category_theory.abelian.ext | 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

70fd9563

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

61b5e275

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Adam Topaz
 -/
-import Algebra.Category.Module.Abelian
+import Algebra.Category.ModuleCat.Abelian
 import CategoryTheory.Functor.LeftDerived
 import CategoryTheory.Linear.Yoneda
 import CategoryTheory.Abelian.Opposite

61b5e275

bump to nightly-2023-12-20-06

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

058cd493

Diff

@@ -47,7 +47,7 @@ def Ext (n : ℕ) : Cᵒᵖ ⥤ C ⥤ ModuleCat R :=
   Functor.flip
     { obj := fun Y => (((linearYoneda R C).obj Y).rightOp.leftDerived n).leftOp
       map := fun Y Y' f => (NatTrans.leftDerived ((linearYoneda R C).map f).rightOp n).leftOp
-      map_id' := by
+      map_id'' := by
         intro X
         ext Y : 2
         dsimp only [nat_trans.id_app, nat_trans.left_op_app, nat_trans.right_op_app,

61b5e275

bump to nightly-2023-12-02-06

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

e637da5d

Diff

@@ -63,7 +63,6 @@ def Ext (n : ℕ) : Cᵒᵖ ⥤ C ⥤ ModuleCat R :=
 
 open scoped ZeroObject
 
-#print extSuccOfProjective /-
 /-- If `X : C` is projective and `n : ℕ`, then `Ext^(n + 1) X Y ≅ 0` for any `Y`. -/
 def extSuccOfProjective (X Y : C) [Projective X] (n : ℕ) :
     ((Ext R C (n + 1)).obj (Opposite.op X)).obj Y ≅ 0 :=
@@ -78,5 +77,4 @@ def extSuccOfProjective (X Y : C) [Projective X] (n : ℕ) :
         dsimp
         decide }
 #align Ext_succ_of_projective extSuccOfProjective
--/

61b5e275

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) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Adam Topaz
 -/
-import Mathbin.Algebra.Category.Module.Abelian
-import Mathbin.CategoryTheory.Functor.LeftDerived
-import Mathbin.CategoryTheory.Linear.Yoneda
-import Mathbin.CategoryTheory.Abelian.Opposite
-import Mathbin.CategoryTheory.Abelian.Projective
+import Algebra.Category.Module.Abelian
+import CategoryTheory.Functor.LeftDerived
+import CategoryTheory.Linear.Yoneda
+import CategoryTheory.Abelian.Opposite
+import CategoryTheory.Abelian.Projective
 
 #align_import category_theory.abelian.ext 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

@@ -2,11 +2,6 @@
 Copyright (c) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Adam Topaz
-
-! This file was ported from Lean 3 source module category_theory.abelian.ext
-! 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.Algebra.Category.Module.Abelian
 import Mathbin.CategoryTheory.Functor.LeftDerived
@@ -14,6 +9,8 @@ import Mathbin.CategoryTheory.Linear.Yoneda
 import Mathbin.CategoryTheory.Abelian.Opposite
 import Mathbin.CategoryTheory.Abelian.Projective
 
+#align_import category_theory.abelian.ext from "leanprover-community/mathlib"@"61b5e2755ccb464b68d05a9acf891ae04992d09d"
+
 /-!
 # Ext

61b5e275

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -66,6 +66,7 @@ def Ext (n : ℕ) : Cᵒᵖ ⥤ C ⥤ ModuleCat R :=
 
 open scoped ZeroObject
 
+#print extSuccOfProjective /-
 /-- If `X : C` is projective and `n : ℕ`, then `Ext^(n + 1) X Y ≅ 0` for any `Y`. -/
 def extSuccOfProjective (X Y : C) [Projective X] (n : ℕ) :
     ((Ext R C (n + 1)).obj (Opposite.op X)).obj Y ≅ 0 :=
@@ -80,4 +81,5 @@ def extSuccOfProjective (X Y : C) [Projective X] (n : ℕ) :
         dsimp
         decide }
 #align Ext_succ_of_projective extSuccOfProjective
+-/

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: Scott Morrison, Adam Topaz
 
 ! This file was ported from Lean 3 source module category_theory.abelian.ext
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! leanprover-community/mathlib commit 61b5e2755ccb464b68d05a9acf891ae04992d09d
 ! 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.Projective
 /-!
 # Ext
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define `Ext R C n : Cᵒᵖ ⥤ C ⥤ Module R` for any `R`-linear abelian category `C`
 by (left) deriving in the first argument of the bifunctor `(X, Y) ↦ Module.of R (unop X ⟶ Y)`.
 
@@ -38,11 +41,12 @@ open CategoryTheory
 variable (R : Type _) [Ring R] (C : Type _) [Category C] [Abelian C] [Linear R C]
   [EnoughProjectives C]
 
+#print Ext /-
 /-- `Ext R C n` is defined by deriving in the first argument of `(X, Y) ↦ Module.of R (unop X ⟶ Y)`
 (which is the second argument of `linear_yoneda`).
 -/
 @[simps obj map]
-def ext (n : ℕ) : Cᵒᵖ ⥤ C ⥤ ModuleCat R :=
+def Ext (n : ℕ) : Cᵒᵖ ⥤ C ⥤ ModuleCat R :=
   Functor.flip
     { obj := fun Y => (((linearYoneda R C).obj Y).rightOp.leftDerived n).leftOp
       map := fun Y Y' f => (NatTrans.leftDerived ((linearYoneda R C).map f).rightOp n).leftOp
@@ -57,13 +61,14 @@ def ext (n : ℕ) : Cᵒᵖ ⥤ C ⥤ ModuleCat R :=
         intro X Y Z f g
         rw [(linear_yoneda R C).map_comp, nat_trans.right_op_comp, nat_trans.left_derived_comp]
         rfl }
-#align Ext ext
+#align Ext Ext
+-/
 
 open scoped ZeroObject
 
 /-- If `X : C` is projective and `n : ℕ`, then `Ext^(n + 1) X Y ≅ 0` for any `Y`. -/
 def extSuccOfProjective (X Y : C) [Projective X] (n : ℕ) :
-    ((ext R C (n + 1)).obj (Opposite.op X)).obj Y ≅ 0 :=
+    ((Ext R C (n + 1)).obj (Opposite.op X)).obj Y ≅ 0 :=
   let E := (((linearYoneda R C).obj Y).rightOp.leftDerivedObjProjectiveSucc n X).unop.symm
   E ≪≫
     { hom := 0

70fd9563

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -59,7 +59,7 @@ def ext (n : ℕ) : Cᵒᵖ ⥤ C ⥤ ModuleCat R :=
         rfl }
 #align Ext ext
 
-open ZeroObject
+open scoped ZeroObject
 
 /-- If `X : C` is projective and `n : ℕ`, then `Ext^(n + 1) X Y ≅ 0` for any `Y`. -/
 def extSuccOfProjective (X Y : C) [Projective X] (n : ℕ) :

70fd9563

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -38,12 +38,6 @@ open CategoryTheory
 variable (R : Type _) [Ring R] (C : Type _) [Category C] [Abelian C] [Linear R C]
   [EnoughProjectives C]
 
-/- warning: Ext -> ext is a dubious translation:
-lean 3 declaration is
-  forall (R : Type.{u_1}) [_inst_1 : Ring.{u_1} R] (C : Type.{u_2}) [_inst_2 : CategoryTheory.Category.{u_3, u_2} C] [_inst_3 : CategoryTheory.Abelian.{u_3, u_2} C _inst_2] [_inst_4 : CategoryTheory.Linear.{u_1, u_3, u_2} R (Ring.toSemiring.{u_1} R _inst_1) C _inst_2 (CategoryTheory.Abelian.toPreadditive.{u_3, u_2} C _inst_2 _inst_3)] [_inst_5 : CategoryTheory.EnoughProjectives.{u_3, u_2} C _inst_2], Nat -> (CategoryTheory.Functor.{u_3, max u_2 u_3, u_2, max u_3 u_2 u_1 (succ u_3)} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_3, u_2} C _inst_2) (CategoryTheory.Functor.{u_3, u_3, u_2, max u_1 (succ u_3)} C _inst_2 (ModuleCat.{u_3, u_1} R _inst_1) (ModuleCat.moduleCategory.{u_3, u_1} R _inst_1)) (CategoryTheory.Functor.category.{u_3, u_3, u_2, max u_1 (succ u_3)} C _inst_2 (ModuleCat.{u_3, u_1} R _inst_1) (ModuleCat.moduleCategory.{u_3, u_1} R _inst_1)))
-but is expected to have type
-  forall {R : Type.{u_1}} [_inst_1 : Semiring.{u_1} R] {C : LaurentPolynomial.{u_1} R _inst_1} {_inst_2 : LaurentPolynomial.{u_1} R _inst_1}, (forall (a : Int), Eq.{succ u_1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Int) => R) a) (FunLike.coe.{succ u_1, 1, succ u_1} (Finsupp.{0, u_1} Int R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R _inst_1))) Int (fun (a : Int) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Int) => R) a) (Finsupp.funLike.{0, u_1} Int R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R _inst_1))) C a) (FunLike.coe.{succ u_1, 1, succ u_1} (Finsupp.{0, u_1} Int R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R _inst_1))) Int (fun (a : Int) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Int) => R) a) (Finsupp.funLike.{0, u_1} Int R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R _inst_1))) _inst_2 a)) -> (Eq.{succ u_1} (LaurentPolynomial.{u_1} R _inst_1) C _inst_2)
-Case conversion may be inaccurate. Consider using '#align Ext extₓ'. -/
 /-- `Ext R C n` is defined by deriving in the first argument of `(X, Y) ↦ Module.of R (unop X ⟶ Y)`
 (which is the second argument of `linear_yoneda`).
 -/

70fd9563

bump to nightly-2023-05-15-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ad820c4997738e2f542f8a20f32911f52020e26

07fedaf5

Diff

@@ -38,6 +38,12 @@ open CategoryTheory
 variable (R : Type _) [Ring R] (C : Type _) [Category C] [Abelian C] [Linear R C]
   [EnoughProjectives C]
 
+/- warning: Ext -> ext is a dubious translation:
+lean 3 declaration is
+  forall (R : Type.{u_1}) [_inst_1 : Ring.{u_1} R] (C : Type.{u_2}) [_inst_2 : CategoryTheory.Category.{u_3, u_2} C] [_inst_3 : CategoryTheory.Abelian.{u_3, u_2} C _inst_2] [_inst_4 : CategoryTheory.Linear.{u_1, u_3, u_2} R (Ring.toSemiring.{u_1} R _inst_1) C _inst_2 (CategoryTheory.Abelian.toPreadditive.{u_3, u_2} C _inst_2 _inst_3)] [_inst_5 : CategoryTheory.EnoughProjectives.{u_3, u_2} C _inst_2], Nat -> (CategoryTheory.Functor.{u_3, max u_2 u_3, u_2, max u_3 u_2 u_1 (succ u_3)} (Opposite.{succ u_2} C) (CategoryTheory.Category.opposite.{u_3, u_2} C _inst_2) (CategoryTheory.Functor.{u_3, u_3, u_2, max u_1 (succ u_3)} C _inst_2 (ModuleCat.{u_3, u_1} R _inst_1) (ModuleCat.moduleCategory.{u_3, u_1} R _inst_1)) (CategoryTheory.Functor.category.{u_3, u_3, u_2, max u_1 (succ u_3)} C _inst_2 (ModuleCat.{u_3, u_1} R _inst_1) (ModuleCat.moduleCategory.{u_3, u_1} R _inst_1)))
+but is expected to have type
+  forall {R : Type.{u_1}} [_inst_1 : Semiring.{u_1} R] {C : LaurentPolynomial.{u_1} R _inst_1} {_inst_2 : LaurentPolynomial.{u_1} R _inst_1}, (forall (a : Int), Eq.{succ u_1} ((fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Int) => R) a) (FunLike.coe.{succ u_1, 1, succ u_1} (Finsupp.{0, u_1} Int R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R _inst_1))) Int (fun (a : Int) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Int) => R) a) (Finsupp.funLike.{0, u_1} Int R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R _inst_1))) C a) (FunLike.coe.{succ u_1, 1, succ u_1} (Finsupp.{0, u_1} Int R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R _inst_1))) Int (fun (a : Int) => (fun (x._@.Mathlib.Data.Finsupp.Defs._hyg.779 : Int) => R) a) (Finsupp.funLike.{0, u_1} Int R (MonoidWithZero.toZero.{u_1} R (Semiring.toMonoidWithZero.{u_1} R _inst_1))) _inst_2 a)) -> (Eq.{succ u_1} (LaurentPolynomial.{u_1} R _inst_1) C _inst_2)
+Case conversion may be inaccurate. Consider using '#align Ext extₓ'. -/
 /-- `Ext R C n` is defined by deriving in the first argument of `(X, Y) ↦ Module.of R (unop X ⟶ Y)`
 (which is the second argument of `linear_yoneda`).
 -/

70fd9563

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

70fd9563

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

@@ -4,10 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Adam Topaz
 -/
 import Mathlib.Algebra.Category.ModuleCat.Abelian
-import Mathlib.CategoryTheory.Functor.LeftDerived
-import Mathlib.CategoryTheory.Linear.Yoneda
+import Mathlib.Algebra.Homology.Opposite
+import Mathlib.CategoryTheory.Abelian.LeftDerived
 import Mathlib.CategoryTheory.Abelian.Opposite
-import Mathlib.CategoryTheory.Abelian.Projective
+import Mathlib.CategoryTheory.Abelian.ProjectiveResolution
+import Mathlib.CategoryTheory.Linear.Yoneda
 
 #align_import category_theory.abelian.ext from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
 
@@ -19,18 +20,16 @@ by (left) deriving in the first argument of the bifunctor `(X, Y) ↦ Module.of
 
 ## Implementation
 
-It's not actually necessary here to assume `C` is abelian,
-but the hypotheses, involving both `C` and `Cᵒᵖ`, are quite lengthy,
-and in practice the abelian case is hopefully enough.
+TODO (@joelriou): When the derived category enters mathlib, the Ext groups shall be
+redefined using morphisms in the derived category, and then it will be possible to
+compute `Ext` using both projective or injective resolutions.
 
-PROJECT: State the alternative definition in terms of
-right deriving in the second argument, and show these agree.
 -/
 
 
 noncomputable section
 
-open CategoryTheory
+open CategoryTheory Limits
 
 variable (R : Type*) [Ring R] (C : Type*) [Category C] [Abelian C] [Linear R C]
   [EnoughProjectives C]
@@ -62,16 +61,41 @@ set_option linter.uppercaseLean3 false in
 
 open ZeroObject
 
+variable {R C}
+
+/-- Given a chain complex `X` and an object `Y`, this is the cochain complex
+which in degree `i` consists of the module of morphisms `X.X i ⟶ Y`. -/
+@[simps! X d]
+def ChainComplex.linearYonedaObj {α : Type*} [AddRightCancelSemigroup α] [One α]
+    (X : ChainComplex C α) (A : Type*) [Ring A] [Linear A C] (Y : C):
+    CochainComplex (ModuleCat A) α :=
+  ((((linearYoneda A C).obj Y).rightOp.mapHomologicalComplex _).obj X).unop
+
+namespace CategoryTheory
+
+namespace ProjectiveResolution
+
+variable {X : C} (P : ProjectiveResolution X)
+
+/-- `Ext` can be computed using a projective resolution. -/
+def isoExt (n : ℕ) (Y : C) : ((Ext R C n).obj (Opposite.op X)).obj Y ≅
+    (P.complex.linearYonedaObj R Y).homology n :=
+  (P.isoLeftDerivedObj ((linearYoneda R C).obj Y).rightOp n).unop.symm ≪≫
+    (HomologicalComplex.homologyUnop _ _).symm
+
+end ProjectiveResolution
+
+end CategoryTheory
+
 /-- If `X : C` is projective and `n : ℕ`, then `Ext^(n + 1) X Y ≅ 0` for any `Y`. -/
-def extSuccOfProjective (X Y : C) [Projective X] (n : ℕ) :
-    ((Ext R C (n + 1)).obj (Opposite.op X)).obj Y ≅ 0 :=
-  let E := (((linearYoneda R C).obj Y).rightOp.leftDerivedObjProjectiveSucc n X).unop.symm
-  E ≪≫
-    { hom := 0
-      inv := 0
-      hom_inv_id := by
-        let Z : (ModuleCat R)ᵒᵖ := 0
-        rw [← (0 : 0 ⟶ Z.unop).unop_op, ← (0 : Z.unop ⟶ 0).unop_op, ← unop_id, ← unop_comp]
-        aesop }
-set_option linter.uppercaseLean3 false in
-#align Ext_succ_of_projective extSuccOfProjective
+lemma isZero_Ext_succ_of_projective (X Y : C) [Projective X] (n : ℕ) :
+    IsZero (((Ext R C (n + 1)).obj (Opposite.op X)).obj Y) := by
+  refine IsZero.of_iso ?_ ((ProjectiveResolution.self X).isoExt (n + 1) Y)
+  rw [← HomologicalComplex.exactAt_iff_isZero_homology, HomologicalComplex.exactAt_iff]
+  refine ShortComplex.exact_of_isZero_X₂ _ ?_
+  dsimp
+  rw [IsZero.iff_id_eq_zero]
+  ext (x : _ ⟶ _)
+  obtain rfl : x = 0 := (HomologicalComplex.isZero_single_obj_X
+    (ComplexShape.down ℕ) 0 X (n + 1) (by simp)).eq_of_src _ _
+  rfl

70fd9563

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

@@ -32,7 +32,7 @@ noncomputable section
 
 open CategoryTheory
 
-variable (R : Type _) [Ring R] (C : Type _) [Category C] [Abelian C] [Linear R C]
+variable (R : Type*) [Ring R] (C : Type*) [Category C] [Abelian C] [Linear R C]
   [EnoughProjectives C]
 
 /-- `Ext R C n` is defined by deriving in the first argument of `(X, Y) ↦ Module.of R (unop X ⟶ Y)`

70fd9563

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) 2021 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Adam Topaz
-
-! This file was ported from Lean 3 source module category_theory.abelian.ext
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.Category.ModuleCat.Abelian
 import Mathlib.CategoryTheory.Functor.LeftDerived
@@ -14,6 +9,8 @@ import Mathlib.CategoryTheory.Linear.Yoneda
 import Mathlib.CategoryTheory.Abelian.Opposite
 import Mathlib.CategoryTheory.Abelian.Projective
 
+#align_import category_theory.abelian.ext from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
 /-!
 # Ext

70fd9563

feat: port CategoryTheory.Abelian.Ext (#4401)

Apologies about the git history, a whole chain of PRs have been opened before the previous one was merged.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr> Co-authored-by: Matthew Ballard <matt@mrb.email>

de26a77f

`category_theory.abelian.ext` ⟷ `Mathlib.CategoryTheory.Abelian.Ext`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 674

category_theory.abelian.ext ⟷ Mathlib.CategoryTheory.Abelian.Ext

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 674

`category_theory.abelian.ext` ⟷ `Mathlib.CategoryTheory.Abelian.Ext`