category_theory.preadditive.yoneda.projective
⟷
Mathlib.CategoryTheory.Preadditive.Yoneda.Projective
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/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -5,8 +5,8 @@ Authors: Markus Himmel, Scott Morrison
-/
import CategoryTheory.Preadditive.Yoneda.Basic
import CategoryTheory.Preadditive.Projective
-import Algebra.Category.Group.EpiMono
-import Algebra.Category.Module.EpiMono
+import Algebra.Category.GroupCat.EpiMono
+import Algebra.Category.ModuleCat.EpiMono
#align_import category_theory.preadditive.yoneda.projective from "leanprover-community/mathlib"@"bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,10 +3,10 @@ Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-/
-import Mathbin.CategoryTheory.Preadditive.Yoneda.Basic
-import Mathbin.CategoryTheory.Preadditive.Projective
-import Mathbin.Algebra.Category.Group.EpiMono
-import Mathbin.Algebra.Category.Module.EpiMono
+import CategoryTheory.Preadditive.Yoneda.Basic
+import CategoryTheory.Preadditive.Projective
+import Algebra.Category.Group.EpiMono
+import Algebra.Category.Module.EpiMono
#align_import category_theory.preadditive.yoneda.projective from "leanprover-community/mathlib"@"bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,17 +2,14 @@
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.preadditive.yoneda.projective
-! leanprover-community/mathlib commit bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Preadditive.Yoneda.Basic
import Mathbin.CategoryTheory.Preadditive.Projective
import Mathbin.Algebra.Category.Group.EpiMono
import Mathbin.Algebra.Category.Module.EpiMono
+#align_import category_theory.preadditive.yoneda.projective from "leanprover-community/mathlib"@"bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de"
+
/-!
> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
> Any changes to this file require a corresponding PR to mathlib4.
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -35,6 +35,7 @@ variable [Preadditive C]
namespace Projective
+#print CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj /-
theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj (P : C) :
Projective P ↔ (preadditiveCoyoneda.obj (op P)).PreservesEpimorphisms :=
by
@@ -47,7 +48,9 @@ theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj (P : C) :
· intro
exact (inferInstance : (preadditive_coyoneda.obj (op P) ⋙ forget _).PreservesEpimorphisms)
#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj
+-/
+#print CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj' /-
theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj' (P : C) :
Projective P ↔ (preadditiveCoyonedaObj (op P)).PreservesEpimorphisms :=
by
@@ -60,6 +63,7 @@ theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj' (P : C) :
· intro
exact (inferInstance : (preadditive_coyoneda_obj (op P) ⋙ forget _).PreservesEpimorphisms)
#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj' CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj'
+-/
end Projective
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -35,12 +35,6 @@ variable [Preadditive C]
namespace Projective
-/- warning: category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj -> CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj is a dubious translation:
-lean 3 declaration is
- forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (P : C), Iff (CategoryTheory.Projective.{u1, u2} C _inst_1 P) (CategoryTheory.Functor.PreservesEpimorphisms.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (CategoryTheory.Functor.obj.{u1, max u2 u1, u2, max u1 u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.preadditiveCoyoneda.{u1, u2} C _inst_1 _inst_2) (Opposite.op.{succ u2} C P)))
-but is expected to have type
- forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (P : C), Iff (CategoryTheory.Projective.{u1, u2} C _inst_1 P) (CategoryTheory.Functor.PreservesEpimorphisms.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1} (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.preadditiveCoyoneda.{u1, u2} C _inst_1 _inst_2)) (Opposite.op.{succ u2} C P)))
-Case conversion may be inaccurate. Consider using '#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_objₓ'. -/
theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj (P : C) :
Projective P ↔ (preadditiveCoyoneda.obj (op P)).PreservesEpimorphisms :=
by
@@ -54,12 +48,6 @@ theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj (P : C) :
exact (inferInstance : (preadditive_coyoneda.obj (op P) ⋙ forget _).PreservesEpimorphisms)
#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj
-/- warning: category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj' -> CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj' is a dubious translation:
-lean 3 declaration is
- forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (P : C), Iff (CategoryTheory.Projective.{u1, u2} C _inst_1 P) (CategoryTheory.Functor.PreservesEpimorphisms.{u1, u1, u2, succ u1} C _inst_1 (ModuleCat.{u1, u1} (CategoryTheory.End.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (Opposite.op.{succ u2} C P)) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Opposite.preadditive.{u2, u1} C _inst_1 _inst_2) (Opposite.op.{succ u2} C P))) (ModuleCat.moduleCategory.{u1, u1} (CategoryTheory.End.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (Opposite.op.{succ u2} C P)) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Opposite.preadditive.{u2, u1} C _inst_1 _inst_2) (Opposite.op.{succ u2} C P))) (CategoryTheory.preadditiveCoyonedaObj.{u1, u2} C _inst_1 _inst_2 (Opposite.op.{succ u2} C P)))
-but is expected to have type
- forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (P : C), Iff (CategoryTheory.Projective.{u1, u2} C _inst_1 P) (CategoryTheory.Functor.PreservesEpimorphisms.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1} (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.preadditiveCoyoneda.{u1, u2} C _inst_1 _inst_2)) (Opposite.op.{succ u2} C P)))
-Case conversion may be inaccurate. Consider using '#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj' CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj'ₓ'. -/
theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj' (P : C) :
Projective P ↔ (preadditiveCoyonedaObj (op P)).PreservesEpimorphisms :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -54,13 +54,13 @@ theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj (P : C) :
exact (inferInstance : (preadditive_coyoneda.obj (op P) ⋙ forget _).PreservesEpimorphisms)
#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj
-/- warning: category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj' -> CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditive_coyoneda_obj' is a dubious translation:
+/- warning: category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj' -> CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj' is a dubious translation:
lean 3 declaration is
forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (P : C), Iff (CategoryTheory.Projective.{u1, u2} C _inst_1 P) (CategoryTheory.Functor.PreservesEpimorphisms.{u1, u1, u2, succ u1} C _inst_1 (ModuleCat.{u1, u1} (CategoryTheory.End.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (Opposite.op.{succ u2} C P)) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Opposite.preadditive.{u2, u1} C _inst_1 _inst_2) (Opposite.op.{succ u2} C P))) (ModuleCat.moduleCategory.{u1, u1} (CategoryTheory.End.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (Opposite.op.{succ u2} C P)) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Opposite.preadditive.{u2, u1} C _inst_1 _inst_2) (Opposite.op.{succ u2} C P))) (CategoryTheory.preadditiveCoyonedaObj.{u1, u2} C _inst_1 _inst_2 (Opposite.op.{succ u2} C P)))
but is expected to have type
forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (P : C), Iff (CategoryTheory.Projective.{u1, u2} C _inst_1 P) (CategoryTheory.Functor.PreservesEpimorphisms.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1} (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.preadditiveCoyoneda.{u1, u2} C _inst_1 _inst_2)) (Opposite.op.{succ u2} C P)))
-Case conversion may be inaccurate. Consider using '#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj' CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditive_coyoneda_obj'ₓ'. -/
-theorem projective_iff_preservesEpimorphisms_preadditive_coyoneda_obj' (P : C) :
+Case conversion may be inaccurate. Consider using '#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj' CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj'ₓ'. -/
+theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj' (P : C) :
Projective P ↔ (preadditiveCoyonedaObj (op P)).PreservesEpimorphisms :=
by
rw [projective_iff_preserves_epimorphisms_coyoneda_obj]
@@ -71,7 +71,7 @@ theorem projective_iff_preservesEpimorphisms_preadditive_coyoneda_obj' (P : C) :
(forget _)
· intro
exact (inferInstance : (preadditive_coyoneda_obj (op P) ⋙ forget _).PreservesEpimorphisms)
-#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj' CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditive_coyoneda_obj'
+#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj' CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj'
end Projective
mathlib commit https://github.com/leanprover-community/mathlib/commit/403190b5419b3f03f1a2893ad9352ca7f7d8bff6
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
! This file was ported from Lean 3 source module category_theory.preadditive.yoneda.projective
-! leanprover-community/mathlib commit f8d8465c3c392a93b9ed226956e26dee00975946
+! leanprover-community/mathlib commit bd15ff41b70f5e2cc210f26f25a8d5c53b20d3de
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.Algebra.Category.Group.EpiMono
import Mathbin.Algebra.Category.Module.EpiMono
/-!
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
An object is projective iff the preadditive coyoneda functor on it preserves epimorphisms.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740
@@ -36,7 +36,7 @@ namespace Projective
lean 3 declaration is
forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (P : C), Iff (CategoryTheory.Projective.{u1, u2} C _inst_1 P) (CategoryTheory.Functor.PreservesEpimorphisms.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (CategoryTheory.Functor.obj.{u1, max u2 u1, u2, max u1 u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.preadditiveCoyoneda.{u1, u2} C _inst_1 _inst_2) (Opposite.op.{succ u2} C P)))
but is expected to have type
- forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (P : C), Iff (CategoryTheory.Projective.{u1, u2} C _inst_1 P) (CategoryTheory.Functor.PreservesEpimorphisms.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.preadditiveCoyoneda.{u1, u2} C _inst_1 _inst_2)) (Opposite.op.{succ u2} C P)))
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (P : C), Iff (CategoryTheory.Projective.{u1, u2} C _inst_1 P) (CategoryTheory.Functor.PreservesEpimorphisms.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1} (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.preadditiveCoyoneda.{u1, u2} C _inst_1 _inst_2)) (Opposite.op.{succ u2} C P)))
Case conversion may be inaccurate. Consider using '#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_objₓ'. -/
theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj (P : C) :
Projective P ↔ (preadditiveCoyoneda.obj (op P)).PreservesEpimorphisms :=
@@ -55,7 +55,7 @@ theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj (P : C) :
lean 3 declaration is
forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (P : C), Iff (CategoryTheory.Projective.{u1, u2} C _inst_1 P) (CategoryTheory.Functor.PreservesEpimorphisms.{u1, u1, u2, succ u1} C _inst_1 (ModuleCat.{u1, u1} (CategoryTheory.End.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (Opposite.op.{succ u2} C P)) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Opposite.preadditive.{u2, u1} C _inst_1 _inst_2) (Opposite.op.{succ u2} C P))) (ModuleCat.moduleCategory.{u1, u1} (CategoryTheory.End.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (Opposite.op.{succ u2} C P)) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Opposite.preadditive.{u2, u1} C _inst_1 _inst_2) (Opposite.op.{succ u2} C P))) (CategoryTheory.preadditiveCoyonedaObj.{u1, u2} C _inst_1 _inst_2 (Opposite.op.{succ u2} C P)))
but is expected to have type
- forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (P : C), Iff (CategoryTheory.Projective.{u1, u2} C _inst_1 P) (CategoryTheory.Functor.PreservesEpimorphisms.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.preadditiveCoyoneda.{u1, u2} C _inst_1 _inst_2)) (Opposite.op.{succ u2} C P)))
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (P : C), Iff (CategoryTheory.Projective.{u1, u2} C _inst_1 P) (CategoryTheory.Functor.PreservesEpimorphisms.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1} (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.preadditiveCoyoneda.{u1, u2} C _inst_1 _inst_2)) (Opposite.op.{succ u2} C P)))
Case conversion may be inaccurate. Consider using '#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj' CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditive_coyoneda_obj'ₓ'. -/
theorem projective_iff_preservesEpimorphisms_preadditive_coyoneda_obj' (P : C) :
Projective P ↔ (preadditiveCoyonedaObj (op P)).PreservesEpimorphisms :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/28b2a92f2996d28e580450863c130955de0ed398
@@ -32,6 +32,12 @@ variable [Preadditive C]
namespace Projective
+/- warning: category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj -> CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj is a dubious translation:
+lean 3 declaration is
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (P : C), Iff (CategoryTheory.Projective.{u1, u2} C _inst_1 P) (CategoryTheory.Functor.PreservesEpimorphisms.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (CategoryTheory.Functor.obj.{u1, max u2 u1, u2, max u1 u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.preadditiveCoyoneda.{u1, u2} C _inst_1 _inst_2) (Opposite.op.{succ u2} C P)))
+but is expected to have type
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (P : C), Iff (CategoryTheory.Projective.{u1, u2} C _inst_1 P) (CategoryTheory.Functor.PreservesEpimorphisms.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.preadditiveCoyoneda.{u1, u2} C _inst_1 _inst_2)) (Opposite.op.{succ u2} C P)))
+Case conversion may be inaccurate. Consider using '#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_objₓ'. -/
theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj (P : C) :
Projective P ↔ (preadditiveCoyoneda.obj (op P)).PreservesEpimorphisms :=
by
@@ -45,6 +51,12 @@ theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj (P : C) :
exact (inferInstance : (preadditive_coyoneda.obj (op P) ⋙ forget _).PreservesEpimorphisms)
#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj
+/- warning: category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj' -> CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditive_coyoneda_obj' is a dubious translation:
+lean 3 declaration is
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (P : C), Iff (CategoryTheory.Projective.{u1, u2} C _inst_1 P) (CategoryTheory.Functor.PreservesEpimorphisms.{u1, u1, u2, succ u1} C _inst_1 (ModuleCat.{u1, u1} (CategoryTheory.End.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (Opposite.op.{succ u2} C P)) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Opposite.preadditive.{u2, u1} C _inst_1 _inst_2) (Opposite.op.{succ u2} C P))) (ModuleCat.moduleCategory.{u1, u1} (CategoryTheory.End.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1)) (Opposite.op.{succ u2} C P)) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Opposite.preadditive.{u2, u1} C _inst_1 _inst_2) (Opposite.op.{succ u2} C P))) (CategoryTheory.preadditiveCoyonedaObj.{u1, u2} C _inst_1 _inst_2 (Opposite.op.{succ u2} C P)))
+but is expected to have type
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (P : C), Iff (CategoryTheory.Projective.{u1, u2} C _inst_1 P) (CategoryTheory.Functor.PreservesEpimorphisms.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (Prefunctor.obj.{succ u1, max (succ u2) (succ u1), u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.toCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1))) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.Functor.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} C _inst_1 AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.preadditiveCoyoneda.{u1, u2} C _inst_1 _inst_2)) (Opposite.op.{succ u2} C P)))
+Case conversion may be inaccurate. Consider using '#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj' CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditive_coyoneda_obj'ₓ'. -/
theorem projective_iff_preservesEpimorphisms_preadditive_coyoneda_obj' (P : C) :
Projective P ↔ (preadditiveCoyonedaObj (op P)).PreservesEpimorphisms :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce11c3c2a285bbe6937e26d9792fda4e51f3fe1a
@@ -6,7 +6,6 @@ Authors: Markus Himmel, Scott Morrison
import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic
import Mathlib.CategoryTheory.Preadditive.Projective
import Mathlib.Algebra.Category.GroupCat.EpiMono
-import Mathlib.Algebra.Category.ModuleCat.EpiMono
#align_import category_theory.preadditive.yoneda.projective from "leanprover-community/mathlib"@"f8d8465c3c392a93b9ed226956e26dee00975946"
@@ -2,17 +2,14 @@
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.preadditive.yoneda.projective
-! 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.Preadditive.Yoneda.Basic
import Mathlib.CategoryTheory.Preadditive.Projective
import Mathlib.Algebra.Category.GroupCat.EpiMono
import Mathlib.Algebra.Category.ModuleCat.EpiMono
+#align_import category_theory.preadditive.yoneda.projective from "leanprover-community/mathlib"@"f8d8465c3c392a93b9ed226956e26dee00975946"
+
/-!
An object is projective iff the preadditive coyoneda functor on it preserves epimorphisms.
-/
@@ -32,7 +32,7 @@ variable [Preadditive C]
namespace Projective
-theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj (P : C):
+theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj (P : C) :
Projective P ↔ (preadditiveCoyoneda.obj (op P)).PreservesEpimorphisms := by
rw [projective_iff_preservesEpimorphisms_coyoneda_obj]
refine' ⟨fun h : (preadditiveCoyoneda.obj (op P) ⋙
@@ -43,7 +43,7 @@ theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj (P : C):
exact (inferInstance : (preadditiveCoyoneda.obj (op P) ⋙ forget _).PreservesEpimorphisms)
#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj
-theorem projective_iff_preservesEpimorphisms_preadditive_coyoneda_obj' (P : C) :
+theorem projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj' (P : C) :
Projective P ↔ (preadditiveCoyoneda.obj (op P)).PreservesEpimorphisms := by
rw [projective_iff_preservesEpimorphisms_coyoneda_obj]
refine' ⟨fun h : (preadditiveCoyoneda.obj (op P) ⋙
@@ -52,7 +52,7 @@ theorem projective_iff_preservesEpimorphisms_preadditive_coyoneda_obj' (P : C) :
(forget _)
· intro
exact (inferInstance : (preadditiveCoyoneda.obj (op P) ⋙ forget _).PreservesEpimorphisms)
-#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj' CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditive_coyoneda_obj'
+#align category_theory.projective.projective_iff_preserves_epimorphisms_preadditive_coyoneda_obj' CategoryTheory.Projective.projective_iff_preservesEpimorphisms_preadditiveCoyoneda_obj'
end Projective
The unported dependencies are