category_theory.abelian.injective
⟷
Mathlib.CategoryTheory.Abelian.Injective
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.
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mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,10 +3,10 @@ Copyright (c) 2022 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-/
-import Mathbin.CategoryTheory.Abelian.Exact
-import Mathbin.CategoryTheory.Preadditive.Injective
-import Mathbin.CategoryTheory.Preadditive.Yoneda.Limits
-import Mathbin.CategoryTheory.Preadditive.Yoneda.Injective
+import CategoryTheory.Abelian.Exact
+import CategoryTheory.Preadditive.Injective
+import CategoryTheory.Preadditive.Yoneda.Limits
+import CategoryTheory.Preadditive.Yoneda.Injective
#align_import category_theory.abelian.injective from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,17 +2,14 @@
Copyright (c) 2022 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-
-! This file was ported from Lean 3 source module category_theory.abelian.injective
-! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Abelian.Exact
import Mathbin.CategoryTheory.Preadditive.Injective
import Mathbin.CategoryTheory.Preadditive.Yoneda.Limits
import Mathbin.CategoryTheory.Preadditive.Yoneda.Injective
+#align_import category_theory.abelian.injective from "leanprover-community/mathlib"@"0b7c740e25651db0ba63648fbae9f9d6f941e31b"
+
/-!
# Injective objects in abelian categories
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -40,6 +40,7 @@ namespace CategoryTheory
variable {C : Type u} [Category.{v} C] [Abelian C]
+#print CategoryTheory.preservesFiniteColimitsPreadditiveYonedaObjOfInjective /-
/-- The preadditive Yoneda functor on `J` preserves colimits if `J` is injective. -/
def preservesFiniteColimitsPreadditiveYonedaObjOfInjective (J : C) [hP : Injective J] :
PreservesFiniteColimits (preadditiveYonedaObj J) :=
@@ -47,7 +48,9 @@ def preservesFiniteColimitsPreadditiveYonedaObjOfInjective (J : C) [hP : Injecti
letI := (injective_iff_preserves_epimorphisms_preadditive_yoneda_obj' J).mp hP
apply functor.preserves_finite_colimits_of_preserves_epis_and_kernels
#align category_theory.preserves_finite_colimits_preadditive_yoneda_obj_of_injective CategoryTheory.preservesFiniteColimitsPreadditiveYonedaObjOfInjective
+-/
+#print CategoryTheory.injective_of_preservesFiniteColimits_preadditiveYonedaObj /-
/-- An object is injective if its preadditive Yoneda functor preserves finite colimits. -/
theorem injective_of_preservesFiniteColimits_preadditiveYonedaObj (J : C)
[hP : PreservesFiniteColimits (preadditiveYonedaObj J)] : Injective J :=
@@ -55,6 +58,7 @@ theorem injective_of_preservesFiniteColimits_preadditiveYonedaObj (J : C)
rw [injective_iff_preserves_epimorphisms_preadditive_yoneda_obj']
infer_instance
#align category_theory.injective_of_preserves_finite_colimits_preadditive_yoneda_obj CategoryTheory.injective_of_preservesFiniteColimits_preadditiveYonedaObj
+-/
end CategoryTheory
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -40,12 +40,6 @@ namespace CategoryTheory
variable {C : Type u} [Category.{v} C] [Abelian C]
-/- warning: category_theory.preserves_finite_colimits_preadditive_yoneda_obj_of_injective -> CategoryTheory.preservesFiniteColimitsPreadditiveYonedaObjOfInjective is a dubious translation:
-lean 3 declaration is
- forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] (J : C) [hP : CategoryTheory.Injective.{u1, u2} C _inst_1 J], CategoryTheory.Limits.PreservesFiniteColimits.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (ModuleCat.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) J) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)) (ModuleCat.moduleCategory.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) J) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)) (CategoryTheory.preadditiveYonedaObj.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)
-but is expected to have type
- forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] (J : C) [hP : CategoryTheory.Injective.{u1, u2} C _inst_1 J], CategoryTheory.Limits.PreservesFiniteColimits.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (ModuleCat.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) J) (CategoryTheory.Preadditive.instRingEndToCategoryStruct.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)) (ModuleCat.moduleCategory.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) J) (CategoryTheory.Preadditive.instRingEndToCategoryStruct.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)) (CategoryTheory.preadditiveYonedaObj.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)
-Case conversion may be inaccurate. Consider using '#align category_theory.preserves_finite_colimits_preadditive_yoneda_obj_of_injective CategoryTheory.preservesFiniteColimitsPreadditiveYonedaObjOfInjectiveₓ'. -/
/-- The preadditive Yoneda functor on `J` preserves colimits if `J` is injective. -/
def preservesFiniteColimitsPreadditiveYonedaObjOfInjective (J : C) [hP : Injective J] :
PreservesFiniteColimits (preadditiveYonedaObj J) :=
@@ -54,12 +48,6 @@ def preservesFiniteColimitsPreadditiveYonedaObjOfInjective (J : C) [hP : Injecti
apply functor.preserves_finite_colimits_of_preserves_epis_and_kernels
#align category_theory.preserves_finite_colimits_preadditive_yoneda_obj_of_injective CategoryTheory.preservesFiniteColimitsPreadditiveYonedaObjOfInjective
-/- warning: category_theory.injective_of_preserves_finite_colimits_preadditive_yoneda_obj -> CategoryTheory.injective_of_preservesFiniteColimits_preadditiveYonedaObj is a dubious translation:
-lean 3 declaration is
- forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] (J : C) [hP : CategoryTheory.Limits.PreservesFiniteColimits.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (ModuleCat.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) J) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)) (ModuleCat.moduleCategory.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) J) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)) (CategoryTheory.preadditiveYonedaObj.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)], CategoryTheory.Injective.{u1, u2} C _inst_1 J
-but is expected to have type
- forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] (J : C) [hP : CategoryTheory.Limits.PreservesFiniteColimits.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (ModuleCat.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) J) (CategoryTheory.Preadditive.instRingEndToCategoryStruct.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)) (ModuleCat.moduleCategory.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) J) (CategoryTheory.Preadditive.instRingEndToCategoryStruct.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)) (CategoryTheory.preadditiveYonedaObj.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)], CategoryTheory.Injective.{u1, u2} C _inst_1 J
-Case conversion may be inaccurate. Consider using '#align category_theory.injective_of_preserves_finite_colimits_preadditive_yoneda_obj CategoryTheory.injective_of_preservesFiniteColimits_preadditiveYonedaObjₓ'. -/
/-- An object is injective if its preadditive Yoneda functor preserves finite colimits. -/
theorem injective_of_preservesFiniteColimits_preadditiveYonedaObj (J : C)
[hP : PreservesFiniteColimits (preadditiveYonedaObj J)] : Injective J :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
! This file was ported from Lean 3 source module category_theory.abelian.injective
-! leanprover-community/mathlib commit f8d8465c3c392a93b9ed226956e26dee00975946
+! leanprover-community/mathlib commit 0b7c740e25651db0ba63648fbae9f9d6f941e31b
! 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.Preadditive.Yoneda.Injective
/-!
# Injective objects in abelian categories
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
* Objects in an abelian categories are injective if and only if the preadditive Yoneda functor
on them preserves finite colimits.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946
@@ -37,6 +37,12 @@ namespace CategoryTheory
variable {C : Type u} [Category.{v} C] [Abelian C]
+/- warning: category_theory.preserves_finite_colimits_preadditive_yoneda_obj_of_injective -> CategoryTheory.preservesFiniteColimitsPreadditiveYonedaObjOfInjective is a dubious translation:
+lean 3 declaration is
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] (J : C) [hP : CategoryTheory.Injective.{u1, u2} C _inst_1 J], CategoryTheory.Limits.PreservesFiniteColimits.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (ModuleCat.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) J) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)) (ModuleCat.moduleCategory.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) J) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)) (CategoryTheory.preadditiveYonedaObj.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)
+but is expected to have type
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] (J : C) [hP : CategoryTheory.Injective.{u1, u2} C _inst_1 J], CategoryTheory.Limits.PreservesFiniteColimits.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (ModuleCat.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) J) (CategoryTheory.Preadditive.instRingEndToCategoryStruct.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)) (ModuleCat.moduleCategory.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) J) (CategoryTheory.Preadditive.instRingEndToCategoryStruct.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)) (CategoryTheory.preadditiveYonedaObj.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)
+Case conversion may be inaccurate. Consider using '#align category_theory.preserves_finite_colimits_preadditive_yoneda_obj_of_injective CategoryTheory.preservesFiniteColimitsPreadditiveYonedaObjOfInjectiveₓ'. -/
/-- The preadditive Yoneda functor on `J` preserves colimits if `J` is injective. -/
def preservesFiniteColimitsPreadditiveYonedaObjOfInjective (J : C) [hP : Injective J] :
PreservesFiniteColimits (preadditiveYonedaObj J) :=
@@ -45,6 +51,12 @@ def preservesFiniteColimitsPreadditiveYonedaObjOfInjective (J : C) [hP : Injecti
apply functor.preserves_finite_colimits_of_preserves_epis_and_kernels
#align category_theory.preserves_finite_colimits_preadditive_yoneda_obj_of_injective CategoryTheory.preservesFiniteColimitsPreadditiveYonedaObjOfInjective
+/- warning: category_theory.injective_of_preserves_finite_colimits_preadditive_yoneda_obj -> CategoryTheory.injective_of_preservesFiniteColimits_preadditiveYonedaObj is a dubious translation:
+lean 3 declaration is
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] (J : C) [hP : CategoryTheory.Limits.PreservesFiniteColimits.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (ModuleCat.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) J) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)) (ModuleCat.moduleCategory.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) J) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)) (CategoryTheory.preadditiveYonedaObj.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)], CategoryTheory.Injective.{u1, u2} C _inst_1 J
+but is expected to have type
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Abelian.{u1, u2} C _inst_1] (J : C) [hP : CategoryTheory.Limits.PreservesFiniteColimits.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (ModuleCat.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) J) (CategoryTheory.Preadditive.instRingEndToCategoryStruct.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)) (ModuleCat.moduleCategory.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) J) (CategoryTheory.Preadditive.instRingEndToCategoryStruct.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)) (CategoryTheory.preadditiveYonedaObj.{u1, u2} C _inst_1 (CategoryTheory.Abelian.toPreadditive.{u1, u2} C _inst_1 _inst_2) J)], CategoryTheory.Injective.{u1, u2} C _inst_1 J
+Case conversion may be inaccurate. Consider using '#align category_theory.injective_of_preserves_finite_colimits_preadditive_yoneda_obj CategoryTheory.injective_of_preservesFiniteColimits_preadditiveYonedaObjₓ'. -/
/-- An object is injective if its preadditive Yoneda functor preserves finite colimits. -/
theorem injective_of_preservesFiniteColimits_preadditiveYonedaObj (J : C)
[hP : PreservesFiniteColimits (preadditiveYonedaObj J)] : Injective J :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a
@@ -4,13 +4,14 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
! This file was ported from Lean 3 source module category_theory.abelian.injective
-! leanprover-community/mathlib commit 09f981f72d43749f1fa072deade828d9c1e185bb
+! leanprover-community/mathlib commit f8d8465c3c392a93b9ed226956e26dee00975946
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Abelian.Exact
import Mathbin.CategoryTheory.Preadditive.Injective
import Mathbin.CategoryTheory.Preadditive.Yoneda.Limits
+import Mathbin.CategoryTheory.Preadditive.Yoneda.Injective
/-!
# Injective objects in abelian categories
mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936
@@ -4,13 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
! This file was ported from Lean 3 source module category_theory.abelian.injective
-! leanprover-community/mathlib commit 8853975ed779665849d3936f1663d917c25f4a68
+! leanprover-community/mathlib commit 09f981f72d43749f1fa072deade828d9c1e185bb
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Abelian.Exact
import Mathbin.CategoryTheory.Preadditive.Injective
-import Mathbin.CategoryTheory.Preadditive.Yoneda
+import Mathbin.CategoryTheory.Preadditive.Yoneda.Limits
/-!
# Injective objects in abelian categories
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -2,17 +2,14 @@
Copyright (c) 2022 Jakob von Raumer. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jakob von Raumer
-
-! This file was ported from Lean 3 source module category_theory.abelian.injective
-! leanprover-community/mathlib commit f8d8465c3c392a93b9ed226956e26dee00975946
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Abelian.Exact
import Mathlib.CategoryTheory.Preadditive.Injective
import Mathlib.CategoryTheory.Preadditive.Yoneda.Limits
import Mathlib.CategoryTheory.Preadditive.Yoneda.Injective
+#align_import category_theory.abelian.injective from "leanprover-community/mathlib"@"f8d8465c3c392a93b9ed226956e26dee00975946"
+
/-!
# Injective objects in abelian categories
The unported dependencies are