [Category.comp_id, Category.id_comp]
-  rw [← homology'Functor_map, HomotopyCategory.homology'Functor_map_factors]
-  simp only [← Functor.map_comp]
-  congr 1
-  apply HomotopyCategory.eq_of_homotopy
-  apply Functor.mapHomotopy
-  apply InjectiveResolution.descHomotopy f
-  · simp
-  · simp only [InjectiveResolution.homotopyEquiv_hom_ι_assoc]
-    rw [← Category.assoc, w, Category.assoc]
-    simp only [InjectiveResolution.homotopyEquiv_inv_ι]
+      (P.isoRightDerivedObj F n).hom ≫
+        (F.mapHomologicalComplex _ ⋙ HomologicalComplex.homologyFunctor _ _ n).map g ≫
+          (Q.isoRightDerivedObj F n).inv := by
+  rw [← cancel_mono (Q.isoRightDerivedObj F n).hom,
+    InjectiveResolution.isoRightDerivedObj_hom_naturality f P Q g _ F n,
+    assoc, assoc, Iso.inv_hom_id, comp_id]
+  rw [← HomologicalComplex.comp_f, w, HomologicalComplex.comp_f,
+    CochainComplex.single₀_map_f_zero]
 #align category_theory.functor.right_derived_map_eq CategoryTheory.Functor.rightDerived_map_eq
 
+/-- The natural transformation
+`F.rightDerivedToHomotopyCategory ⟶ G.rightDerivedToHomotopyCategory` induced by
+a natural transformation `F ⟶ G` between additive functors. -/
+noncomputable def NatTrans.rightDerivedToHomotopyCategory
+    {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶ G) :
+    F.rightDerivedToHomotopyCategory ⟶ G.rightDerivedToHomotopyCategory :=
+  whiskerLeft _ (NatTrans.mapHomotopyCategory α (ComplexShape.up ℕ))
+
+lemma InjectiveResolution.rightDerivedToHomotopyCategory_app_eq
+    {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶ G) {X : C} (P : InjectiveResolution X) :
+    (NatTrans.rightDerivedToHomotopyCategory α).app X =
+      (P.isoRightDerivedToHomotopyCategoryObj F).hom ≫
+        (HomotopyCategory.quotient _ _).map
+          ((NatTrans.mapHomologicalComplex α _).app P.cocomplex) ≫
+          (P.isoRightDerivedToHomotopyCategoryObj G).inv := by
+  rw [← cancel_mono (P.isoRightDerivedToHomotopyCategoryObj G).hom, assoc, assoc,
+      Iso.inv_hom_id, comp_id]
+  dsimp [isoRightDerivedToHomotopyCategoryObj, Functor.mapHomotopyCategoryFactors,
+    NatTrans.rightDerivedToHomotopyCategory]
+  rw [assoc]
+  erw [id_comp, comp_id]
+  obtain ⟨β, hβ⟩ := (HomotopyCategory.quotient _ _).map_surjective (iso P).hom
+  rw [← hβ]
+  dsimp
+  simp only [← Functor.map_comp, NatTrans.mapHomologicalComplex_naturality]
+  rfl
+
+@[simp]
+lemma NatTrans.rightDerivedToHomotopyCategory_id (F : C ⥤ D) [F.Additive] :
+    NatTrans.rightDerivedToHomotopyCategory (𝟙 F) = 𝟙 _ := rfl
+
+@[simp, reassoc]
+lemma NatTrans.rightDerivedToHomotopyCategory_comp {F G H : C ⥤ D} (α : F ⟶ G) (β : G ⟶ H)
+    [F.Additive] [G.Additive] [H.Additive] :
+    NatTrans.rightDerivedToHomotopyCategory (α ≫ β) =
+      NatTrans.rightDerivedToHomotopyCategory α ≫
+        NatTrans.rightDerivedToHomotopyCategory β := rfl
+
 /-- The natural transformation between right-derived functors induced by a natural transformation.-/
-@[simps!]
-def NatTrans.rightDerived {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶ G) (n : ℕ) :
+noncomputable def NatTrans.rightDerived
+    {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶ G) (n : ℕ) :
     F.rightDerived n ⟶ G.rightDerived n :=
-  whiskerLeft (injectiveResolutions C)
-    (whiskerRight (NatTrans.mapHomotopyCategory α _) (HomotopyCategory.homology'Functor D _ n))
+  whiskerRight (NatTrans.rightDerivedToHomotopyCategory α) _
 #align category_theory.nat_trans.right_derived CategoryTheory.NatTrans.rightDerived
 
 @[simp]
 theorem NatTrans.rightDerived_id (F : C ⥤ D) [F.Additive] (n : ℕ) :
     NatTrans.rightDerived (𝟙 F) n = 𝟙 (F.rightDerived n) := by
-  simp [NatTrans.rightDerived]
+  dsimp only [rightDerived]
+  simp only [rightDerivedToHomotopyCategory_id, whiskerRight_id']
   rfl
 #align category_theory.nat_trans.right_derived_id CategoryTheory.NatTrans.rightDerived_id
 
-@[simp, nolint simpNF]
+@[simp, reassoc]
 theorem NatTrans.rightDerived_comp {F G H : C ⥤ D} [F.Additive] [G.Additive] [H.Additive]
     (α : F ⟶ G) (β : G ⟶ H) (n : ℕ) :
     NatTrans.rightDerived (α ≫ β) n = NatTrans.rightDerived α n ≫ NatTrans.rightDerived β n := by
   simp [NatTrans.rightDerived]
 #align category_theory.nat_trans.right_derived_comp CategoryTheory.NatTrans.rightDerived_comp
 
+namespace InjectiveResolution
+
 /-- A component of the natural transformation between right-derived functors can be computed
-using a chosen injective resolution.
--/
-theorem NatTrans.rightDerived_eq {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶ G) (n : ℕ) {X : C}
-    (P : InjectiveResolution X) :
-    (NatTrans.rightDerived α n).app X =
-      (F.rightDerivedObjIso n P).hom ≫
-        (homology'Functor D _ n).map ((NatTrans.mapHomologicalComplex α _).app P.cocomplex) ≫
-          (G.rightDerivedObjIso n P).inv := by
-  symm
-  dsimp [NatTrans.rightDerived, Functor.rightDerivedObjIso]
-  simp only [Category.comp_id, Category.id_comp]
-  rw [← homology'Functor_map, HomotopyCategory.homology'Functor_map_factors]
-  simp only [← Functor.map_comp]
-  congr 1
-  apply HomotopyCategory.eq_of_homotopy
-  simp only [NatTrans.mapHomologicalComplex_naturality_assoc, ← Functor.map_comp]
-  apply Homotopy.compLeftId
-  rw [← Functor.map_id]
-  apply Functor.mapHomotopy
-  apply HomotopyEquiv.homotopyHomInvId
-#align category_theory.nat_trans.right_derived_eq CategoryTheory.NatTrans.rightDerived_eq
+using a chosen injective resolution. -/
+lemma rightDerived_app_eq
+    {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶ G) {X : C} (P : InjectiveResolution X)
+    (n : ℕ) : (NatTrans.rightDerived α n).app X =
+      (P.isoRightDerivedObj F n).hom ≫
+        (HomologicalComplex.homologyFunctor D (ComplexShape.up ℕ) n).map
+        ((NatTrans.mapHomologicalComplex α _).app P.cocomplex) ≫
+        (P.isoRightDerivedObj G n).inv := by
+  dsimp [NatTrans.rightDerived, isoRightDerivedObj]
+  rw [InjectiveResolution.rightDerivedToHomotopyCategory_app_eq α P,
+    Functor.map_comp, Functor.map_comp, assoc]
+  erw [← (HomotopyCategory.homologyFunctorFactors D (ComplexShape.up ℕ) n).hom.naturality_assoc
+    ((NatTrans.mapHomologicalComplex α (ComplexShape.up ℕ)).app P.cocomplex)]
+  simp only [Functor.comp_map, Iso.hom_inv_id_app_assoc]
+
+/-- If `P : InjectiveResolution X` and `F` is an additive functor, this is
+the canonical morphism from `F.obj X` to the cycles in degree `0` of
+`(F.mapHomologicalComplex _).obj P.cocomplex`. -/
+noncomputable def toRightDerivedZero' {X : C}
+    (P : InjectiveResolution X) (F : C ⥤ D) [F.Additive] :
+    F.obj X ⟶ ((F.mapHomologicalComplex _).obj P.cocomplex).cycles 0 :=
+  HomologicalComplex.liftCycles _ (F.map (P.ι.f 0)) 1 (by simp) (by
+    dsimp
+    rw [← F.map_comp, HomologicalComplex.Hom.comm, HomologicalComplex.single_obj_d,
+      zero_comp, F.map_zero])
+
+@[reassoc (attr := simp)]
+lemma toRightDerivedZero'_comp_iCycles {X : C}
+    (P : InjectiveResolution X) (F : C ⥤ D) [F.Additive] :
+    P.toRightDerivedZero' F ≫
+      HomologicalComplex.iCycles _ _ = F.map (P.ι.f 0) := by
+  simp [toRightDerivedZero']
+
+@[reassoc]
+lemma toRightDerivedZero'_naturality {X Y : C} (f : X ⟶ Y)
+    (P : InjectiveResolution X) (Q : InjectiveResolution Y)
+    (φ : P.cocomplex ⟶ Q.cocomplex) (comm : P.ι.f 0 ≫ φ.f 0 = f ≫ Q.ι.f 0)
+    (F : C ⥤ D) [F.Additive] :
+    F.map f ≫ Q.toRightDerivedZero' F =
+      P.toRightDerivedZero' F ≫
+        HomologicalComplex.cyclesMap ((F.mapHomologicalComplex _).map φ) 0 := by
+  simp only [← cancel_mono (HomologicalComplex.iCycles _ _),
+    Functor.mapHomologicalComplex_obj_X, assoc, toRightDerivedZero'_comp_iCycles,
+    CochainComplex.single₀_obj_zero, HomologicalComplex.cyclesMap_i,
+    Functor.mapHomologicalComplex_map_f, toRightDerivedZero'_comp_iCycles_assoc,
+    ← F.map_comp, comm]
+
+instance (F : C ⥤ D) [F.Additive] (X : C) [Injective X] :
+    IsIso ((InjectiveResolution.self X).toRightDerivedZero' F) := by
+  dsimp [InjectiveResolution.toRightDerivedZero']
+  rw [CochainComplex.isIso_liftCycles_iff]
+  refine' ⟨ShortComplex.Splitting.exact _, inferInstance⟩
+  exact
+    { r := 𝟙 _
+      s := 0
+      s_g := (F.map_isZero (isZero_zero _)).eq_of_src _ _ }
+
+end InjectiveResolution
+
+/-- The natural transformation `F ⟶ F.rightDerived 0`. -/
+noncomputable def Functor.toRightDerivedZero (F : C ⥤ D) [F.Additive] :
+    F ⟶ F.rightDerived 0 where
+  app X := (injectiveResolution X).toRightDerivedZero' F ≫
+    (CochainComplex.isoHomologyπ₀ _).hom ≫
+      (HomotopyCategory.homologyFunctorFactors D (ComplexShape.up ℕ) 0).inv.app _
+  naturality {X Y} f := by
+    dsimp [rightDerived]
+    rw [assoc, assoc, InjectiveResolution.toRightDerivedZero'_naturality_assoc f
+      (injectiveResolution X) (injectiveResolution Y)
+      (InjectiveResolution.desc f _ _) (by simp),
+      ← HomologicalComplex.homologyπ_naturality_assoc]
+    erw [← NatTrans.naturality]
+    rfl
+
+lemma InjectiveResolution.toRightDerivedZero_eq
+    {X : C} (I : InjectiveResolution X) (F : C ⥤ D) [F.Additive] :
+    F.toRightDerivedZero.app X = I.toRightDerivedZero' F ≫
+      (CochainComplex.isoHomologyπ₀ _).hom ≫ (I.isoRightDerivedObj F 0).inv := by
+  dsimp [Functor.toRightDerivedZero, isoRightDerivedObj]
+  have h₁ := InjectiveResolution.toRightDerivedZero'_naturality
+    (𝟙 X) (injectiveResolution X) I (desc (𝟙 X) _ _) (by simp) F
+  simp only [Functor.map_id, id_comp] at h₁
+  have h₂ : (I.isoRightDerivedToHomotopyCategoryObj F).hom =
+    (F.mapHomologicalComplex _ ⋙ HomotopyCategory.quotient _ _).map (desc (𝟙 X) _ _) :=
+    comp_id _
+  rw [← cancel_mono ((HomotopyCategory.homologyFunctor _ _ 0).map
+      (I.isoRightDerivedToHomotopyCategoryObj F).hom),
+    assoc, assoc, assoc, assoc, assoc, ← Functor.map_comp,
+    Iso.inv_hom_id, Functor.map_id, comp_id,
+    reassoc_of% h₁, h₂, ← HomologicalComplex.homologyπ_naturality_assoc]
+  erw [← NatTrans.naturality]
+  rfl
 
-end CategoryTheory
+instance (F : C ⥤ D) [F.Additive] (X : C) [Injective X] :
+    IsIso (F.toRightDerivedZero.app X) := by
+  rw [(InjectiveResolution.self X).toRightDerivedZero_eq F]
+  infer_instance
 
 section
 
-universe w v u
-
-open CategoryTheory.Limits CategoryTheory CategoryTheory.Functor
-
-variable {C : Type u} [Category.{w} C] {D : Type u} [Category.{w} D]
-
-variable (F : C ⥤ D) {X Y Z : C} {f : X ⟶ Y} {g : Y ⟶ Z}
-
-namespace CategoryTheory.Abelian.Functor
-
-open CategoryTheory.Preadditive
-
-variable [Abelian C] [Abelian D] [Additive F]
-
-/-- If `PreservesFiniteLimits F` and `Mono f`, then `Exact (F.map f) (F.map g)` if
-`Exact f g`. -/
-theorem preserves_exact_of_preservesFiniteLimits_of_mono [PreservesFiniteLimits F] [Mono f]
-    (ex : Exact f g) : Exact (F.map f) (F.map g) :=
-  Abelian.exact_of_is_kernel _ _ (by simp [← Functor.map_comp, ex.w]) <|
-    Limits.isLimitForkMapOfIsLimit' _ ex.w (Abelian.isLimitOfExactOfMono _ _ ex)
-#align category_theory.abelian.functor.preserves_exact_of_preserves_finite_limits_of_mono CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteLimits_of_mono
-
-theorem exact_of_map_injectiveResolution (P : InjectiveResolution X) [PreservesFiniteLimits F] :
-    Exact (F.map (P.ι.f 0))
-      (((F.mapHomologicalComplex (ComplexShape.up ℕ)).obj P.cocomplex).dFrom 0) :=
-  Preadditive.exact_of_iso_of_exact' (F.map (P.ι.f 0)) (F.map (P.cocomplex.d 0 1)) _ _ (Iso.refl _)
-    (Iso.refl _)
-    (HomologicalComplex.xNextIso ((F.mapHomologicalComplex _).obj P.cocomplex) rfl).symm (by simp)
-    (by rw [Iso.refl_hom, Category.id_comp, Iso.symm_hom, HomologicalComplex.dFrom_eq] <;> congr)
-    (preserves_exact_of_preservesFiniteLimits_of_mono _ P.exact₀)
-#align category_theory.abelian.functor.exact_of_map_injective_resolution CategoryTheory.Abelian.Functor.exact_of_map_injectiveResolution
-
-/-- Given `P : InjectiveResolution X`, a morphism `(F.rightDerived 0).obj X ⟶ F.obj X` given
-`PreservesFiniteLimits F`. -/
-def rightDerivedZeroToSelfApp [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
-    (P : InjectiveResolution X) : (F.rightDerived 0).obj X ⟶ F.obj X :=
-  (rightDerivedObjIso F 0 P).hom ≫
-    (homology'IsoKernelDesc _ _ _).hom ≫
-      kernel.map _ (((F.mapHomologicalComplex (ComplexShape.up ℕ)).obj P.cocomplex).dFrom 0)
-      (cokernel.desc _ (𝟙 _) (by simp)) (𝟙 _)
-          (by
-            -- Porting note: was ext; simp
-            ext
-            dsimp
-            simp) ≫
-        -- Porting note: isIso_kernel_lift_of_exact_of_mono is no longer allowed as an
-        -- instance for reasons I am not privy to
-        have : IsIso <| kernel.lift _ _ (exact_of_map_injectiveResolution F P).w :=
-          isIso_kernel_lift_of_exact_of_mono _ _ (exact_of_map_injectiveResolution F P)
-        (asIso (kernel.lift _ _ (exact_of_map_injectiveResolution F P).w)).inv
-#align category_theory.abelian.functor.right_derived_zero_to_self_app CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp
-
-/-- Given `P : InjectiveResolution X`, a morphism `F.obj X ⟶ (F.rightDerived 0).obj X`. -/
-def rightDerivedZeroToSelfAppInv [EnoughInjectives C] {X : C} (P : InjectiveResolution X) :
-    F.obj X ⟶ (F.rightDerived 0).obj X :=
-  homology'.lift _ _ _ (F.map (P.ι.f 0) ≫ cokernel.π _)
-      (by
-        have : (ComplexShape.up ℕ).Rel 0 1 := rfl
-        rw [Category.assoc, cokernel.π_desc, HomologicalComplex.dFrom_eq _ this,
-          mapHomologicalComplex_obj_d, ← Category.assoc, ← Functor.map_comp]
-        simp only [InjectiveResolution.ι_f_zero_comp_complex_d, Functor.map_zero, zero_comp]) ≫
-    (rightDerivedObjIso F 0 P).inv
-#align category_theory.abelian.functor.right_derived_zero_to_self_app_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv
-
-theorem rightDerivedZeroToSelfApp_comp_inv [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
-    (P : InjectiveResolution X) :
-    rightDerivedZeroToSelfApp F P ≫ rightDerivedZeroToSelfAppInv F P = 𝟙 _ := by
-  dsimp [rightDerivedZeroToSelfApp, rightDerivedZeroToSelfAppInv]
-  rw [← Category.assoc, Iso.comp_inv_eq, Category.id_comp, Category.assoc, Category.assoc, ←
-    Iso.eq_inv_comp, Iso.inv_hom_id]
-  -- Porting note: broken ext
-  apply homology'.hom_to_ext
-  apply homology'.hom_from_ext
-  rw [Category.assoc, Category.assoc, homology'.lift_ι, Category.id_comp]
-  erw [homology'.π'_ι] -- Porting note: had to insist
-  rw [Category.assoc, ← Category.assoc _ _ (cokernel.π _),
-    Abelian.kernel.lift.inv, ← Category.assoc,
-    ← Category.assoc _ (kernel.ι _), Limits.kernel.lift_ι, Category.assoc, Category.assoc, ←
-    Category.assoc (homology'IsoKernelDesc _ _ _).hom _ _, ← homology'.ι, ← Category.assoc]
-  erw [homology'.π'_ι] -- Porting note: had to insist
-  rw [Category.assoc, ← Category.assoc (cokernel.π _)]
-  erw [cokernel.π_desc] -- Porting note: had to insist
-  rw [whisker_eq]
-  dsimp; simp -- Porting note: was convert
-  apply exact_of_map_injectiveResolution -- Porting note: Abelian.kernel.lift.inv
-  -- created an Exact goal which was no longer automatically discharged
-#align category_theory.abelian.functor.right_derived_zero_to_self_app_comp_inv CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfApp_comp_inv
-
-theorem rightDerivedZeroToSelfAppInv_comp [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
-    (P : InjectiveResolution X) :
-    rightDerivedZeroToSelfAppInv F P ≫ rightDerivedZeroToSelfApp F P = 𝟙 _ := by
-  dsimp [rightDerivedZeroToSelfApp, rightDerivedZeroToSelfAppInv]
-  rw [← Category.assoc _ (F.rightDerivedObjIso 0 P).hom,
-    Category.assoc _ _ (F.rightDerivedObjIso 0 P).hom, Iso.inv_hom_id, Category.comp_id, ←
-    Category.assoc, ← Category.assoc]
-  -- Porting note: this IsIso instance used to be filled automatically
-  apply (@IsIso.comp_inv_eq D _ _ _ _ _ ?_ _ _).mpr
-  · rw [Category.id_comp]
-    ext
-    simp only [Limits.kernel.lift_ι_assoc,
-      Category.assoc, Limits.kernel.lift_ι, homology'.lift]
-    rw [← Category.assoc, ← Category.assoc,
-      Category.assoc _ _ (homology'IsoKernelDesc _ _ _).hom]
-    simp
-    -- Porting note: this used to be an instance in ML3
-  · apply isIso_kernel_lift_of_exact_of_mono _ _ (exact_of_map_injectiveResolution F P)
-#align category_theory.abelian.functor.right_derived_zero_to_self_app_inv_comp CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppInv_comp
-
-/-- Given `P : InjectiveResolution X`, the isomorphism `(F.rightDerived 0).obj X ≅ F.obj X` if
-`PreservesFiniteLimits F`. -/
-def rightDerivedZeroToSelfAppIso [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
-    (P : InjectiveResolution X) : (F.rightDerived 0).obj X ≅ F.obj X where
-  hom := rightDerivedZeroToSelfApp _ P
-  inv := rightDerivedZeroToSelfAppInv _ P
-  hom_inv_id := rightDerivedZeroToSelfApp_comp_inv _ P
-  inv_hom_id := rightDerivedZeroToSelfAppInv_comp _ P
-#align category_theory.abelian.functor.right_derived_zero_to_self_app_iso CategoryTheory.Abelian.Functor.rightDerivedZeroToSelfAppIso
-
-/-- Given `P : InjectiveResolution X` and `Q : InjectiveResolution Y` and a morphism `f : X ⟶ Y`,
-naturality of the square given by `rightDerivedZeroToSelf_natural`. -/
-theorem rightDerivedZeroToSelf_natural [EnoughInjectives C] {X : C} {Y : C} (f : X ⟶ Y)
-    (P : InjectiveResolution X) (Q : InjectiveResolution Y) :
-    F.map f ≫ rightDerivedZeroToSelfAppInv F Q =
-      rightDerivedZeroToSelfAppInv F P ≫ (F.rightDerived 0).map f := by
-  dsimp [rightDerivedZeroToSelfAppInv]
-  simp only [CategoryTheory.Functor.map_id, Category.id_comp, ← Category.assoc]
-  rw [Iso.comp_inv_eq, rightDerived_map_eq F 0 f (InjectiveResolution.desc f Q P) (by simp),
-    Category.assoc, Category.assoc, Category.assoc, Category.assoc, Iso.inv_hom_id,
-    Category.comp_id, ← Category.assoc (F.rightDerivedObjIso 0 P).inv, Iso.inv_hom_id,
-    Category.id_comp]
-  dsimp only [homology'Functor_map]
-  -- Porting note: broken ext
-  apply homology'.hom_to_ext
-  rw [Category.assoc, homology'.lift_ι, Category.assoc]
-  erw [homology'.map_ι] -- Porting note: need to insist
-  rw [←Category.assoc (homology'.lift _ _ _ _ _) _ _]
-  erw [homology'.lift_ι] -- Porting note: need to insist
-  rw [Category.assoc]
-  erw [cokernel.π_desc] -- Porting note: need to insist
-  rw [← Category.assoc, ← Functor.map_comp, ← Category.assoc,
-    HomologicalComplex.Hom.sqFrom_left, mapHomologicalComplex_map_f, ← Functor.map_comp,
-    InjectiveResolution.desc_commutes_zero f Q P]
-  rfl -- Porting note: extra rfl
-#align category_theory.abelian.functor.right_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.rightDerivedZeroToSelf_natural
-
-/-- Given `PreservesFiniteLimits F`, the natural isomorphism `(F.rightDerived 0) ≅ F`. -/
-def rightDerivedZeroIsoSelf [EnoughInjectives C] [PreservesFiniteLimits F] : F.rightDerived 0 ≅ F :=
-  Iso.symm <|
-    NatIso.ofComponents
-      (fun X => (rightDerivedZeroToSelfAppIso _ (InjectiveResolution.of X)).symm) fun _ =>
-      rightDerivedZeroToSelf_natural _ _ _ _
-#align category_theory.abelian.functor.right_derived_zero_iso_self CategoryTheory.Abelian.Functor.rightDerivedZeroIsoSelf
-
-end CategoryTheory.Abelian.Functor
+variable (F : C ⥤ D) [F.Additive] [PreservesFiniteLimits F]
+
+instance {X : C} (P : InjectiveResolution X) :
+    IsIso (P.toRightDerivedZero' F) := by
+  dsimp [InjectiveResolution.toRightDerivedZero']
+  rw [CochainComplex.isIso_liftCycles_iff, ShortComplex.exact_and_mono_f_iff_f_is_kernel]
+  exact ⟨KernelFork.mapIsLimit _ (P.isLimitKernelFork) F⟩
+
+instance (X : C) : IsIso (F.toRightDerivedZero.app X) := by
+  dsimp [Functor.toRightDerivedZero]
+  infer_instance
+
+instance [PreservesFiniteLimits F] : IsIso F.toRightDerivedZero :=
+  NatIso.isIso_of_isIso_app _
+
+namespace Functor
+
+/-- The canonical isomorphism `F.rightDerived 0 ≅ F` when `F` is left exact
+(i.e. preserves finite limits). -/
+@[simps! inv]
+noncomputable def rightDerivedZeroIsoSelf : F.rightDerived 0 ≅ F :=
+  (asIso F.toRightDerivedZero).symm
+
+@[reassoc (attr := simp)]
+lemma rightDerivedZeroIsoSelf_hom_inv_id :
+    F.rightDerivedZeroIsoSelf.hom ≫ F.toRightDerivedZero = 𝟙 _ :=
+  F.rightDerivedZeroIsoSelf.hom_inv_id
+
+@[reassoc (attr := simp)]
+lemma rightDerivedZeroIsoSelf_inv_hom_id :
+    F.toRightDerivedZero ≫ F.rightDerivedZeroIsoSelf.hom = 𝟙 _ :=
+  F.rightDerivedZeroIsoSelf.inv_hom_id
+
+@[reassoc (attr := simp)]
+lemma rightDerivedZeroIsoSelf_hom_inv_id_app (X : C) :
+    F.rightDerivedZeroIsoSelf.hom.app X ≫ F.toRightDerivedZero.app X = 𝟙 _ :=
+  F.rightDerivedZeroIsoSelf.hom_inv_id_app X
+
+@[reassoc (attr := simp)]
+lemma rightDerivedZeroIsoSelf_inv_hom_id_app (X : C) :
+    F.toRightDerivedZero.app X ≫ F.rightDerivedZeroIsoSelf.hom.app X = 𝟙 _ :=
+  F.rightDerivedZeroIsoSelf.inv_hom_id_app X
+
+end Functor
+
+end
+
+end CategoryTheory

024a4231

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

@@ -84,7 +84,8 @@ def Functor.rightDerivedObjIso (F : C ⥤ D) [F.Additive] (n : ℕ) {X : C}
 def Functor.rightDerivedObjInjectiveZero (F : C ⥤ D) [F.Additive] (X : C) [Injective X] :
     (F.rightDerived 0).obj X ≅ F.obj X :=
   F.rightDerivedObjIso 0 (InjectiveResolution.self X) ≪≫
-    (homology'Functor _ _ _).mapIso ((CochainComplex.single₀MapHomologicalComplex F).app X) ≪≫
+    (homology'Functor _ _ _).mapIso
+      ((HomologicalComplex.singleMapHomologicalComplex F (ComplexShape.up ℕ) 0).app X) ≪≫
       (CochainComplex.homologyFunctor0Single₀ D).app (F.obj X)
 #align category_theory.functor.right_derived_obj_injective_zero CategoryTheory.Functor.rightDerivedObjInjectiveZero
 
@@ -95,7 +96,8 @@ open ZeroObject
 def Functor.rightDerivedObjInjectiveSucc (F : C ⥤ D) [F.Additive] (n : ℕ) (X : C) [Injective X] :
     (F.rightDerived (n + 1)).obj X ≅ 0 :=
   F.rightDerivedObjIso (n + 1) (InjectiveResolution.self X) ≪≫
-    (homology'Functor _ _ _).mapIso ((CochainComplex.single₀MapHomologicalComplex F).app X) ≪≫
+    (homology'Functor _ _ _).mapIso
+      ((HomologicalComplex.singleMapHomologicalComplex F (ComplexShape.up ℕ) _).app X) ≪≫
       (CochainComplex.homology'FunctorSuccSingle₀ D n).app (F.obj X) ≪≫ (Functor.zero_obj _).isoZero
 #align category_theory.functor.right_derived_obj_injective_succ CategoryTheory.Functor.rightDerivedObjInjectiveSucc
 
@@ -314,8 +316,7 @@ theorem rightDerivedZeroToSelf_natural [EnoughInjectives C] {X : C} {Y : C} (f :
   erw [cokernel.π_desc] -- Porting note: need to insist
   rw [← Category.assoc, ← Functor.map_comp, ← Category.assoc,
     HomologicalComplex.Hom.sqFrom_left, mapHomologicalComplex_map_f, ← Functor.map_comp,
-    show f ≫ Q.ι.f 0 = P.ι.f 0 ≫ (InjectiveResolution.desc f Q P).f 0 from
-      HomologicalComplex.congr_hom (InjectiveResolution.desc_commutes f Q P).symm 0]
+    InjectiveResolution.desc_commutes_zero f Q P]
   rfl -- Porting note: extra rfl
 #align category_theory.abelian.functor.right_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.rightDerivedZeroToSelf_natural

024a4231

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

@@ -64,7 +64,7 @@ variable [Abelian C] [HasInjectiveResolutions C] [Abelian D]
 
 /-- The right derived functors of an additive functor. -/
 def Functor.rightDerived (F : C ⥤ D) [F.Additive] (n : ℕ) : C ⥤ D :=
-  injectiveResolutions C ⋙ F.mapHomotopyCategory _ ⋙ HomotopyCategory.homologyFunctor D _ n
+  injectiveResolutions C ⋙ F.mapHomotopyCategory _ ⋙ HomotopyCategory.homology'Functor D _ n
 #align category_theory.functor.right_derived CategoryTheory.Functor.rightDerived
 
 /-- We can compute a right derived functor using a chosen injective resolution. -/
@@ -72,11 +72,11 @@ def Functor.rightDerived (F : C ⥤ D) [F.Additive] (n : ℕ) : C ⥤ D :=
 def Functor.rightDerivedObjIso (F : C ⥤ D) [F.Additive] (n : ℕ) {X : C}
     (P : InjectiveResolution X) :
     (F.rightDerived n).obj X ≅
-      (homologyFunctor D _ n).obj ((F.mapHomologicalComplex _).obj P.cocomplex) :=
-  (HomotopyCategory.homologyFunctor D _ n).mapIso
+      (homology'Functor D _ n).obj ((F.mapHomologicalComplex _).obj P.cocomplex) :=
+  (HomotopyCategory.homology'Functor D _ n).mapIso
       (HomotopyCategory.isoOfHomotopyEquiv
         (F.mapHomotopyEquiv (InjectiveResolution.homotopyEquiv _ P))) ≪≫
-    (HomotopyCategory.homologyFactors D _ n).app _
+    (HomotopyCategory.homology'Factors D _ n).app _
 #align category_theory.functor.right_derived_obj_iso CategoryTheory.Functor.rightDerivedObjIso
 
 /-- The 0-th derived functor of `F` on an injective object `X` is just `F.obj X`. -/
@@ -84,7 +84,7 @@ def Functor.rightDerivedObjIso (F : C ⥤ D) [F.Additive] (n : ℕ) {X : C}
 def Functor.rightDerivedObjInjectiveZero (F : C ⥤ D) [F.Additive] (X : C) [Injective X] :
     (F.rightDerived 0).obj X ≅ F.obj X :=
   F.rightDerivedObjIso 0 (InjectiveResolution.self X) ≪≫
-    (homologyFunctor _ _ _).mapIso ((CochainComplex.single₀MapHomologicalComplex F).app X) ≪≫
+    (homology'Functor _ _ _).mapIso ((CochainComplex.single₀MapHomologicalComplex F).app X) ≪≫
       (CochainComplex.homologyFunctor0Single₀ D).app (F.obj X)
 #align category_theory.functor.right_derived_obj_injective_zero CategoryTheory.Functor.rightDerivedObjInjectiveZero
 
@@ -95,8 +95,8 @@ open ZeroObject
 def Functor.rightDerivedObjInjectiveSucc (F : C ⥤ D) [F.Additive] (n : ℕ) (X : C) [Injective X] :
     (F.rightDerived (n + 1)).obj X ≅ 0 :=
   F.rightDerivedObjIso (n + 1) (InjectiveResolution.self X) ≪≫
-    (homologyFunctor _ _ _).mapIso ((CochainComplex.single₀MapHomologicalComplex F).app X) ≪≫
-      (CochainComplex.homologyFunctorSuccSingle₀ D n).app (F.obj X) ≪≫ (Functor.zero_obj _).isoZero
+    (homology'Functor _ _ _).mapIso ((CochainComplex.single₀MapHomologicalComplex F).app X) ≪≫
+      (CochainComplex.homology'FunctorSuccSingle₀ D n).app (F.obj X) ≪≫ (Functor.zero_obj _).isoZero
 #align category_theory.functor.right_derived_obj_injective_succ CategoryTheory.Functor.rightDerivedObjInjectiveSucc
 
 /-- We can compute a right derived functor on a morphism using a descent of that morphism
@@ -107,12 +107,12 @@ theorem Functor.rightDerived_map_eq (F : C ⥤ D) [F.Additive] (n : ℕ) {X Y :
     (w : Q.ι ≫ g = (CochainComplex.single₀ C).map f ≫ P.ι) :
     (F.rightDerived n).map f =
       (F.rightDerivedObjIso n Q).hom ≫
-        (homologyFunctor D _ n).map ((F.mapHomologicalComplex _).map g) ≫
+        (homology'Functor D _ n).map ((F.mapHomologicalComplex _).map g) ≫
           (F.rightDerivedObjIso n P).inv := by
   dsimp only [Functor.rightDerived, Functor.rightDerivedObjIso]
   dsimp
   simp only [Category.comp_id, Category.id_comp]
-  rw [← homologyFunctor_map, HomotopyCategory.homologyFunctor_map_factors]
+  rw [← homology'Functor_map, HomotopyCategory.homology'Functor_map_factors]
   simp only [← Functor.map_comp]
   congr 1
   apply HomotopyCategory.eq_of_homotopy
@@ -129,7 +129,7 @@ theorem Functor.rightDerived_map_eq (F : C ⥤ D) [F.Additive] (n : ℕ) {X Y :
 def NatTrans.rightDerived {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶ G) (n : ℕ) :
     F.rightDerived n ⟶ G.rightDerived n :=
   whiskerLeft (injectiveResolutions C)
-    (whiskerRight (NatTrans.mapHomotopyCategory α _) (HomotopyCategory.homologyFunctor D _ n))
+    (whiskerRight (NatTrans.mapHomotopyCategory α _) (HomotopyCategory.homology'Functor D _ n))
 #align category_theory.nat_trans.right_derived CategoryTheory.NatTrans.rightDerived
 
 @[simp]
@@ -153,12 +153,12 @@ theorem NatTrans.rightDerived_eq {F G : C ⥤ D} [F.Additive] [G.Additive] (α :
     (P : InjectiveResolution X) :
     (NatTrans.rightDerived α n).app X =
       (F.rightDerivedObjIso n P).hom ≫
-        (homologyFunctor D _ n).map ((NatTrans.mapHomologicalComplex α _).app P.cocomplex) ≫
+        (homology'Functor D _ n).map ((NatTrans.mapHomologicalComplex α _).app P.cocomplex) ≫
           (G.rightDerivedObjIso n P).inv := by
   symm
   dsimp [NatTrans.rightDerived, Functor.rightDerivedObjIso]
   simp only [Category.comp_id, Category.id_comp]
-  rw [← homologyFunctor_map, HomotopyCategory.homologyFunctor_map_factors]
+  rw [← homology'Functor_map, HomotopyCategory.homology'Functor_map_factors]
   simp only [← Functor.map_comp]
   congr 1
   apply HomotopyCategory.eq_of_homotopy
@@ -210,7 +210,7 @@ theorem exact_of_map_injectiveResolution (P : InjectiveResolution X) [PreservesF
 def rightDerivedZeroToSelfApp [EnoughInjectives C] [PreservesFiniteLimits F] {X : C}
     (P : InjectiveResolution X) : (F.rightDerived 0).obj X ⟶ F.obj X :=
   (rightDerivedObjIso F 0 P).hom ≫
-    (homologyIsoKernelDesc _ _ _).hom ≫
+    (homology'IsoKernelDesc _ _ _).hom ≫
       kernel.map _ (((F.mapHomologicalComplex (ComplexShape.up ℕ)).obj P.cocomplex).dFrom 0)
       (cokernel.desc _ (𝟙 _) (by simp)) (𝟙 _)
           (by
@@ -228,7 +228,7 @@ def rightDerivedZeroToSelfApp [EnoughInjectives C] [PreservesFiniteLimits F] {X
 /-- Given `P : InjectiveResolution X`, a morphism `F.obj X ⟶ (F.rightDerived 0).obj X`. -/
 def rightDerivedZeroToSelfAppInv [EnoughInjectives C] {X : C} (P : InjectiveResolution X) :
     F.obj X ⟶ (F.rightDerived 0).obj X :=
-  homology.lift _ _ _ (F.map (P.ι.f 0) ≫ cokernel.π _)
+  homology'.lift _ _ _ (F.map (P.ι.f 0) ≫ cokernel.π _)
       (by
         have : (ComplexShape.up ℕ).Rel 0 1 := rfl
         rw [Category.assoc, cokernel.π_desc, HomologicalComplex.dFrom_eq _ this,
@@ -244,15 +244,15 @@ theorem rightDerivedZeroToSelfApp_comp_inv [EnoughInjectives C] [PreservesFinite
   rw [← Category.assoc, Iso.comp_inv_eq, Category.id_comp, Category.assoc, Category.assoc, ←
     Iso.eq_inv_comp, Iso.inv_hom_id]
   -- Porting note: broken ext
-  apply homology.hom_to_ext
-  apply homology.hom_from_ext
-  rw [Category.assoc, Category.assoc, homology.lift_ι, Category.id_comp]
-  erw [homology.π'_ι] -- Porting note: had to insist
+  apply homology'.hom_to_ext
+  apply homology'.hom_from_ext
+  rw [Category.assoc, Category.assoc, homology'.lift_ι, Category.id_comp]
+  erw [homology'.π'_ι] -- Porting note: had to insist
   rw [Category.assoc, ← Category.assoc _ _ (cokernel.π _),
     Abelian.kernel.lift.inv, ← Category.assoc,
     ← Category.assoc _ (kernel.ι _), Limits.kernel.lift_ι, Category.assoc, Category.assoc, ←
-    Category.assoc (homologyIsoKernelDesc _ _ _).hom _ _, ← homology.ι, ← Category.assoc]
-  erw [homology.π'_ι] -- Porting note: had to insist
+    Category.assoc (homology'IsoKernelDesc _ _ _).hom _ _, ← homology'.ι, ← Category.assoc]
+  erw [homology'.π'_ι] -- Porting note: had to insist
   rw [Category.assoc, ← Category.assoc (cokernel.π _)]
   erw [cokernel.π_desc] -- Porting note: had to insist
   rw [whisker_eq]
@@ -273,9 +273,9 @@ theorem rightDerivedZeroToSelfAppInv_comp [EnoughInjectives C] [PreservesFiniteL
   · rw [Category.id_comp]
     ext
     simp only [Limits.kernel.lift_ι_assoc,
-      Category.assoc, Limits.kernel.lift_ι, homology.lift]
+      Category.assoc, Limits.kernel.lift_ι, homology'.lift]
     rw [← Category.assoc, ← Category.assoc,
-      Category.assoc _ _ (homologyIsoKernelDesc _ _ _).hom]
+      Category.assoc _ _ (homology'IsoKernelDesc _ _ _).hom]
     simp
     -- Porting note: this used to be an instance in ML3
   · apply isIso_kernel_lift_of_exact_of_mono _ _ (exact_of_map_injectiveResolution F P)
@@ -303,13 +303,13 @@ theorem rightDerivedZeroToSelf_natural [EnoughInjectives C] {X : C} {Y : C} (f :
     Category.assoc, Category.assoc, Category.assoc, Category.assoc, Iso.inv_hom_id,
     Category.comp_id, ← Category.assoc (F.rightDerivedObjIso 0 P).inv, Iso.inv_hom_id,
     Category.id_comp]
-  dsimp only [homologyFunctor_map]
+  dsimp only [homology'Functor_map]
   -- Porting note: broken ext
-  apply homology.hom_to_ext
-  rw [Category.assoc, homology.lift_ι, Category.assoc]
-  erw [homology.map_ι] -- Porting note: need to insist
-  rw [←Category.assoc (homology.lift _ _ _ _ _) _ _]
-  erw [homology.lift_ι] -- Porting note: need to insist
+  apply homology'.hom_to_ext
+  rw [Category.assoc, homology'.lift_ι, Category.assoc]
+  erw [homology'.map_ι] -- Porting note: need to insist
+  rw [←Category.assoc (homology'.lift _ _ _ _ _) _ _]
+  erw [homology'.lift_ι] -- Porting note: need to insist
   rw [Category.assoc]
   erw [cokernel.π_desc] -- Porting note: need to insist
   rw [← Category.assoc, ← Functor.map_comp, ← Category.assoc,

024a4231

chore: cleanup some spaces (#7484)

Purely cosmetic PR.

c93575a3

Diff

@@ -201,7 +201,7 @@ theorem exact_of_map_injectiveResolution (P : InjectiveResolution X) [PreservesF
   Preadditive.exact_of_iso_of_exact' (F.map (P.ι.f 0)) (F.map (P.cocomplex.d 0 1)) _ _ (Iso.refl _)
     (Iso.refl _)
     (HomologicalComplex.xNextIso ((F.mapHomologicalComplex _).obj P.cocomplex) rfl).symm (by simp)
-    (by rw [Iso.refl_hom, Category.id_comp, Iso.symm_hom, HomologicalComplex.dFrom_eq] <;> congr )
+    (by rw [Iso.refl_hom, Category.id_comp, Iso.symm_hom, HomologicalComplex.dFrom_eq] <;> congr)
     (preserves_exact_of_preservesFiniteLimits_of_mono _ P.exact₀)
 #align category_theory.abelian.functor.exact_of_map_injective_resolution CategoryTheory.Abelian.Functor.exact_of_map_injectiveResolution

024a4231

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

@@ -58,7 +58,7 @@ namespace CategoryTheory
 
 universe v u
 
-variable {C : Type u} [Category.{v} C] {D : Type _} [Category D]
+variable {C : Type u} [Category.{v} C] {D : Type*} [Category D]
 
 variable [Abelian C] [HasInjectiveResolutions C] [Abelian D]

024a4231

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,11 +2,6 @@
 Copyright (c) 2022 Jujian Zhang. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jujian Zhang, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.abelian.right_derived
-! leanprover-community/mathlib commit 024a4231815538ac739f52d08dd20a55da0d6b23
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Abelian.InjectiveResolution
 import Mathlib.Algebra.Homology.Additive
@@ -14,6 +9,8 @@ import Mathlib.CategoryTheory.Limits.Constructions.EpiMono
 import Mathlib.CategoryTheory.Abelian.Homology
 import Mathlib.CategoryTheory.Abelian.Exact
 
+#align_import category_theory.abelian.right_derived from "leanprover-community/mathlib"@"024a4231815538ac739f52d08dd20a55da0d6b23"
+
 /-!
 # Right-derived functors

024a4231

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

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

dbae2f17

Diff

@@ -218,11 +218,11 @@ def rightDerivedZeroToSelfApp [EnoughInjectives C] [PreservesFiniteLimits F] {X
       (cokernel.desc _ (𝟙 _) (by simp)) (𝟙 _)
           (by
             -- Porting note: was ext; simp
-            apply coequalizer.hom_ext
+            ext
             dsimp
             simp) ≫
         -- Porting note: isIso_kernel_lift_of_exact_of_mono is no longer allowed as an
-        -- instance for reasons am I not privy to
+        -- instance for reasons I am not privy to
         have : IsIso <| kernel.lift _ _ (exact_of_map_injectiveResolution F P).w :=
           isIso_kernel_lift_of_exact_of_mono _ _ (exact_of_map_injectiveResolution F P)
         (asIso (kernel.lift _ _ (exact_of_map_injectiveResolution F P).w)).inv
@@ -274,8 +274,7 @@ theorem rightDerivedZeroToSelfAppInv_comp [EnoughInjectives C] [PreservesFiniteL
   -- Porting note: this IsIso instance used to be filled automatically
   apply (@IsIso.comp_inv_eq D _ _ _ _ _ ?_ _ _).mpr
   · rw [Category.id_comp]
-    -- Porting note: broken ext
-    apply equalizer.hom_ext
+    ext
     simp only [Limits.kernel.lift_ι_assoc,
       Category.assoc, Limits.kernel.lift_ι, homology.lift]
     rw [← Category.assoc, ← Category.assoc,

024a4231

chore: tidy various files (#4757)

ea80818c

Diff

@@ -22,7 +22,7 @@ out of a category with injective resolutions.
 
 The definition is
 ```
-injective_resolutions C ⋙ F.mapHomotopyCategory _ ⋙ HomotopyCategory.homologyFunctor D _ n
+injectiveResolutions C ⋙ F.mapHomotopyCategory _ ⋙ HomotopyCategory.homologyFunctor D _ n
 ```
 that is, we pick an injective resolution (thought of as an object of the homotopy category),
 we apply `F` objectwise, and compute `n`-th homology.
@@ -191,7 +191,7 @@ open CategoryTheory.Preadditive
 variable [Abelian C] [Abelian D] [Additive F]
 
 /-- If `PreservesFiniteLimits F` and `Mono f`, then `Exact (F.map f) (F.map g)` if
-`exact f g`. -/
+`Exact f g`. -/
 theorem preserves_exact_of_preservesFiniteLimits_of_mono [PreservesFiniteLimits F] [Mono f]
     (ex : Exact f g) : Exact (F.map f) (F.map g) :=
   Abelian.exact_of_is_kernel _ _ (by simp [← Functor.map_comp, ex.w]) <|
@@ -332,4 +332,3 @@ def rightDerivedZeroIsoSelf [EnoughInjectives C] [PreservesFiniteLimits F] : F.r
 #align category_theory.abelian.functor.right_derived_zero_iso_self CategoryTheory.Abelian.Functor.rightDerivedZeroIsoSelf
 
 end CategoryTheory.Abelian.Functor
-

024a4231

feat: port CategoryTheory.Abelian.RightDerived (#4284)

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

e425f617

`category_theory.abelian.right_derived` ⟷ `Mathlib.CategoryTheory.Abelian.RightDerived`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 546

category_theory.abelian.right_derived ⟷ Mathlib.CategoryTheory.Abelian.RightDerived

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 8 + 546

`category_theory.abelian.right_derived` ⟷ `Mathlib.CategoryTheory.Abelian.RightDerived`