category_theory.abelian.generator
⟷
Mathlib.CategoryTheory.Abelian.Generator
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
@@ -3,11 +3,11 @@ Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-/
-import Mathbin.CategoryTheory.Abelian.Subobject
-import Mathbin.CategoryTheory.Limits.EssentiallySmall
-import Mathbin.CategoryTheory.Preadditive.Injective
-import Mathbin.CategoryTheory.Preadditive.Generator
-import Mathbin.CategoryTheory.Abelian.Opposite
+import CategoryTheory.Abelian.Subobject
+import CategoryTheory.Limits.EssentiallySmall
+import CategoryTheory.Preadditive.Injective
+import CategoryTheory.Preadditive.Generator
+import CategoryTheory.Abelian.Opposite
#align_import category_theory.abelian.generator from "leanprover-community/mathlib"@"6cf5900728239efa287df7761ec2a1ac9cf39b29"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,11 +2,6 @@
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-
-! This file was ported from Lean 3 source module category_theory.abelian.generator
-! leanprover-community/mathlib commit 6cf5900728239efa287df7761ec2a1ac9cf39b29
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Abelian.Subobject
import Mathbin.CategoryTheory.Limits.EssentiallySmall
@@ -14,6 +9,8 @@ import Mathbin.CategoryTheory.Preadditive.Injective
import Mathbin.CategoryTheory.Preadditive.Generator
import Mathbin.CategoryTheory.Abelian.Opposite
+#align_import category_theory.abelian.generator from "leanprover-community/mathlib"@"6cf5900728239efa287df7761ec2a1ac9cf39b29"
+
/-!
# A complete abelian category with enough injectives and a separator has an injective coseparator
mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
! This file was ported from Lean 3 source module category_theory.abelian.generator
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit 6cf5900728239efa287df7761ec2a1ac9cf39b29
! 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.Opposite
/-!
# A complete abelian category with enough injectives and a separator has an injective coseparator
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
## Future work
* Once we know that Grothendieck categories have enough injectives, we can use this to conclude
that Grothendieck categories have an injective coseparator.
mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740
@@ -35,6 +35,7 @@ namespace CategoryTheory.Abelian
variable {C : Type u} [Category.{v} C] [Abelian C]
+#print CategoryTheory.Abelian.has_injective_coseparator /-
theorem has_injective_coseparator [HasLimits C] [EnoughInjectives C] (G : C) (hG : IsSeparator G) :
∃ G : C, Injective G ∧ IsCoseparator G :=
by
@@ -57,13 +58,16 @@ theorem has_injective_coseparator [HasLimits C] [EnoughInjectives C] (G : C) (hG
rw [← injective.comp_factor_thru q (limits.image.ι (h ≫ f)), limits.image.fac_assoc,
category.assoc, hf, comp_zero])
#align category_theory.abelian.has_injective_coseparator CategoryTheory.Abelian.has_injective_coseparator
+-/
+#print CategoryTheory.Abelian.has_projective_separator /-
theorem has_projective_separator [HasColimits C] [EnoughProjectives C] (G : C)
(hG : IsCoseparator G) : ∃ G : C, Projective G ∧ IsSeparator G :=
by
obtain ⟨T, hT₁, hT₂⟩ := has_injective_coseparator (op G) ((is_separator_op_iff _).2 hG)
exact ⟨unop T, inferInstance, (is_separator_unop_iff _).2 hT₂⟩
#align category_theory.abelian.has_projective_separator CategoryTheory.Abelian.has_projective_separator
+-/
end CategoryTheory.Abelian
mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
! This file was ported from Lean 3 source module category_theory.abelian.generator
-! leanprover-community/mathlib commit 09f981f72d43749f1fa072deade828d9c1e185bb
+! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -12,7 +12,7 @@ import Mathbin.CategoryTheory.Abelian.Subobject
import Mathbin.CategoryTheory.Limits.EssentiallySmall
import Mathbin.CategoryTheory.Preadditive.Injective
import Mathbin.CategoryTheory.Preadditive.Generator
-import Mathbin.CategoryTheory.Preadditive.Yoneda.Limits
+import Mathbin.CategoryTheory.Abelian.Opposite
/-!
# A complete abelian category with enough injectives and a separator has an injective coseparator
mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
! This file was ported from Lean 3 source module category_theory.abelian.generator
-! leanprover-community/mathlib commit 53e5dd300e5d752bda3516889049f7c35f3d4427
+! leanprover-community/mathlib commit 09f981f72d43749f1fa072deade828d9c1e185bb
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -12,6 +12,7 @@ import Mathbin.CategoryTheory.Abelian.Subobject
import Mathbin.CategoryTheory.Limits.EssentiallySmall
import Mathbin.CategoryTheory.Preadditive.Injective
import Mathbin.CategoryTheory.Preadditive.Generator
+import Mathbin.CategoryTheory.Preadditive.Yoneda.Limits
/-!
# A complete abelian category with enough injectives and a separator has an injective coseparator
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
have
, replace
and suffices
(#10640)
No changes to tactic file, it's just boring fixes throughout the library.
This follows on from #6964.
Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
@@ -39,8 +39,8 @@ theorem has_injective_coseparator [HasLimits C] [EnoughInjectives C] (G : C) (hG
let T : C := Injective.under (piObj fun P : Subobject (op G) => unop P)
refine' ⟨T, inferInstance, (Preadditive.isCoseparator_iff _).2 fun X Y f hf => _⟩
refine' (Preadditive.isSeparator_iff _).1 hG _ fun h => _
- suffices hh : factorThruImage (h ≫ f) = 0
- · rw [← Limits.image.fac (h ≫ f), hh, zero_comp]
+ suffices hh : factorThruImage (h ≫ f) = 0 by
+ rw [← Limits.image.fac (h ≫ f), hh, zero_comp]
let R := Subobject.mk (factorThruImage (h ≫ f)).op
let q₁ : image (h ≫ f) ⟶ unop R :=
(Subobject.underlyingIso (factorThruImage (h ≫ f)).op).unop.hom
@@ -2,11 +2,6 @@
Copyright (c) 2022 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel
-
-! This file was ported from Lean 3 source module category_theory.abelian.generator
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Abelian.Subobject
import Mathlib.CategoryTheory.Limits.EssentiallySmall
@@ -14,6 +9,8 @@ import Mathlib.CategoryTheory.Preadditive.Injective
import Mathlib.CategoryTheory.Preadditive.Generator
import Mathlib.CategoryTheory.Abelian.Opposite
+#align_import category_theory.abelian.generator from "leanprover-community/mathlib"@"f0c8bf9245297a541f468be517f1bde6195105e9"
+
/-!
# A complete abelian category with enough injectives and a separator has an injective coseparator
The unported dependencies are