category_theory.abelian.left_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

8001ea54

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

61b5e275

bump to nightly-2023-12-02-06

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

e637da5d

Diff

@@ -47,27 +47,23 @@ open CategoryTheory.Preadditive
 
 variable [Abelian C] [Abelian D] [Additive F]
 
-#print CategoryTheory.Abelian.Functor.preserves_exact_of_PreservesFiniteColimits_of_epi /-
 /-- If `preserves_finite_colimits F` and `epi g`, then `exact (F.map f) (F.map g)` if
 `exact f g`. -/
-theorem preserves_exact_of_PreservesFiniteColimits_of_epi [PreservesFiniteColimits F] [Epi g]
+theorem preserves_exact_of_preservesFiniteColimits_of_epi [PreservesFiniteColimits F] [Epi g]
     (ex : Exact f g) : Exact (F.map f) (F.map g) :=
   Abelian.exact_of_is_cokernel _ _ (by simp [← functor.map_comp, ex.w]) <|
     Limits.isColimitCoforkMapOfIsColimit' _ ex.w (Abelian.isColimitOfExactOfEpi _ _ ex)
-#align category_theory.abelian.functor.preserves_exact_of_preserves_finite_colimits_of_epi CategoryTheory.Abelian.Functor.preserves_exact_of_PreservesFiniteColimits_of_epi
--/
+#align category_theory.abelian.functor.preserves_exact_of_preserves_finite_colimits_of_epi CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteColimits_of_epi
 
-#print CategoryTheory.Abelian.Functor.exact_of_map_projectiveResolution /-
-theorem exact_of_map_projectiveResolution (P : ProjectiveResolution X) [PreservesFiniteColimits F] :
+theorem exact_of_map_projective_resolution (P : ProjectiveResolution X)
+    [PreservesFiniteColimits F] :
     Exact (((F.mapHomologicalComplex (ComplexShape.down ℕ)).obj P.complex).dTo 0)
       (F.map (P.π.f 0)) :=
   Preadditive.exact_of_iso_of_exact' (F.map (P.complex.d 1 0)) (F.map (P.π.f 0)) _ _
     (HomologicalComplex.xPrevIso ((F.mapHomologicalComplex _).obj P.complex) rfl).symm (Iso.refl _)
-    (Iso.refl _) (by simp) (by simp) (preserves_exact_of_PreservesFiniteColimits_of_epi _ P.exact₀)
-#align category_theory.abelian.functor.exact_of_map_projective_resolution CategoryTheory.Abelian.Functor.exact_of_map_projectiveResolution
--/
+    (Iso.refl _) (by simp) (by simp) (preserves_exact_of_preservesFiniteColimits_of_epi _ P.exact₀)
+#align category_theory.abelian.functor.exact_of_map_projective_resolution CategoryTheory.Abelian.Functor.exact_of_map_projective_resolution
 
-#print CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfApp /-
 /-- Given `P : ProjectiveResolution X`, a morphism `(F.left_derived 0).obj X ⟶ F.obj X`. -/
 @[nolint unused_arguments]
 def leftDerivedZeroToSelfApp [EnoughProjectives C] {X : C} (P : ProjectiveResolution X) :
@@ -80,9 +76,7 @@ def leftDerivedZeroToSelfApp [EnoughProjectives C] {X : C} (P : ProjectiveResolu
           map_homological_complex_obj_d, category.assoc, ← functor.map_comp]
         simp)
 #align category_theory.abelian.functor.left_derived_zero_to_self_app CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfApp
--/
 
-#print CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppInv /-
 /-- Given `P : ProjectiveResolution X`, a morphism `F.obj X ⟶ (F.left_derived 0).obj X` given
 `preserves_finite_colimits F`. -/
 def leftDerivedZeroToSelfAppInv [EnoughProjectives C] [PreservesFiniteColimits F] {X : C}
@@ -93,9 +87,7 @@ def leftDerivedZeroToSelfAppInv [EnoughProjectives C] [PreservesFiniteColimits F
       _ ≫ (homology'IsoCokernelLift _ _ _).inv ≫ (left_derived_obj_iso F 0 P).inv
   exact cokernel.map _ _ (𝟙 _) (kernel.lift _ (𝟙 _) (by simp)) (by ext; simp)
 #align category_theory.abelian.functor.left_derived_zero_to_self_app_inv CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppInv
--/
 
-#print CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfApp_comp_inv /-
 theorem leftDerivedZeroToSelfApp_comp_inv [EnoughProjectives C] [PreservesFiniteColimits F] {X : C}
     (P : ProjectiveResolution X) :
     leftDerivedZeroToSelfApp F P ≫ leftDerivedZeroToSelfAppInv F P = 𝟙 _ :=
@@ -113,9 +105,7 @@ theorem leftDerivedZeroToSelfApp_comp_inv [EnoughProjectives C] [PreservesFinite
   ext
   rw [category.id_comp, category.assoc, equalizer_as_kernel, kernel.lift_ι, category.comp_id]
 #align category_theory.abelian.functor.left_derived_zero_to_self_app_comp_inv CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfApp_comp_inv
--/
 
-#print CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppInv_comp /-
 theorem leftDerivedZeroToSelfAppInv_comp [EnoughProjectives C] [PreservesFiniteColimits F] {X : C}
     (P : ProjectiveResolution X) :
     leftDerivedZeroToSelfAppInv F P ≫ leftDerivedZeroToSelfApp F P = 𝟙 _ :=
@@ -130,9 +120,7 @@ theorem leftDerivedZeroToSelfAppInv_comp [EnoughProjectives C] [PreservesFiniteC
     category.id_comp]
   simp only [category.assoc, cokernel.π_desc, kernel.lift_ι_assoc, category.id_comp]
 #align category_theory.abelian.functor.left_derived_zero_to_self_app_inv_comp CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppInv_comp
--/
 
-#print CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppIso /-
 /-- Given `P : ProjectiveResolution X`, the isomorphism `(F.left_derived 0).obj X ≅ F.obj X` if
 `preserves_finite_colimits F`. -/
 def leftDerivedZeroToSelfAppIso [EnoughProjectives C] [PreservesFiniteColimits F] {X : C}
@@ -143,9 +131,7 @@ def leftDerivedZeroToSelfAppIso [EnoughProjectives C] [PreservesFiniteColimits F
   hom_inv_id' := leftDerivedZeroToSelfApp_comp_inv _ P
   inv_hom_id' := leftDerivedZeroToSelfAppInv_comp _ P
 #align category_theory.abelian.functor.left_derived_zero_to_self_app_iso CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppIso
--/
 
-#print CategoryTheory.Abelian.Functor.leftDerived_zero_to_self_natural /-
 /-- Given `P : ProjectiveResolution X` and `Q : ProjectiveResolution Y` and a morphism `f : X ⟶ Y`,
 naturality of the square given by `left_derived_zero_to_self_obj_hom. -/
 theorem leftDerived_zero_to_self_natural [EnoughProjectives C] {X : C} {Y : C} (f : X ⟶ Y)
@@ -165,16 +151,13 @@ theorem leftDerived_zero_to_self_natural [EnoughProjectives C] {X : C} {Y : C} (
     show (ProjectiveResolution.lift f P Q).f 0 ≫ _ = _ ≫ f from
       HomologicalComplex.congr_hom (ProjectiveResolution.lift_commutes f P Q) 0]
 #align category_theory.abelian.functor.left_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.leftDerived_zero_to_self_natural
--/
 
-#print CategoryTheory.Abelian.Functor.leftDerivedZeroIsoSelf /-
 /-- Given `preserves_finite_colimits F`, the natural isomorphism `(F.left_derived 0) ≅ F`. -/
 def leftDerivedZeroIsoSelf [EnoughProjectives C] [PreservesFiniteColimits F] :
     F.leftDerived 0 ≅ F :=
   NatIso.ofComponents (fun X => leftDerivedZeroToSelfAppIso _ (ProjectiveResolution.of X))
     fun X Y f => leftDerived_zero_to_self_natural _ _ _ _
 #align category_theory.abelian.functor.left_derived_zero_iso_self CategoryTheory.Abelian.Functor.leftDerivedZeroIsoSelf
--/
 
 end CategoryTheory.Abelian.Functor

61b5e275

bump to nightly-2023-10-29-06

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

abdd1870

Diff

@@ -73,7 +73,7 @@ theorem exact_of_map_projectiveResolution (P : ProjectiveResolution X) [Preserve
 def leftDerivedZeroToSelfApp [EnoughProjectives C] {X : C} (P : ProjectiveResolution X) :
     (F.leftDerived 0).obj X ⟶ F.obj X :=
   (leftDerivedObjIso F 0 P).Hom ≫
-    homology.desc' _ _ _ (kernel.ι _ ≫ F.map (P.π.f 0))
+    homology'.desc' _ _ _ (kernel.ι _ ≫ F.map (P.π.f 0))
       (by
         rw [kernel.lift_ι_assoc,
           HomologicalComplex.dTo_eq _ (by simp : (ComplexShape.down ℕ).Rel 1 0),
@@ -90,7 +90,7 @@ def leftDerivedZeroToSelfAppInv [EnoughProjectives C] [PreservesFiniteColimits F
   by
   refine'
     (as_iso (cokernel.desc _ _ (exact_of_map_projective_resolution F P).w)).inv ≫
-      _ ≫ (homologyIsoCokernelLift _ _ _).inv ≫ (left_derived_obj_iso F 0 P).inv
+      _ ≫ (homology'IsoCokernelLift _ _ _).inv ≫ (left_derived_obj_iso F 0 P).inv
   exact cokernel.map _ _ (𝟙 _) (kernel.lift _ (𝟙 _) (by simp)) (by ext; simp)
 #align category_theory.abelian.functor.left_derived_zero_to_self_app_inv CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppInv
 -/
@@ -106,8 +106,8 @@ theorem leftDerivedZeroToSelfApp_comp_inv [EnoughProjectives C] [PreservesFinite
   convert category.comp_id _
   rw [← category.assoc, ← category.assoc, iso.comp_inv_eq, category.id_comp]
   ext
-  rw [← category.assoc, ← category.assoc, homology.π'_desc', category.assoc, category.assoc, ←
-    category.assoc (F.map _), abelian.cokernel.desc.inv, cokernel.π_desc, homology.π',
+  rw [← category.assoc, ← category.assoc, homology'.π'_desc', category.assoc, category.assoc, ←
+    category.assoc (F.map _), abelian.cokernel.desc.inv, cokernel.π_desc, homology'.π',
     category.assoc, iso.inv_hom_id, category.comp_id, ← category.assoc]
   convert category.id_comp _ using 2
   ext
@@ -125,8 +125,8 @@ theorem leftDerivedZeroToSelfAppInv_comp [EnoughProjectives C] [PreservesFiniteC
     category.assoc (F.left_derived_obj_iso 0 P).inv, iso.inv_hom_id, category.id_comp,
     is_iso.inv_comp_eq, category.comp_id]
   ext
-  simp only [cokernel.π_desc_assoc, category.assoc, cokernel.π_desc, homology.desc']
-  rw [← category.assoc, ← category.assoc (homologyIsoCokernelLift _ _ _).inv, iso.inv_hom_id,
+  simp only [cokernel.π_desc_assoc, category.assoc, cokernel.π_desc, homology'.desc']
+  rw [← category.assoc, ← category.assoc (homology'IsoCokernelLift _ _ _).inv, iso.inv_hom_id,
     category.id_comp]
   simp only [category.assoc, cokernel.π_desc, kernel.lift_ι_assoc, category.id_comp]
 #align category_theory.abelian.functor.left_derived_zero_to_self_app_inv_comp CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppInv_comp
@@ -157,11 +157,11 @@ theorem leftDerived_zero_to_self_natural [EnoughProjectives C] {X : C} {Y : C} (
   rw [functor.left_derived_map_eq F 0 f (ProjectiveResolution.lift f P Q) (by simp), category.assoc,
     category.assoc, ← category.assoc _ (F.left_derived_obj_iso 0 Q).Hom, iso.inv_hom_id,
     category.id_comp, category.assoc, whisker_eq]
-  dsimp only [homologyFunctor_map]
+  dsimp only [homology'Functor_map]
   ext
   simp only [HomologicalComplex.Hom.sqTo_right, map_homological_complex_map_f,
-    homology.π'_map_assoc, homology.π'_desc', kernel.lift_ι_assoc, category.assoc,
-    homology.π'_desc'_assoc, ← map_comp,
+    homology'.π'_map_assoc, homology'.π'_desc', kernel.lift_ι_assoc, category.assoc,
+    homology'.π'_desc'_assoc, ← map_comp,
     show (ProjectiveResolution.lift f P Q).f 0 ≫ _ = _ ≫ f from
       HomologicalComplex.congr_hom (ProjectiveResolution.lift_commutes f P Q) 0]
 #align category_theory.abelian.functor.left_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.leftDerived_zero_to_self_natural

61b5e275

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,10 +3,10 @@ Copyright (c) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca, Adam Topaz
 -/
-import Mathbin.CategoryTheory.Abelian.Homology
-import Mathbin.CategoryTheory.Functor.LeftDerived
-import Mathbin.CategoryTheory.Abelian.Projective
-import Mathbin.CategoryTheory.Limits.Constructions.EpiMono
+import CategoryTheory.Abelian.Homology
+import CategoryTheory.Functor.LeftDerived
+import CategoryTheory.Abelian.Projective
+import CategoryTheory.Limits.Constructions.EpiMono
 
 #align_import category_theory.abelian.left_derived from "leanprover-community/mathlib"@"61b5e2755ccb464b68d05a9acf891ae04992d09d"

61b5e275

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,17 +2,14 @@
 Copyright (c) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca, Adam Topaz
-
-! This file was ported from Lean 3 source module category_theory.abelian.left_derived
-! leanprover-community/mathlib commit 61b5e2755ccb464b68d05a9acf891ae04992d09d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Abelian.Homology
 import Mathbin.CategoryTheory.Functor.LeftDerived
 import Mathbin.CategoryTheory.Abelian.Projective
 import Mathbin.CategoryTheory.Limits.Constructions.EpiMono
 
+#align_import category_theory.abelian.left_derived from "leanprover-community/mathlib"@"61b5e2755ccb464b68d05a9acf891ae04992d09d"
+
 /-!
 # Zeroth left derived functors

61b5e275

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -50,6 +50,7 @@ open CategoryTheory.Preadditive
 
 variable [Abelian C] [Abelian D] [Additive F]
 
+#print CategoryTheory.Abelian.Functor.preserves_exact_of_PreservesFiniteColimits_of_epi /-
 /-- If `preserves_finite_colimits F` and `epi g`, then `exact (F.map f) (F.map g)` if
 `exact f g`. -/
 theorem preserves_exact_of_PreservesFiniteColimits_of_epi [PreservesFiniteColimits F] [Epi g]
@@ -57,7 +58,9 @@ theorem preserves_exact_of_PreservesFiniteColimits_of_epi [PreservesFiniteColimi
   Abelian.exact_of_is_cokernel _ _ (by simp [← functor.map_comp, ex.w]) <|
     Limits.isColimitCoforkMapOfIsColimit' _ ex.w (Abelian.isColimitOfExactOfEpi _ _ ex)
 #align category_theory.abelian.functor.preserves_exact_of_preserves_finite_colimits_of_epi CategoryTheory.Abelian.Functor.preserves_exact_of_PreservesFiniteColimits_of_epi
+-/
 
+#print CategoryTheory.Abelian.Functor.exact_of_map_projectiveResolution /-
 theorem exact_of_map_projectiveResolution (P : ProjectiveResolution X) [PreservesFiniteColimits F] :
     Exact (((F.mapHomologicalComplex (ComplexShape.down ℕ)).obj P.complex).dTo 0)
       (F.map (P.π.f 0)) :=
@@ -65,7 +68,9 @@ theorem exact_of_map_projectiveResolution (P : ProjectiveResolution X) [Preserve
     (HomologicalComplex.xPrevIso ((F.mapHomologicalComplex _).obj P.complex) rfl).symm (Iso.refl _)
     (Iso.refl _) (by simp) (by simp) (preserves_exact_of_PreservesFiniteColimits_of_epi _ P.exact₀)
 #align category_theory.abelian.functor.exact_of_map_projective_resolution CategoryTheory.Abelian.Functor.exact_of_map_projectiveResolution
+-/
 
+#print CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfApp /-
 /-- Given `P : ProjectiveResolution X`, a morphism `(F.left_derived 0).obj X ⟶ F.obj X`. -/
 @[nolint unused_arguments]
 def leftDerivedZeroToSelfApp [EnoughProjectives C] {X : C} (P : ProjectiveResolution X) :
@@ -78,7 +83,9 @@ def leftDerivedZeroToSelfApp [EnoughProjectives C] {X : C} (P : ProjectiveResolu
           map_homological_complex_obj_d, category.assoc, ← functor.map_comp]
         simp)
 #align category_theory.abelian.functor.left_derived_zero_to_self_app CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfApp
+-/
 
+#print CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppInv /-
 /-- Given `P : ProjectiveResolution X`, a morphism `F.obj X ⟶ (F.left_derived 0).obj X` given
 `preserves_finite_colimits F`. -/
 def leftDerivedZeroToSelfAppInv [EnoughProjectives C] [PreservesFiniteColimits F] {X : C}
@@ -89,7 +96,9 @@ def leftDerivedZeroToSelfAppInv [EnoughProjectives C] [PreservesFiniteColimits F
       _ ≫ (homologyIsoCokernelLift _ _ _).inv ≫ (left_derived_obj_iso F 0 P).inv
   exact cokernel.map _ _ (𝟙 _) (kernel.lift _ (𝟙 _) (by simp)) (by ext; simp)
 #align category_theory.abelian.functor.left_derived_zero_to_self_app_inv CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppInv
+-/
 
+#print CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfApp_comp_inv /-
 theorem leftDerivedZeroToSelfApp_comp_inv [EnoughProjectives C] [PreservesFiniteColimits F] {X : C}
     (P : ProjectiveResolution X) :
     leftDerivedZeroToSelfApp F P ≫ leftDerivedZeroToSelfAppInv F P = 𝟙 _ :=
@@ -107,7 +116,9 @@ theorem leftDerivedZeroToSelfApp_comp_inv [EnoughProjectives C] [PreservesFinite
   ext
   rw [category.id_comp, category.assoc, equalizer_as_kernel, kernel.lift_ι, category.comp_id]
 #align category_theory.abelian.functor.left_derived_zero_to_self_app_comp_inv CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfApp_comp_inv
+-/
 
+#print CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppInv_comp /-
 theorem leftDerivedZeroToSelfAppInv_comp [EnoughProjectives C] [PreservesFiniteColimits F] {X : C}
     (P : ProjectiveResolution X) :
     leftDerivedZeroToSelfAppInv F P ≫ leftDerivedZeroToSelfApp F P = 𝟙 _ :=
@@ -122,7 +133,9 @@ theorem leftDerivedZeroToSelfAppInv_comp [EnoughProjectives C] [PreservesFiniteC
     category.id_comp]
   simp only [category.assoc, cokernel.π_desc, kernel.lift_ι_assoc, category.id_comp]
 #align category_theory.abelian.functor.left_derived_zero_to_self_app_inv_comp CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppInv_comp
+-/
 
+#print CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppIso /-
 /-- Given `P : ProjectiveResolution X`, the isomorphism `(F.left_derived 0).obj X ≅ F.obj X` if
 `preserves_finite_colimits F`. -/
 def leftDerivedZeroToSelfAppIso [EnoughProjectives C] [PreservesFiniteColimits F] {X : C}
@@ -133,7 +146,9 @@ def leftDerivedZeroToSelfAppIso [EnoughProjectives C] [PreservesFiniteColimits F
   hom_inv_id' := leftDerivedZeroToSelfApp_comp_inv _ P
   inv_hom_id' := leftDerivedZeroToSelfAppInv_comp _ P
 #align category_theory.abelian.functor.left_derived_zero_to_self_app_iso CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppIso
+-/
 
+#print CategoryTheory.Abelian.Functor.leftDerived_zero_to_self_natural /-
 /-- Given `P : ProjectiveResolution X` and `Q : ProjectiveResolution Y` and a morphism `f : X ⟶ Y`,
 naturality of the square given by `left_derived_zero_to_self_obj_hom. -/
 theorem leftDerived_zero_to_self_natural [EnoughProjectives C] {X : C} {Y : C} (f : X ⟶ Y)
@@ -153,6 +168,7 @@ theorem leftDerived_zero_to_self_natural [EnoughProjectives C] {X : C} {Y : C} (
     show (ProjectiveResolution.lift f P Q).f 0 ≫ _ = _ ≫ f from
       HomologicalComplex.congr_hom (ProjectiveResolution.lift_commutes f P Q) 0]
 #align category_theory.abelian.functor.left_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.leftDerived_zero_to_self_natural
+-/
 
 #print CategoryTheory.Abelian.Functor.leftDerivedZeroIsoSelf /-
 /-- Given `preserves_finite_colimits F`, the natural isomorphism `(F.left_derived 0) ≅ F`. -/

61b5e275

bump to nightly-2023-06-07-05

mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3

a8c3b45a

Diff

@@ -58,13 +58,13 @@ theorem preserves_exact_of_PreservesFiniteColimits_of_epi [PreservesFiniteColimi
     Limits.isColimitCoforkMapOfIsColimit' _ ex.w (Abelian.isColimitOfExactOfEpi _ _ ex)
 #align category_theory.abelian.functor.preserves_exact_of_preserves_finite_colimits_of_epi CategoryTheory.Abelian.Functor.preserves_exact_of_PreservesFiniteColimits_of_epi
 
-theorem exact_of_map_ProjectiveResolution (P : ProjectiveResolution X) [PreservesFiniteColimits F] :
+theorem exact_of_map_projectiveResolution (P : ProjectiveResolution X) [PreservesFiniteColimits F] :
     Exact (((F.mapHomologicalComplex (ComplexShape.down ℕ)).obj P.complex).dTo 0)
       (F.map (P.π.f 0)) :=
   Preadditive.exact_of_iso_of_exact' (F.map (P.complex.d 1 0)) (F.map (P.π.f 0)) _ _
     (HomologicalComplex.xPrevIso ((F.mapHomologicalComplex _).obj P.complex) rfl).symm (Iso.refl _)
     (Iso.refl _) (by simp) (by simp) (preserves_exact_of_PreservesFiniteColimits_of_epi _ P.exact₀)
-#align category_theory.abelian.functor.exact_of_map_projective_resolution CategoryTheory.Abelian.Functor.exact_of_map_ProjectiveResolution
+#align category_theory.abelian.functor.exact_of_map_projective_resolution CategoryTheory.Abelian.Functor.exact_of_map_projectiveResolution
 
 /-- Given `P : ProjectiveResolution X`, a morphism `(F.left_derived 0).obj X ⟶ F.obj X`. -/
 @[nolint unused_arguments]

61b5e275

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca, Adam Topaz
 
 ! This file was ported from Lean 3 source module category_theory.abelian.left_derived
-! leanprover-community/mathlib commit 8001ea54ece3bd5c0d0932f1e4f6d0f142ea20d9
+! leanprover-community/mathlib commit 61b5e2755ccb464b68d05a9acf891ae04992d09d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.CategoryTheory.Limits.Constructions.EpiMono
 /-!
 # Zeroth left derived functors
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 If `F : C ⥤ D` is an additive right exact functor between abelian categories, where `C` has enough
 projectives, we provide the natural isomorphism `F.left_derived 0 ≅ F`.
 
@@ -49,20 +52,19 @@ variable [Abelian C] [Abelian D] [Additive F]
 
 /-- If `preserves_finite_colimits F` and `epi g`, then `exact (F.map f) (F.map g)` if
 `exact f g`. -/
-theorem preserves_exact_of_preservesFiniteColimits_of_epi [PreservesFiniteColimits F] [Epi g]
+theorem preserves_exact_of_PreservesFiniteColimits_of_epi [PreservesFiniteColimits F] [Epi g]
     (ex : Exact f g) : Exact (F.map f) (F.map g) :=
   Abelian.exact_of_is_cokernel _ _ (by simp [← functor.map_comp, ex.w]) <|
     Limits.isColimitCoforkMapOfIsColimit' _ ex.w (Abelian.isColimitOfExactOfEpi _ _ ex)
-#align category_theory.abelian.functor.preserves_exact_of_preserves_finite_colimits_of_epi CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteColimits_of_epi
+#align category_theory.abelian.functor.preserves_exact_of_preserves_finite_colimits_of_epi CategoryTheory.Abelian.Functor.preserves_exact_of_PreservesFiniteColimits_of_epi
 
-theorem exact_of_map_projective_resolution (P : ProjectiveResolution X)
-    [PreservesFiniteColimits F] :
+theorem exact_of_map_ProjectiveResolution (P : ProjectiveResolution X) [PreservesFiniteColimits F] :
     Exact (((F.mapHomologicalComplex (ComplexShape.down ℕ)).obj P.complex).dTo 0)
       (F.map (P.π.f 0)) :=
   Preadditive.exact_of_iso_of_exact' (F.map (P.complex.d 1 0)) (F.map (P.π.f 0)) _ _
     (HomologicalComplex.xPrevIso ((F.mapHomologicalComplex _).obj P.complex) rfl).symm (Iso.refl _)
-    (Iso.refl _) (by simp) (by simp) (preserves_exact_of_preservesFiniteColimits_of_epi _ P.exact₀)
-#align category_theory.abelian.functor.exact_of_map_projective_resolution CategoryTheory.Abelian.Functor.exact_of_map_projective_resolution
+    (Iso.refl _) (by simp) (by simp) (preserves_exact_of_PreservesFiniteColimits_of_epi _ P.exact₀)
+#align category_theory.abelian.functor.exact_of_map_projective_resolution CategoryTheory.Abelian.Functor.exact_of_map_ProjectiveResolution
 
 /-- Given `P : ProjectiveResolution X`, a morphism `(F.left_derived 0).obj X ⟶ F.obj X`. -/
 @[nolint unused_arguments]
@@ -152,12 +154,14 @@ theorem leftDerived_zero_to_self_natural [EnoughProjectives C] {X : C} {Y : C} (
       HomologicalComplex.congr_hom (ProjectiveResolution.lift_commutes f P Q) 0]
 #align category_theory.abelian.functor.left_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.leftDerived_zero_to_self_natural
 
+#print CategoryTheory.Abelian.Functor.leftDerivedZeroIsoSelf /-
 /-- Given `preserves_finite_colimits F`, the natural isomorphism `(F.left_derived 0) ≅ F`. -/
 def leftDerivedZeroIsoSelf [EnoughProjectives C] [PreservesFiniteColimits F] :
     F.leftDerived 0 ≅ F :=
   NatIso.ofComponents (fun X => leftDerivedZeroToSelfAppIso _ (ProjectiveResolution.of X))
     fun X Y f => leftDerived_zero_to_self_natural _ _ _ _
 #align category_theory.abelian.functor.left_derived_zero_iso_self CategoryTheory.Abelian.Functor.leftDerivedZeroIsoSelf
+-/
 
 end CategoryTheory.Abelian.Functor

8001ea54

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -85,11 +85,7 @@ def leftDerivedZeroToSelfAppInv [EnoughProjectives C] [PreservesFiniteColimits F
   refine'
     (as_iso (cokernel.desc _ _ (exact_of_map_projective_resolution F P).w)).inv ≫
       _ ≫ (homologyIsoCokernelLift _ _ _).inv ≫ (left_derived_obj_iso F 0 P).inv
-  exact
-    cokernel.map _ _ (𝟙 _) (kernel.lift _ (𝟙 _) (by simp))
-      (by
-        ext
-        simp)
+  exact cokernel.map _ _ (𝟙 _) (kernel.lift _ (𝟙 _) (by simp)) (by ext; simp)
 #align category_theory.abelian.functor.left_derived_zero_to_self_app_inv CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppInv
 
 theorem leftDerivedZeroToSelfApp_comp_inv [EnoughProjectives C] [PreservesFiniteColimits F] {X : C}

8001ea54

bump to nightly-2023-04-20-00

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

d6678ca6

Diff

@@ -49,19 +49,20 @@ variable [Abelian C] [Abelian D] [Additive F]
 
 /-- If `preserves_finite_colimits F` and `epi g`, then `exact (F.map f) (F.map g)` if
 `exact f g`. -/
-theorem preservesExactOfPreservesFiniteColimitsOfEpi [PreservesFiniteColimits F] [Epi g]
+theorem preserves_exact_of_preservesFiniteColimits_of_epi [PreservesFiniteColimits F] [Epi g]
     (ex : Exact f g) : Exact (F.map f) (F.map g) :=
-  Abelian.exactOfIsCokernel _ _ (by simp [← functor.map_comp, ex.w]) <|
+  Abelian.exact_of_is_cokernel _ _ (by simp [← functor.map_comp, ex.w]) <|
     Limits.isColimitCoforkMapOfIsColimit' _ ex.w (Abelian.isColimitOfExactOfEpi _ _ ex)
-#align category_theory.abelian.functor.preserves_exact_of_preserves_finite_colimits_of_epi CategoryTheory.Abelian.Functor.preservesExactOfPreservesFiniteColimitsOfEpi
+#align category_theory.abelian.functor.preserves_exact_of_preserves_finite_colimits_of_epi CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteColimits_of_epi
 
-theorem exactOfMapProjectiveResolution (P : ProjectiveResolution X) [PreservesFiniteColimits F] :
+theorem exact_of_map_projective_resolution (P : ProjectiveResolution X)
+    [PreservesFiniteColimits F] :
     Exact (((F.mapHomologicalComplex (ComplexShape.down ℕ)).obj P.complex).dTo 0)
       (F.map (P.π.f 0)) :=
-  Preadditive.exactOfIsoOfExact' (F.map (P.complex.d 1 0)) (F.map (P.π.f 0)) _ _
+  Preadditive.exact_of_iso_of_exact' (F.map (P.complex.d 1 0)) (F.map (P.π.f 0)) _ _
     (HomologicalComplex.xPrevIso ((F.mapHomologicalComplex _).obj P.complex) rfl).symm (Iso.refl _)
-    (Iso.refl _) (by simp) (by simp) (preservesExactOfPreservesFiniteColimitsOfEpi _ P.exact₀)
-#align category_theory.abelian.functor.exact_of_map_projective_resolution CategoryTheory.Abelian.Functor.exactOfMapProjectiveResolution
+    (Iso.refl _) (by simp) (by simp) (preserves_exact_of_preservesFiniteColimits_of_epi _ P.exact₀)
+#align category_theory.abelian.functor.exact_of_map_projective_resolution CategoryTheory.Abelian.Functor.exact_of_map_projective_resolution
 
 /-- Given `P : ProjectiveResolution X`, a morphism `(F.left_derived 0).obj X ⟶ F.obj X`. -/
 @[nolint unused_arguments]

8001ea54

bump to nightly-2023-04-18-00

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

7809aa1d

Diff

@@ -49,20 +49,19 @@ variable [Abelian C] [Abelian D] [Additive F]
 
 /-- If `preserves_finite_colimits F` and `epi g`, then `exact (F.map f) (F.map g)` if
 `exact f g`. -/
-theorem preserves_exact_of_preservesFiniteColimits_of_epi [PreservesFiniteColimits F] [Epi g]
+theorem preservesExactOfPreservesFiniteColimitsOfEpi [PreservesFiniteColimits F] [Epi g]
     (ex : Exact f g) : Exact (F.map f) (F.map g) :=
-  Abelian.exact_of_is_cokernel _ _ (by simp [← functor.map_comp, ex.w]) <|
+  Abelian.exactOfIsCokernel _ _ (by simp [← functor.map_comp, ex.w]) <|
     Limits.isColimitCoforkMapOfIsColimit' _ ex.w (Abelian.isColimitOfExactOfEpi _ _ ex)
-#align category_theory.abelian.functor.preserves_exact_of_preserves_finite_colimits_of_epi CategoryTheory.Abelian.Functor.preserves_exact_of_preservesFiniteColimits_of_epi
+#align category_theory.abelian.functor.preserves_exact_of_preserves_finite_colimits_of_epi CategoryTheory.Abelian.Functor.preservesExactOfPreservesFiniteColimitsOfEpi
 
-theorem exact_of_map_projective_resolution (P : ProjectiveResolution X)
-    [PreservesFiniteColimits F] :
+theorem exactOfMapProjectiveResolution (P : ProjectiveResolution X) [PreservesFiniteColimits F] :
     Exact (((F.mapHomologicalComplex (ComplexShape.down ℕ)).obj P.complex).dTo 0)
       (F.map (P.π.f 0)) :=
-  Preadditive.exact_of_iso_of_exact' (F.map (P.complex.d 1 0)) (F.map (P.π.f 0)) _ _
+  Preadditive.exactOfIsoOfExact' (F.map (P.complex.d 1 0)) (F.map (P.π.f 0)) _ _
     (HomologicalComplex.xPrevIso ((F.mapHomologicalComplex _).obj P.complex) rfl).symm (Iso.refl _)
-    (Iso.refl _) (by simp) (by simp) (preserves_exact_of_preservesFiniteColimits_of_epi _ P.exact₀)
-#align category_theory.abelian.functor.exact_of_map_projective_resolution CategoryTheory.Abelian.Functor.exact_of_map_projective_resolution
+    (Iso.refl _) (by simp) (by simp) (preservesExactOfPreservesFiniteColimitsOfEpi _ P.exact₀)
+#align category_theory.abelian.functor.exact_of_map_projective_resolution CategoryTheory.Abelian.Functor.exactOfMapProjectiveResolution
 
 /-- Given `P : ProjectiveResolution X`, a morphism `(F.left_derived 0).obj X ⟶ F.obj X`. -/
 @[nolint unused_arguments]

8001ea54

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

8001ea54

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

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

3556ded2

Diff

@@ -196,7 +196,7 @@ lemma NatTrans.leftDerivedToHomotopyCategory_comp {F G H : C ⥤ D} (α : F ⟶
       NatTrans.leftDerivedToHomotopyCategory α ≫
         NatTrans.leftDerivedToHomotopyCategory β := rfl
 
-/-- The natural transformation between left-derived functors induced by a natural transformation.-/
+/-- The natural transformation between left-derived functors induced by a natural transformation. -/
 noncomputable def NatTrans.leftDerived
     {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶ G) (n : ℕ) :
     F.leftDerived n ⟶ G.leftDerived n :=

8001ea54

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

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

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

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

41529d1e

Diff

@@ -1,185 +1,365 @@
 /-
-Copyright (c) 2022 Riccardo Brasca. All rights reserved.
+Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
-Authors: Riccardo Brasca, Adam Topaz
+Authors: Scott Morrison, Riccardo Brasca, Adam Topaz, Jujian Zhang, Joël Riou
 -/
 import Mathlib.CategoryTheory.Abelian.Homology
-import Mathlib.CategoryTheory.Functor.LeftDerived
-import Mathlib.CategoryTheory.Abelian.Projective
-import Mathlib.CategoryTheory.Limits.Constructions.EpiMono
+import Mathlib.CategoryTheory.Abelian.ProjectiveResolution
+import Mathlib.Algebra.Homology.Additive
 
 #align_import category_theory.abelian.left_derived from "leanprover-community/mathlib"@"8001ea54ece3bd5c0d0932f1e4f6d0f142ea20d9"
 
 /-!
-# Zeroth left derived functors
+# Left-derived functors
 
-If `F : C ⥤ D` is an additive right exact functor between abelian categories, where `C` has enough
-projectives, we provide the natural isomorphism `F.leftDerived 0 ≅ F`.
+We define the left-derived functors `F.leftDerived n : C ⥤ D` for any additive functor `F`
+out of a category with projective resolutions.
 
-## Main definitions
+We first define a functor
+`F.leftDerivedToHomotopyCategory : C ⥤ HomotopyCategory D (ComplexShape.down ℕ)` which is
+`projectiveResolutions C ⋙ F.mapHomotopyCategory _`. We show that if `X : C` and
+`P : ProjectiveResolution X`, then `F.leftDerivedToHomotopyCategory.obj X` identifies
+to the image in the homotopy category of the functor `F` applied objectwise to `P.complex`
+(this isomorphism is `P.isoLeftDerivedToHomotopyCategoryObj F`).
 
-* `CategoryTheory.Abelian.Functor.leftDerivedZeroIsoSelf`: the natural isomorphism
-  `(F.leftDerived 0) ≅ F`.
+Then, the left-derived functors `F.leftDerived n : C ⥤ D` are obtained by composing
+`F.leftDerivedToHomotopyCategory` with the homology functors on the homotopy category.
+
+Similarly we define natural transformations between left-derived functors coming from
+natural transformations between the original additive functors,
+and show how to compute the components.
 
 ## Main results
-* `preserves_exact_of_PreservesFiniteColimits_of_epi`: if `PreservesFiniteColimits F` and
-  `Epi g`, then `Exact (F.map f) (F.map g)` if `exact f g`.
+* `Functor.isZero_leftDerived_obj_projective_succ`: projective objects have no higher
+  left derived functor.
+* `NatTrans.leftDerived`: the natural isomorphism between left derived functors
+  induced by natural transformation.
+* `Functor.fromLeftDerivedZero`: the natural transformation `F.leftDerived 0 ⟶ F`,
+  which is an isomorphism when `F` is right exact (i.e. preserves finite colimits),
+  see also `Functor.leftDerivedZeroIsoSelf`.
+-/
+
+universe v u
+
+namespace CategoryTheory
+
+open Category Limits
+
+variable {C : Type u} [Category.{v} C] {D : Type*} [Category D]
+  [Abelian C] [HasProjectiveResolutions C] [Abelian D]
+
+/-- When `F : C ⥤ D` is an additive functor, this is
+the functor `C ⥤ HomotopyCategory D (ComplexShape.down ℕ)` which
+sends `X : C` to `F` applied to a projective resolution of `X`. -/
+noncomputable def Functor.leftDerivedToHomotopyCategory (F : C ⥤ D) [F.Additive] :
+    C ⥤ HomotopyCategory D (ComplexShape.down ℕ) :=
+  projectiveResolutions C ⋙ F.mapHomotopyCategory _
+
+/-- If `P : ProjectiveResolution Z` and `F : C ⥤ D` is an additive functor, this is
+an isomorphism between `F.leftDerivedToHomotopyCategory.obj X` and the complex
+obtained by applying `F` to `P.complex`. -/
+noncomputable def ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj {X : C}
+    (P : ProjectiveResolution X) (F : C ⥤ D) [F.Additive] :
+    F.leftDerivedToHomotopyCategory.obj X ≅
+      (F.mapHomologicalComplex _ ⋙ HomotopyCategory.quotient _ _).obj P.complex :=
+  (F.mapHomotopyCategory _).mapIso P.iso ≪≫
+    (F.mapHomotopyCategoryFactors _).app P.complex
+
+@[reassoc]
+lemma ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_inv_naturality
+    {X Y : C} (f : X ⟶ Y) (P : ProjectiveResolution X) (Q : ProjectiveResolution Y)
+    (φ : P.complex ⟶ Q.complex) (comm : φ.f 0 ≫ Q.π.f 0 = P.π.f 0 ≫ f)
+    (F : C ⥤ D) [F.Additive] :
+    (P.isoLeftDerivedToHomotopyCategoryObj F).inv ≫ F.leftDerivedToHomotopyCategory.map f =
+      (F.mapHomologicalComplex _ ⋙ HomotopyCategory.quotient _ _).map φ ≫
+        (Q.isoLeftDerivedToHomotopyCategoryObj F).inv := by
+  dsimp [Functor.leftDerivedToHomotopyCategory, isoLeftDerivedToHomotopyCategoryObj]
+  rw [assoc, ← Functor.map_comp, iso_inv_naturality f P Q φ comm, Functor.map_comp]
+  erw [(F.mapHomotopyCategoryFactors (ComplexShape.down ℕ)).inv.naturality_assoc]
+  rfl
+
+@[reassoc]
+lemma ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_hom_naturality
+    {X Y : C} (f : X ⟶ Y) (P : ProjectiveResolution X) (Q : ProjectiveResolution Y)
+    (φ : P.complex ⟶ Q.complex) (comm : φ.f 0 ≫ Q.π.f 0 = P.π.f 0 ≫ f)
+    (F : C ⥤ D) [F.Additive] :
+    F.leftDerivedToHomotopyCategory.map f ≫ (Q.isoLeftDerivedToHomotopyCategoryObj F).hom =
+      (P.isoLeftDerivedToHomotopyCategoryObj F).hom ≫
+        (F.mapHomologicalComplex _ ⋙ HomotopyCategory.quotient _ _).map φ := by
+    dsimp
+    rw [← cancel_epi (P.isoLeftDerivedToHomotopyCategoryObj F).inv, Iso.inv_hom_id_assoc,
+      isoLeftDerivedToHomotopyCategoryObj_inv_naturality_assoc f P Q φ comm F,
+      Iso.inv_hom_id, comp_id]
+
+/-- The left derived functors of an additive functor. -/
+noncomputable def Functor.leftDerived (F : C ⥤ D) [F.Additive] (n : ℕ) : C ⥤ D :=
+  F.leftDerivedToHomotopyCategory ⋙ HomotopyCategory.homologyFunctor D _ n
+#align category_theory.functor.left_derived CategoryTheory.Functor.leftDerived
 
+/-- We can compute a left derived functor using a chosen projective resolution. -/
+noncomputable def ProjectiveResolution.isoLeftDerivedObj {X : C} (P : ProjectiveResolution X)
+    (F : C ⥤ D) [F.Additive] (n : ℕ) :
+    (F.leftDerived n).obj X ≅
+      (HomologicalComplex.homologyFunctor D _ n).obj
+        ((F.mapHomologicalComplex _).obj P.complex) :=
+  (HomotopyCategory.homologyFunctor D _ n).mapIso
+    (P.isoLeftDerivedToHomotopyCategoryObj F) ≪≫
+    (HomotopyCategory.homologyFunctorFactors D (ComplexShape.down ℕ) n).app _
+
+@[reassoc]
+lemma ProjectiveResolution.isoLeftDerivedObj_hom_naturality
+    {X Y : C} (f : X ⟶ Y) (P : ProjectiveResolution X) (Q : ProjectiveResolution Y)
+    (φ : P.complex ⟶ Q.complex) (comm : φ.f 0 ≫ Q.π.f 0 = P.π.f 0 ≫ f)
+    (F : C ⥤ D) [F.Additive] (n : ℕ) :
+    (F.leftDerived n).map f ≫ (Q.isoLeftDerivedObj F n).hom =
+      (P.isoLeftDerivedObj F n).hom ≫
+        (F.mapHomologicalComplex _ ⋙ HomologicalComplex.homologyFunctor _ _ n).map φ := by
+  dsimp [isoLeftDerivedObj, Functor.leftDerived]
+  rw [assoc, ← Functor.map_comp_assoc,
+    ProjectiveResolution.isoLeftDerivedToHomotopyCategoryObj_hom_naturality f P Q φ comm F,
+    Functor.map_comp, assoc]
+  erw [(HomotopyCategory.homologyFunctorFactors D (ComplexShape.down ℕ) n).hom.naturality]
+  rfl
+
+@[reassoc]
+lemma ProjectiveResolution.isoLeftDerivedObj_inv_naturality
+    {X Y : C} (f : X ⟶ Y) (P : ProjectiveResolution X) (Q : ProjectiveResolution Y)
+    (φ : P.complex ⟶ Q.complex) (comm : φ.f 0 ≫ Q.π.f 0 = P.π.f 0 ≫ f)
+    (F : C ⥤ D) [F.Additive] (n : ℕ) :
+    (P.isoLeftDerivedObj F n).inv ≫ (F.leftDerived n).map f =
+        (F.mapHomologicalComplex _ ⋙ HomologicalComplex.homologyFunctor _ _ n).map φ ≫
+          (Q.isoLeftDerivedObj F n).inv := by
+  rw [← cancel_mono (Q.isoLeftDerivedObj F n).hom, assoc, assoc,
+    ProjectiveResolution.isoLeftDerivedObj_hom_naturality f P Q φ comm F n,
+    Iso.inv_hom_id_assoc, Iso.inv_hom_id, comp_id]
+
+/-- The higher derived functors vanish on projective objects. -/
+lemma Functor.isZero_leftDerived_obj_projective_succ
+    (F : C ⥤ D) [F.Additive] (n : ℕ) (X : C) [Projective X] :
+    IsZero ((F.leftDerived (n + 1)).obj X) := by
+  refine IsZero.of_iso ?_ ((ProjectiveResolution.self X).isoLeftDerivedObj 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 left derived functor on a morphism using a descent of that morphism
+to a chain map between chosen projective resolutions.
 -/
+theorem Functor.leftDerived_map_eq (F : C ⥤ D) [F.Additive] (n : ℕ) {X Y : C} (f : X ⟶ Y)
+    {P : ProjectiveResolution X} {Q : ProjectiveResolution Y} (g : P.complex ⟶ Q.complex)
+    (w : g ≫ Q.π = P.π ≫ (ChainComplex.single₀ C).map f) :
+    (F.leftDerived n).map f =
+      (P.isoLeftDerivedObj F n).hom ≫
+        (F.mapHomologicalComplex _ ⋙ HomologicalComplex.homologyFunctor _ _ n).map g ≫
+          (Q.isoLeftDerivedObj F n).inv := by
+  rw [← cancel_mono (Q.isoLeftDerivedObj F n).hom,
+    ProjectiveResolution.isoLeftDerivedObj_hom_naturality f P Q g _ F n,
+    assoc, assoc, Iso.inv_hom_id, comp_id]
+  rw [← HomologicalComplex.comp_f, w, HomologicalComplex.comp_f,
+    ChainComplex.single₀_map_f_zero]
+#align category_theory.functor.left_derived_map_eq CategoryTheory.Functor.leftDerived_map_eq
+
+/-- The natural transformation
+`F.leftDerivedToHomotopyCategory ⟶ G.leftDerivedToHomotopyCategory` induced by
+a natural transformation `F ⟶ G` between additive functors. -/
+noncomputable def NatTrans.leftDerivedToHomotopyCategory
+    {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶ G) :
+    F.leftDerivedToHomotopyCategory ⟶ G.leftDerivedToHomotopyCategory :=
+  whiskerLeft _ (NatTrans.mapHomotopyCategory α (ComplexShape.down ℕ))
+
+lemma ProjectiveResolution.leftDerivedToHomotopyCategory_app_eq
+    {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶ G) {X : C} (P : ProjectiveResolution X) :
+    (NatTrans.leftDerivedToHomotopyCategory α).app X =
+      (P.isoLeftDerivedToHomotopyCategoryObj F).hom ≫
+        (HomotopyCategory.quotient _ _).map
+          ((NatTrans.mapHomologicalComplex α _).app P.complex) ≫
+          (P.isoLeftDerivedToHomotopyCategoryObj G).inv := by
+  rw [← cancel_mono (P.isoLeftDerivedToHomotopyCategoryObj G).hom, assoc, assoc,
+      Iso.inv_hom_id, comp_id]
+  dsimp [isoLeftDerivedToHomotopyCategoryObj, Functor.mapHomotopyCategoryFactors,
+    NatTrans.leftDerivedToHomotopyCategory]
+  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.leftDerivedToHomotopyCategory_id (F : C ⥤ D) [F.Additive] :
+    NatTrans.leftDerivedToHomotopyCategory (𝟙 F) = 𝟙 _ := rfl
+
+@[simp, reassoc]
+lemma NatTrans.leftDerivedToHomotopyCategory_comp {F G H : C ⥤ D} (α : F ⟶ G) (β : G ⟶ H)
+    [F.Additive] [G.Additive] [H.Additive] :
+    NatTrans.leftDerivedToHomotopyCategory (α ≫ β) =
+      NatTrans.leftDerivedToHomotopyCategory α ≫
+        NatTrans.leftDerivedToHomotopyCategory β := rfl
+
+/-- The natural transformation between left-derived functors induced by a natural transformation.-/
+noncomputable def NatTrans.leftDerived
+    {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶ G) (n : ℕ) :
+    F.leftDerived n ⟶ G.leftDerived n :=
+  whiskerRight (NatTrans.leftDerivedToHomotopyCategory α) _
+#align category_theory.nat_trans.left_derived CategoryTheory.NatTrans.leftDerived
+
+@[simp]
+theorem NatTrans.leftDerived_id (F : C ⥤ D) [F.Additive] (n : ℕ) :
+    NatTrans.leftDerived (𝟙 F) n = 𝟙 (F.leftDerived n) := by
+  dsimp only [leftDerived]
+  simp only [leftDerivedToHomotopyCategory_id, whiskerRight_id']
+  rfl
+#align category_theory.nat_trans.left_derived_id CategoryTheory.NatTrans.leftDerived_id
+
+@[simp, reassoc]
+theorem NatTrans.leftDerived_comp {F G H : C ⥤ D} [F.Additive] [G.Additive] [H.Additive]
+    (α : F ⟶ G) (β : G ⟶ H) (n : ℕ) :
+    NatTrans.leftDerived (α ≫ β) n = NatTrans.leftDerived α n ≫ NatTrans.leftDerived β n := by
+  simp [NatTrans.leftDerived]
+#align category_theory.nat_trans.left_derived_comp CategoryTheory.NatTrans.leftDerived_comp
+
+namespace ProjectiveResolution
+
+/-- A component of the natural transformation between left-derived functors can be computed
+using a chosen projective resolution. -/
+lemma leftDerived_app_eq
+    {F G : C ⥤ D} [F.Additive] [G.Additive] (α : F ⟶ G) {X : C} (P : ProjectiveResolution X)
+    (n : ℕ) : (NatTrans.leftDerived α n).app X =
+      (P.isoLeftDerivedObj F n).hom ≫
+        (HomologicalComplex.homologyFunctor D (ComplexShape.down ℕ) n).map
+        ((NatTrans.mapHomologicalComplex α _).app P.complex) ≫
+        (P.isoLeftDerivedObj G n).inv := by
+  dsimp [NatTrans.leftDerived, isoLeftDerivedObj]
+  rw [ProjectiveResolution.leftDerivedToHomotopyCategory_app_eq α P,
+    Functor.map_comp, Functor.map_comp, assoc]
+  erw [← (HomotopyCategory.homologyFunctorFactors D (ComplexShape.down ℕ) n).hom.naturality_assoc
+    ((NatTrans.mapHomologicalComplex α (ComplexShape.down ℕ)).app P.complex)]
+  simp only [Functor.comp_map, Iso.hom_inv_id_app_assoc]
+
+/-- If `P : ProjectiveResolution X` and `F` is an additive functor, this is
+the canonical morphism from the opcycles in degree `0` of
+`(F.mapHomologicalComplex _).obj P.complex` to `F.obj X`. -/
+noncomputable def fromLeftDerivedZero' {X : C}
+    (P : ProjectiveResolution X) (F : C ⥤ D) [F.Additive] :
+    ((F.mapHomologicalComplex _).obj P.complex).opcycles 0 ⟶ F.obj X :=
+  HomologicalComplex.descOpcycles _ (F.map (P.π.f 0)) 1 (by simp) (by
+    dsimp
+    rw [← F.map_comp, complex_d_comp_π_f_zero, F.map_zero])
+
+@[reassoc (attr := simp)]
+lemma pOpcycles_comp_fromLeftDerivedZero' {X : C}
+    (P : ProjectiveResolution X) (F : C ⥤ D) [F.Additive] :
+    HomologicalComplex.pOpcycles _ _ ≫ P.fromLeftDerivedZero' F = F.map (P.π.f 0) := by
+  simp [fromLeftDerivedZero']
+
+@[reassoc]
+lemma fromLeftDerivedZero'_naturality {X Y : C} (f : X ⟶ Y)
+    (P : ProjectiveResolution X) (Q : ProjectiveResolution Y)
+    (φ : P.complex ⟶ Q.complex) (comm : φ.f 0 ≫ Q.π.f 0 = P.π.f 0 ≫ f)
+    (F : C ⥤ D) [F.Additive] :
+    HomologicalComplex.opcyclesMap ((F.mapHomologicalComplex _).map φ) 0 ≫
+        Q.fromLeftDerivedZero' F = P.fromLeftDerivedZero' F ≫ F.map f := by
+  simp only [← cancel_epi (HomologicalComplex.pOpcycles _ _), ← F.map_comp, comm,
+    HomologicalComplex.p_opcyclesMap_assoc, Functor.mapHomologicalComplex_map_f,
+    pOpcycles_comp_fromLeftDerivedZero', pOpcycles_comp_fromLeftDerivedZero'_assoc]
+
+instance (F : C ⥤ D) [F.Additive] (X : C) [Projective X] :
+    IsIso ((ProjectiveResolution.self X).fromLeftDerivedZero' F) := by
+  dsimp [ProjectiveResolution.fromLeftDerivedZero']
+  rw [ChainComplex.isIso_descOpcycles_iff]
+  refine' ⟨ShortComplex.Splitting.exact _, inferInstance⟩
+  exact
+    { r := 0
+      s := 𝟙 _
+      f_r := (F.map_isZero (isZero_zero _)).eq_of_src _ _ }
+
+end ProjectiveResolution
+
+/-- The natural transformation `F.leftDerived 0 ⟶ F`. -/
+noncomputable def Functor.fromLeftDerivedZero (F : C ⥤ D) [F.Additive] :
+    F.leftDerived 0 ⟶ F where
+  app X := (HomotopyCategory.homologyFunctorFactors D (ComplexShape.down ℕ) 0).hom.app _ ≫
+      (ChainComplex.isoHomologyι₀ _).hom ≫ (projectiveResolution X).fromLeftDerivedZero' F
+  naturality {X Y} f := by
+    dsimp [leftDerived]
+    rw [assoc, assoc, ← ProjectiveResolution.fromLeftDerivedZero'_naturality f
+      (projectiveResolution X) (projectiveResolution Y)
+      (ProjectiveResolution.lift f _ _) (by simp),
+      ← HomologicalComplex.homologyι_naturality_assoc]
+    erw [← NatTrans.naturality_assoc]
+    rfl
+
+lemma ProjectiveResolution.fromLeftDerivedZero_eq
+    {X : C} (P : ProjectiveResolution X) (F : C ⥤ D) [F.Additive] :
+    F.fromLeftDerivedZero.app X = (P.isoLeftDerivedObj F 0).hom ≫
+      (ChainComplex.isoHomologyι₀ _).hom ≫
+        P.fromLeftDerivedZero' F := by
+  dsimp [Functor.fromLeftDerivedZero, isoLeftDerivedObj]
+  have h₁ := ProjectiveResolution.fromLeftDerivedZero'_naturality
+    (𝟙 X) P (projectiveResolution X) (lift (𝟙 X) _ _) (by simp) F
+  have h₂ : (P.isoLeftDerivedToHomotopyCategoryObj F).inv =
+    (F.mapHomologicalComplex _ ⋙ HomotopyCategory.quotient _ _).map (lift (𝟙 X) _ _) :=
+      id_comp _
+  simp only [Functor.map_id, comp_id] at h₁
+  rw [assoc, ← cancel_epi ((HomotopyCategory.homologyFunctor _ _ 0).map
+      (P.isoLeftDerivedToHomotopyCategoryObj F).inv), ← Functor.map_comp_assoc,
+      Iso.inv_hom_id, Functor.map_id, id_comp, ← h₁, h₂,
+      ← HomologicalComplex.homologyι_naturality_assoc]
+  erw [← NatTrans.naturality_assoc]
+  rfl
+
+instance (F : C ⥤ D) [F.Additive] (X : C) [Projective X] :
+    IsIso (F.fromLeftDerivedZero.app X) := by
+  rw [(ProjectiveResolution.self X).fromLeftDerivedZero_eq F]
+  infer_instance
+
+section
+
+variable (F : C ⥤ D) [F.Additive] [PreservesFiniteColimits F]
+
+instance {X : C} (P : ProjectiveResolution X) :
+    IsIso (P.fromLeftDerivedZero' F) := by
+  dsimp [ProjectiveResolution.fromLeftDerivedZero']
+  rw [ChainComplex.isIso_descOpcycles_iff, ShortComplex.exact_and_epi_g_iff_g_is_cokernel]
+  exact ⟨CokernelCofork.mapIsColimit _ (P.isColimitCokernelCofork) F⟩
+
+instance (X : C) : IsIso (F.fromLeftDerivedZero.app X) := by
+  dsimp [Functor.fromLeftDerivedZero]
+  infer_instance
+
+instance : IsIso F.fromLeftDerivedZero :=
+  NatIso.isIso_of_isIso_app _
+
+namespace Functor
+
+/-- The canonical isomorphism `F.leftDerived 0 ≅ F` when `F` is right exact
+(i.e. preserves finite colimits). -/
+@[simps! hom]
+noncomputable def leftDerivedZeroIsoSelf : F.leftDerived 0 ≅ F :=
+  (asIso F.fromLeftDerivedZero)
+
+@[reassoc (attr := simp)]
+lemma leftDerivedZeroIsoSelf_hom_inv_id :
+    F.fromLeftDerivedZero ≫ F.leftDerivedZeroIsoSelf.inv = 𝟙 _ :=
+  F.leftDerivedZeroIsoSelf.hom_inv_id
+
+@[reassoc (attr := simp)]
+lemma leftDerivedZeroIsoSelf_inv_hom_id :
+    F.leftDerivedZeroIsoSelf.inv ≫ F.fromLeftDerivedZero =  𝟙 _ :=
+  F.leftDerivedZeroIsoSelf.inv_hom_id
+
+@[reassoc (attr := simp)]
+lemma leftDerivedZeroIsoSelf_hom_inv_id_app (X : C) :
+    F.fromLeftDerivedZero.app X ≫ F.leftDerivedZeroIsoSelf.inv.app X = 𝟙 _ :=
+  F.leftDerivedZeroIsoSelf.hom_inv_id_app X
+
+@[reassoc (attr := simp)]
+lemma leftDerivedZeroIsoSelf_inv_hom_id_app (X : C) :
+    F.leftDerivedZeroIsoSelf.inv.app X ≫ F.fromLeftDerivedZero.app X = 𝟙 _ :=
+  F.leftDerivedZeroIsoSelf.inv_hom_id_app X
+
+end Functor
 
+end
 
-noncomputable 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 `PreservesFiniteColimits F` and `Epi g`, then `Exact (F.map f) (F.map g)` if
-`Exact f g`. -/
-theorem preserves_exact_of_PreservesFiniteColimits_of_epi [PreservesFiniteColimits F] [Epi g]
-    (ex : Exact f g) : Exact (F.map f) (F.map g) :=
-  Abelian.exact_of_is_cokernel _ _ (by simp [← Functor.map_comp, ex.w]) <|
-    Limits.isColimitCoforkMapOfIsColimit' _ ex.w (Abelian.isColimitOfExactOfEpi _ _ ex)
-#align category_theory.abelian.functor.preserves_exact_of_preserves_finite_colimits_of_epi CategoryTheory.Abelian.Functor.preserves_exact_of_PreservesFiniteColimits_of_epi
-
-theorem exact_of_map_projectiveResolution (P : ProjectiveResolution X)
-    [PreservesFiniteColimits F] :
-    Exact (((F.mapHomologicalComplex (ComplexShape.down ℕ)).obj P.complex).dTo 0)
-      (F.map (P.π.f 0)) :=
-  Preadditive.exact_of_iso_of_exact' (F.map (P.complex.d 1 0)) (F.map (P.π.f 0)) _ _
-    (HomologicalComplex.xPrevIso ((F.mapHomologicalComplex _).obj P.complex) rfl).symm (Iso.refl _)
-    (Iso.refl _) (by
-      -- Porting note: simp used to be able to do this
-      simp only [Iso.symm_hom, HomologicalComplex.xPrevIso_comp_dTo]
-      simp only [mapHomologicalComplex_obj_d, Iso.refl_hom, Category.comp_id]
-      rfl) (by simp) (preserves_exact_of_PreservesFiniteColimits_of_epi _ P.exact₀)
-#align category_theory.abelian.functor.exact_of_map_projective_resolution CategoryTheory.Abelian.Functor.exact_of_map_projectiveResolution
-
-/-- Given `P : ProjectiveResolution X`, a morphism `(F.leftDerived 0).obj X ⟶ F.obj X`. -/
-def leftDerivedZeroToSelfApp [EnoughProjectives C] {X : C} (P : ProjectiveResolution X) :
-    (F.leftDerived 0).obj X ⟶ F.obj X :=
-  (leftDerivedObjIso F 0 P).hom ≫
-    homology'.desc' _ _ _ (kernel.ι _ ≫ F.map (P.π.f 0))
-      (by
-        rw [kernel.lift_ι_assoc,
-          HomologicalComplex.dTo_eq _ (by simp : (ComplexShape.down ℕ).Rel 1 0),
-          mapHomologicalComplex_obj_d, Category.assoc, ← Functor.map_comp]
-        simp)
-#align category_theory.abelian.functor.left_derived_zero_to_self_app CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfApp
-
-/-- Given `P : ProjectiveResolution X`, a morphism `F.obj X ⟶ (F.leftDerived 0).obj X` given
-`PreservesFiniteColimits F`. -/
-def leftDerivedZeroToSelfAppInv [EnoughProjectives C] [PreservesFiniteColimits F] {X : C}
-    (P : ProjectiveResolution X) : F.obj X ⟶ (F.leftDerived 0).obj X := by
-  -- Porting note: this is no longer an instance
-  have := isIso_cokernel_desc_of_exact_of_epi _ _ (exact_of_map_projectiveResolution F P)
-  refine'
-    (asIso (cokernel.desc _ _ (exact_of_map_projectiveResolution F P).w)).inv ≫
-      _ ≫ (homology'IsoCokernelLift _ _ _).inv ≫ (leftDerivedObjIso F 0 P).inv
-  refine' cokernel.map _ _ (𝟙 _) (kernel.lift _ (𝟙 _) (by simp)) _
-  ext
-  -- Porting note: this used to just be `simp`
-  simp only [Category.assoc, kernel.lift_ι, Category.comp_id, Category.id_comp]
-#align category_theory.abelian.functor.left_derived_zero_to_self_app_inv CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppInv
-
-theorem leftDerivedZeroToSelfApp_comp_inv [EnoughProjectives C] [PreservesFiniteColimits F] {X : C}
-    (P : ProjectiveResolution X) :
-    leftDerivedZeroToSelfApp F P ≫ leftDerivedZeroToSelfAppInv F P = 𝟙 _ := by
-  dsimp [leftDerivedZeroToSelfApp, leftDerivedZeroToSelfAppInv]
-  rw [← Category.assoc, ← Category.assoc, ← Category.assoc, Iso.comp_inv_eq]
-  -- Porting note: working around 'motive is not type correct'
-  simp only [Category.id_comp]
-  rw [Category.assoc, Category.assoc, Category.assoc]
-  convert Category.comp_id (leftDerivedObjIso F 0 P).hom
-  rw [← Category.assoc, ← Category.assoc, Iso.comp_inv_eq]
-  -- Porting note: broken ext
-  apply homology'.hom_from_ext
-  simp only [← Category.assoc]
-  erw [homology'.π'_desc', Category.assoc, Category.assoc, ←
-    Category.assoc (F.map _), Abelian.cokernel.desc.inv _ _ (exact_of_map_projectiveResolution F P),
-    cokernel.π_desc, homology'.π', Category.comp_id, Category.assoc (cokernel.π _), Iso.inv_hom_id,
-    Category.comp_id, ← Category.assoc]
-  -- Porting note: restructured proof to avoid `convert`
-  conv_rhs => rw [← Category.id_comp (cokernel.π _)]
-  congr
-  ext
-  -- Porting note: working around 'motive is not type correct'
-  simp only [Category.id_comp]
-  rw [Category.assoc, equalizer_as_kernel, kernel.lift_ι]
-  simp only [Category.comp_id]
-#align category_theory.abelian.functor.left_derived_zero_to_self_app_comp_inv CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfApp_comp_inv
-
--- Porting note: linter thinks the `have` below is unused, but removing it makes a typeclass
--- search fail
-@[nolint unusedHavesSuffices]
-theorem leftDerivedZeroToSelfAppInv_comp [EnoughProjectives C] [PreservesFiniteColimits F] {X : C}
-    (P : ProjectiveResolution X) :
-    leftDerivedZeroToSelfAppInv F P ≫ leftDerivedZeroToSelfApp F P = 𝟙 _ := by
-  dsimp [leftDerivedZeroToSelfApp, leftDerivedZeroToSelfAppInv]
-  rw [Category.assoc, Category.assoc]
-  -- Porting note: working around 'motive is not type correct'
-  simp only [Category.assoc]
-  rw [← Category.assoc (F.leftDerivedObjIso 0 P).inv, Iso.inv_hom_id]
-  -- Porting note: working around 'motive is not type correct'
-  simp only [Category.id_comp]
-  -- Porting note: instance not found even though it is present in the goal
-  have : IsIso (cokernel.desc (F.map
-    (HomologicalComplex.d P.complex (ComplexShape.prev (ComplexShape.down ℕ) 0) 0))
-      (F.map (HomologicalComplex.Hom.f P.π 0)) (exact_of_map_projectiveResolution F P).w) :=
-    isIso_cokernel_desc_of_exact_of_epi _ _ (exact_of_map_projectiveResolution F P)
-  rw [IsIso.inv_comp_eq]
-  -- Porting note: working around 'motive is not type correct'
-  simp only [Category.comp_id]
-  ext
-  simp only [cokernel.π_desc_assoc, Category.assoc, cokernel.π_desc, homology'.desc']
-  rw [← Category.assoc, ← Category.assoc (homology'IsoCokernelLift _ _ _).inv, Iso.inv_hom_id]
-  simp only [Category.assoc, cokernel.π_desc, kernel.lift_ι_assoc, Category.id_comp]
-#align category_theory.abelian.functor.left_derived_zero_to_self_app_inv_comp CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppInv_comp
-
-/-- Given `P : ProjectiveResolution X`, the isomorphism `(F.leftDerived 0).obj X ≅ F.obj X` if
-`PreservesFiniteColimits F`. -/
-def leftDerivedZeroToSelfAppIso [EnoughProjectives C] [PreservesFiniteColimits F] {X : C}
-    (P : ProjectiveResolution X) : (F.leftDerived 0).obj X ≅ F.obj X where
-  hom := leftDerivedZeroToSelfApp _ P
-  inv := leftDerivedZeroToSelfAppInv _ P
-  hom_inv_id := leftDerivedZeroToSelfApp_comp_inv _ P
-  inv_hom_id := leftDerivedZeroToSelfAppInv_comp _ P
-#align category_theory.abelian.functor.left_derived_zero_to_self_app_iso CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppIso
-
-/-- Given `P : ProjectiveResolution X` and `Q : ProjectiveResolution Y` and a morphism `f : X ⟶ Y`,
-naturality of the square given by `leftDerived_zero_to_self_obj_hom`. -/
-theorem leftDerived_zero_to_self_natural [EnoughProjectives C] {X : C} {Y : C} (f : X ⟶ Y)
-    (P : ProjectiveResolution X) (Q : ProjectiveResolution Y) :
-    (F.leftDerived 0).map f ≫ leftDerivedZeroToSelfApp F Q =
-      leftDerivedZeroToSelfApp F P ≫ F.map f := by
-  dsimp only [leftDerivedZeroToSelfApp]
-  rw [Functor.leftDerived_map_eq F 0 f (ProjectiveResolution.lift f P Q) (by simp), Category.assoc,
-    Category.assoc, ← Category.assoc _ (F.leftDerivedObjIso 0 Q).hom, Iso.inv_hom_id,
-    Category.id_comp, Category.assoc, whisker_eq]
-  dsimp only [homology'Functor_map]
-  -- Porting note: broken ext
-  apply homology'.hom_from_ext
-  simp only [HomologicalComplex.Hom.sqTo_right, mapHomologicalComplex_map_f,
-    homology'.π'_map_assoc, homology'.π'_desc', kernel.lift_ι_assoc, Category.assoc,
-    homology'.π'_desc'_assoc, ← map_comp,
-    ProjectiveResolution.lift_commutes_zero f P Q]
-#align category_theory.abelian.functor.left_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.leftDerived_zero_to_self_natural
-
-/-- Given `PreservesFiniteColimits F`, the natural isomorphism `(F.leftDerived 0) ≅ F`. -/
-def leftDerivedZeroIsoSelf [EnoughProjectives C] [PreservesFiniteColimits F] :
-    F.leftDerived 0 ≅ F :=
-  NatIso.ofComponents (fun X => leftDerivedZeroToSelfAppIso _ (ProjectiveResolution.of X))
-    fun {_ _} _ => leftDerived_zero_to_self_natural _ _ _ _
-#align category_theory.abelian.functor.left_derived_zero_iso_self CategoryTheory.Abelian.Functor.leftDerivedZeroIsoSelf
-
-end CategoryTheory.Abelian.Functor
+end CategoryTheory

8001ea54

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

@@ -172,8 +172,7 @@ theorem leftDerived_zero_to_self_natural [EnoughProjectives C] {X : C} {Y : C} (
   simp only [HomologicalComplex.Hom.sqTo_right, mapHomologicalComplex_map_f,
     homology'.π'_map_assoc, homology'.π'_desc', kernel.lift_ι_assoc, Category.assoc,
     homology'.π'_desc'_assoc, ← map_comp,
-    show (ProjectiveResolution.lift f P Q).f 0 ≫ _ = _ ≫ f from
-      HomologicalComplex.congr_hom (ProjectiveResolution.lift_commutes f P Q) 0]
+    ProjectiveResolution.lift_commutes_zero f P Q]
 #align category_theory.abelian.functor.left_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.leftDerived_zero_to_self_natural
 
 /-- Given `PreservesFiniteColimits F`, the natural isomorphism `(F.leftDerived 0) ≅ F`. -/

8001ea54

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

@@ -69,7 +69,7 @@ theorem exact_of_map_projectiveResolution (P : ProjectiveResolution X)
 def leftDerivedZeroToSelfApp [EnoughProjectives C] {X : C} (P : ProjectiveResolution X) :
     (F.leftDerived 0).obj X ⟶ F.obj X :=
   (leftDerivedObjIso F 0 P).hom ≫
-    homology.desc' _ _ _ (kernel.ι _ ≫ F.map (P.π.f 0))
+    homology'.desc' _ _ _ (kernel.ι _ ≫ F.map (P.π.f 0))
       (by
         rw [kernel.lift_ι_assoc,
           HomologicalComplex.dTo_eq _ (by simp : (ComplexShape.down ℕ).Rel 1 0),
@@ -85,7 +85,7 @@ def leftDerivedZeroToSelfAppInv [EnoughProjectives C] [PreservesFiniteColimits F
   have := isIso_cokernel_desc_of_exact_of_epi _ _ (exact_of_map_projectiveResolution F P)
   refine'
     (asIso (cokernel.desc _ _ (exact_of_map_projectiveResolution F P).w)).inv ≫
-      _ ≫ (homologyIsoCokernelLift _ _ _).inv ≫ (leftDerivedObjIso F 0 P).inv
+      _ ≫ (homology'IsoCokernelLift _ _ _).inv ≫ (leftDerivedObjIso F 0 P).inv
   refine' cokernel.map _ _ (𝟙 _) (kernel.lift _ (𝟙 _) (by simp)) _
   ext
   -- Porting note: this used to just be `simp`
@@ -103,11 +103,11 @@ theorem leftDerivedZeroToSelfApp_comp_inv [EnoughProjectives C] [PreservesFinite
   convert Category.comp_id (leftDerivedObjIso F 0 P).hom
   rw [← Category.assoc, ← Category.assoc, Iso.comp_inv_eq]
   -- Porting note: broken ext
-  apply homology.hom_from_ext
+  apply homology'.hom_from_ext
   simp only [← Category.assoc]
-  erw [homology.π'_desc', Category.assoc, Category.assoc, ←
+  erw [homology'.π'_desc', Category.assoc, Category.assoc, ←
     Category.assoc (F.map _), Abelian.cokernel.desc.inv _ _ (exact_of_map_projectiveResolution F P),
-    cokernel.π_desc, homology.π', Category.comp_id, Category.assoc (cokernel.π _), Iso.inv_hom_id,
+    cokernel.π_desc, homology'.π', Category.comp_id, Category.assoc (cokernel.π _), Iso.inv_hom_id,
     Category.comp_id, ← Category.assoc]
   -- Porting note: restructured proof to avoid `convert`
   conv_rhs => rw [← Category.id_comp (cokernel.π _)]
@@ -141,8 +141,8 @@ theorem leftDerivedZeroToSelfAppInv_comp [EnoughProjectives C] [PreservesFiniteC
   -- Porting note: working around 'motive is not type correct'
   simp only [Category.comp_id]
   ext
-  simp only [cokernel.π_desc_assoc, Category.assoc, cokernel.π_desc, homology.desc']
-  rw [← Category.assoc, ← Category.assoc (homologyIsoCokernelLift _ _ _).inv, Iso.inv_hom_id]
+  simp only [cokernel.π_desc_assoc, Category.assoc, cokernel.π_desc, homology'.desc']
+  rw [← Category.assoc, ← Category.assoc (homology'IsoCokernelLift _ _ _).inv, Iso.inv_hom_id]
   simp only [Category.assoc, cokernel.π_desc, kernel.lift_ι_assoc, Category.id_comp]
 #align category_theory.abelian.functor.left_derived_zero_to_self_app_inv_comp CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppInv_comp
 
@@ -166,12 +166,12 @@ theorem leftDerived_zero_to_self_natural [EnoughProjectives C] {X : C} {Y : C} (
   rw [Functor.leftDerived_map_eq F 0 f (ProjectiveResolution.lift f P Q) (by simp), Category.assoc,
     Category.assoc, ← Category.assoc _ (F.leftDerivedObjIso 0 Q).hom, Iso.inv_hom_id,
     Category.id_comp, Category.assoc, whisker_eq]
-  dsimp only [homologyFunctor_map]
+  dsimp only [homology'Functor_map]
   -- Porting note: broken ext
-  apply homology.hom_from_ext
+  apply homology'.hom_from_ext
   simp only [HomologicalComplex.Hom.sqTo_right, mapHomologicalComplex_map_f,
-    homology.π'_map_assoc, homology.π'_desc', kernel.lift_ι_assoc, Category.assoc,
-    homology.π'_desc'_assoc, ← map_comp,
+    homology'.π'_map_assoc, homology'.π'_desc', kernel.lift_ι_assoc, Category.assoc,
+    homology'.π'_desc'_assoc, ← map_comp,
     show (ProjectiveResolution.lift f P Q).f 0 ≫ _ = _ ≫ f from
       HomologicalComplex.congr_hom (ProjectiveResolution.lift_commutes f P Q) 0]
 #align category_theory.abelian.functor.left_derived_zero_to_self_natural CategoryTheory.Abelian.Functor.leftDerived_zero_to_self_natural

8001ea54

chore: remove unused simps (#6632)

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

916c75c1

Diff

@@ -102,8 +102,6 @@ theorem leftDerivedZeroToSelfApp_comp_inv [EnoughProjectives C] [PreservesFinite
   rw [Category.assoc, Category.assoc, Category.assoc]
   convert Category.comp_id (leftDerivedObjIso F 0 P).hom
   rw [← Category.assoc, ← Category.assoc, Iso.comp_inv_eq]
-  -- Porting note: working around 'motive is not type correct'
-  simp only [Category.id_comp]
   -- Porting note: broken ext
   apply homology.hom_from_ext
   simp only [← Category.assoc]

8001ea54

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

@@ -2,17 +2,14 @@
 Copyright (c) 2022 Riccardo Brasca. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Riccardo Brasca, Adam Topaz
-
-! This file was ported from Lean 3 source module category_theory.abelian.left_derived
-! leanprover-community/mathlib commit 8001ea54ece3bd5c0d0932f1e4f6d0f142ea20d9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Abelian.Homology
 import Mathlib.CategoryTheory.Functor.LeftDerived
 import Mathlib.CategoryTheory.Abelian.Projective
 import Mathlib.CategoryTheory.Limits.Constructions.EpiMono
 
+#align_import category_theory.abelian.left_derived from "leanprover-community/mathlib"@"8001ea54ece3bd5c0d0932f1e4f6d0f142ea20d9"
+
 /-!
 # Zeroth left derived functors

8001ea54

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

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

dbae2f17

Diff

@@ -90,8 +90,8 @@ def leftDerivedZeroToSelfAppInv [EnoughProjectives C] [PreservesFiniteColimits F
     (asIso (cokernel.desc _ _ (exact_of_map_projectiveResolution F P).w)).inv ≫
       _ ≫ (homologyIsoCokernelLift _ _ _).inv ≫ (leftDerivedObjIso F 0 P).inv
   refine' cokernel.map _ _ (𝟙 _) (kernel.lift _ (𝟙 _) (by simp)) _
-  -- Porting note: this used to be ext ; simp
-  apply equalizer.hom_ext
+  ext
+  -- Porting note: this used to just be `simp`
   simp only [Category.assoc, kernel.lift_ι, Category.comp_id, Category.id_comp]
 #align category_theory.abelian.functor.left_derived_zero_to_self_app_inv CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppInv
 
@@ -117,7 +117,7 @@ theorem leftDerivedZeroToSelfApp_comp_inv [EnoughProjectives C] [PreservesFinite
   -- Porting note: restructured proof to avoid `convert`
   conv_rhs => rw [← Category.id_comp (cokernel.π _)]
   congr
-  apply equalizer.hom_ext
+  ext
   -- Porting note: working around 'motive is not type correct'
   simp only [Category.id_comp]
   rw [Category.assoc, equalizer_as_kernel, kernel.lift_ι]
@@ -145,7 +145,7 @@ theorem leftDerivedZeroToSelfAppInv_comp [EnoughProjectives C] [PreservesFiniteC
   rw [IsIso.inv_comp_eq]
   -- Porting note: working around 'motive is not type correct'
   simp only [Category.comp_id]
-  apply coequalizer.hom_ext
+  ext
   simp only [cokernel.π_desc_assoc, Category.assoc, cokernel.π_desc, homology.desc']
   rw [← Category.assoc, ← Category.assoc (homologyIsoCokernelLift _ _ _).inv, Iso.inv_hom_id]
   simp only [Category.assoc, cokernel.π_desc, kernel.lift_ι_assoc, Category.id_comp]

8001ea54

chore: fix backtick in docs (#5077)

I wrote a script to find lines that contain an odd number of backticks

878d95c4

Diff

@@ -162,7 +162,7 @@ def leftDerivedZeroToSelfAppIso [EnoughProjectives C] [PreservesFiniteColimits F
 #align category_theory.abelian.functor.left_derived_zero_to_self_app_iso CategoryTheory.Abelian.Functor.leftDerivedZeroToSelfAppIso
 
 /-- Given `P : ProjectiveResolution X` and `Q : ProjectiveResolution Y` and a morphism `f : X ⟶ Y`,
-naturality of the square given by `left_derived_zero_to_self_obj_hom. -/
+naturality of the square given by `leftDerived_zero_to_self_obj_hom`. -/
 theorem leftDerived_zero_to_self_natural [EnoughProjectives C] {X : C} {Y : C} (f : X ⟶ Y)
     (P : ProjectiveResolution X) (Q : ProjectiveResolution Y) :
     (F.leftDerived 0).map f ≫ leftDerivedZeroToSelfApp F Q =

8001ea54

chore: tidy various files (#4757)

ea80818c

Diff

@@ -47,15 +47,15 @@ open CategoryTheory.Preadditive
 
 variable [Abelian C] [Abelian D] [Additive F]
 
-/-- If `PreservesFiniteColimits F` and `epi g`, then `exact (F.map f) (F.map g)` if
-`exact f g`. -/
+/-- If `PreservesFiniteColimits F` and `Epi g`, then `Exact (F.map f) (F.map g)` if
+`Exact f g`. -/
 theorem preserves_exact_of_PreservesFiniteColimits_of_epi [PreservesFiniteColimits F] [Epi g]
     (ex : Exact f g) : Exact (F.map f) (F.map g) :=
   Abelian.exact_of_is_cokernel _ _ (by simp [← Functor.map_comp, ex.w]) <|
     Limits.isColimitCoforkMapOfIsColimit' _ ex.w (Abelian.isColimitOfExactOfEpi _ _ ex)
 #align category_theory.abelian.functor.preserves_exact_of_preserves_finite_colimits_of_epi CategoryTheory.Abelian.Functor.preserves_exact_of_PreservesFiniteColimits_of_epi
 
-theorem exact_of_map_ProjectiveResolution (P : ProjectiveResolution X)
+theorem exact_of_map_projectiveResolution (P : ProjectiveResolution X)
     [PreservesFiniteColimits F] :
     Exact (((F.mapHomologicalComplex (ComplexShape.down ℕ)).obj P.complex).dTo 0)
       (F.map (P.π.f 0)) :=
@@ -66,7 +66,7 @@ theorem exact_of_map_ProjectiveResolution (P : ProjectiveResolution X)
       simp only [Iso.symm_hom, HomologicalComplex.xPrevIso_comp_dTo]
       simp only [mapHomologicalComplex_obj_d, Iso.refl_hom, Category.comp_id]
       rfl) (by simp) (preserves_exact_of_PreservesFiniteColimits_of_epi _ P.exact₀)
-#align category_theory.abelian.functor.exact_of_map_projective_resolution CategoryTheory.Abelian.Functor.exact_of_map_ProjectiveResolution
+#align category_theory.abelian.functor.exact_of_map_projective_resolution CategoryTheory.Abelian.Functor.exact_of_map_projectiveResolution
 
 /-- Given `P : ProjectiveResolution X`, a morphism `(F.leftDerived 0).obj X ⟶ F.obj X`. -/
 def leftDerivedZeroToSelfApp [EnoughProjectives C] {X : C} (P : ProjectiveResolution X) :
@@ -85,9 +85,9 @@ def leftDerivedZeroToSelfApp [EnoughProjectives C] {X : C} (P : ProjectiveResolu
 def leftDerivedZeroToSelfAppInv [EnoughProjectives C] [PreservesFiniteColimits F] {X : C}
     (P : ProjectiveResolution X) : F.obj X ⟶ (F.leftDerived 0).obj X := by
   -- Porting note: this is no longer an instance
-  have := isIso_cokernel_desc_of_exact_of_epi _ _ (exact_of_map_ProjectiveResolution F P)
+  have := isIso_cokernel_desc_of_exact_of_epi _ _ (exact_of_map_projectiveResolution F P)
   refine'
-    (asIso (cokernel.desc _ _ (exact_of_map_ProjectiveResolution F P).w)).inv ≫
+    (asIso (cokernel.desc _ _ (exact_of_map_projectiveResolution F P).w)).inv ≫
       _ ≫ (homologyIsoCokernelLift _ _ _).inv ≫ (leftDerivedObjIso F 0 P).inv
   refine' cokernel.map _ _ (𝟙 _) (kernel.lift _ (𝟙 _) (by simp)) _
   -- Porting note: this used to be ext ; simp
@@ -111,7 +111,7 @@ theorem leftDerivedZeroToSelfApp_comp_inv [EnoughProjectives C] [PreservesFinite
   apply homology.hom_from_ext
   simp only [← Category.assoc]
   erw [homology.π'_desc', Category.assoc, Category.assoc, ←
-    Category.assoc (F.map _), Abelian.cokernel.desc.inv _ _ (exact_of_map_ProjectiveResolution F P),
+    Category.assoc (F.map _), Abelian.cokernel.desc.inv _ _ (exact_of_map_projectiveResolution F P),
     cokernel.π_desc, homology.π', Category.comp_id, Category.assoc (cokernel.π _), Iso.inv_hom_id,
     Category.comp_id, ← Category.assoc]
   -- Porting note: restructured proof to avoid `convert`
@@ -140,8 +140,8 @@ theorem leftDerivedZeroToSelfAppInv_comp [EnoughProjectives C] [PreservesFiniteC
   -- Porting note: instance not found even though it is present in the goal
   have : IsIso (cokernel.desc (F.map
     (HomologicalComplex.d P.complex (ComplexShape.prev (ComplexShape.down ℕ) 0) 0))
-      (F.map (HomologicalComplex.Hom.f P.π 0)) (exact_of_map_ProjectiveResolution F P).w) :=
-    isIso_cokernel_desc_of_exact_of_epi _ _ (exact_of_map_ProjectiveResolution F P)
+      (F.map (HomologicalComplex.Hom.f P.π 0)) (exact_of_map_projectiveResolution F P).w) :=
+    isIso_cokernel_desc_of_exact_of_epi _ _ (exact_of_map_projectiveResolution F P)
   rw [IsIso.inv_comp_eq]
   -- Porting note: working around 'motive is not type correct'
   simp only [Category.comp_id]

8001ea54

feat: port CategoryTheory.Abelian.LeftDerived (#4477)

0e56a9ea

`category_theory.abelian.left_derived` ⟷ `Mathlib.CategoryTheory.Abelian.LeftDerived`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 673

category_theory.abelian.left_derived ⟷ Mathlib.CategoryTheory.Abelian.LeftDerived

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 673

`category_theory.abelian.left_derived` ⟷ `Mathlib.CategoryTheory.Abelian.LeftDerived`