category_theory.preadditive.generator
⟷
Mathlib.CategoryTheory.Preadditive.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/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -64,7 +64,7 @@ theorem Preadditive.isCoseparator_iff (G : C) :
#print CategoryTheory.isSeparator_iff_faithful_preadditiveCoyoneda /-
theorem isSeparator_iff_faithful_preadditiveCoyoneda (G : C) :
- IsSeparator G ↔ Faithful (preadditiveCoyoneda.obj (op G)) :=
+ IsSeparator G ↔ CategoryTheory.Functor.Faithful (preadditiveCoyoneda.obj (op G)) :=
by
rw [is_separator_iff_faithful_coyoneda_obj, ← whiskering_preadditive_coyoneda, functor.comp_obj,
whiskering_right_obj_obj]
@@ -74,7 +74,7 @@ theorem isSeparator_iff_faithful_preadditiveCoyoneda (G : C) :
#print CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObj /-
theorem isSeparator_iff_faithful_preadditiveCoyonedaObj (G : C) :
- IsSeparator G ↔ Faithful (preadditiveCoyonedaObj (op G)) :=
+ IsSeparator G ↔ CategoryTheory.Functor.Faithful (preadditiveCoyonedaObj (op G)) :=
by
rw [is_separator_iff_faithful_preadditive_coyoneda, preadditive_coyoneda_obj_2]
exact ⟨fun h => faithful.of_comp _ (forget₂ _ AddCommGroupCat.{v}), fun h => faithful.comp _ _⟩
@@ -83,7 +83,7 @@ theorem isSeparator_iff_faithful_preadditiveCoyonedaObj (G : C) :
#print CategoryTheory.isCoseparator_iff_faithful_preadditiveYoneda /-
theorem isCoseparator_iff_faithful_preadditiveYoneda (G : C) :
- IsCoseparator G ↔ Faithful (preadditiveYoneda.obj G) :=
+ IsCoseparator G ↔ CategoryTheory.Functor.Faithful (preadditiveYoneda.obj G) :=
by
rw [is_coseparator_iff_faithful_yoneda_obj, ← whiskering_preadditive_yoneda, functor.comp_obj,
whiskering_right_obj_obj]
@@ -93,7 +93,7 @@ theorem isCoseparator_iff_faithful_preadditiveYoneda (G : C) :
#print CategoryTheory.isCoseparator_iff_faithful_preadditiveYonedaObj /-
theorem isCoseparator_iff_faithful_preadditiveYonedaObj (G : C) :
- IsCoseparator G ↔ Faithful (preadditiveYonedaObj G) :=
+ IsCoseparator G ↔ CategoryTheory.Functor.Faithful (preadditiveYonedaObj G) :=
by
rw [is_coseparator_iff_faithful_preadditive_yoneda, preadditive_yoneda_obj_2]
exact ⟨fun h => faithful.of_comp _ (forget₂ _ AddCommGroupCat.{v}), fun h => faithful.comp _ _⟩
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ 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.Generator
-import Mathbin.CategoryTheory.Preadditive.Yoneda.Basic
+import CategoryTheory.Generator
+import CategoryTheory.Preadditive.Yoneda.Basic
#align_import category_theory.preadditive.generator from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
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.preadditive.generator
-! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Generator
import Mathbin.CategoryTheory.Preadditive.Yoneda.Basic
+#align_import category_theory.preadditive.generator from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+
/-!
# Separators in preadditive categories
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -65,6 +65,7 @@ theorem Preadditive.isCoseparator_iff (G : C) :
#align category_theory.preadditive.is_coseparator_iff CategoryTheory.Preadditive.isCoseparator_iff
-/
+#print CategoryTheory.isSeparator_iff_faithful_preadditiveCoyoneda /-
theorem isSeparator_iff_faithful_preadditiveCoyoneda (G : C) :
IsSeparator G ↔ Faithful (preadditiveCoyoneda.obj (op G)) :=
by
@@ -72,14 +73,18 @@ theorem isSeparator_iff_faithful_preadditiveCoyoneda (G : C) :
whiskering_right_obj_obj]
exact ⟨fun h => faithful.of_comp _ (forget AddCommGroupCat), fun h => faithful.comp _ _⟩
#align category_theory.is_separator_iff_faithful_preadditive_coyoneda CategoryTheory.isSeparator_iff_faithful_preadditiveCoyoneda
+-/
+#print CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObj /-
theorem isSeparator_iff_faithful_preadditiveCoyonedaObj (G : C) :
IsSeparator G ↔ Faithful (preadditiveCoyonedaObj (op G)) :=
by
rw [is_separator_iff_faithful_preadditive_coyoneda, preadditive_coyoneda_obj_2]
exact ⟨fun h => faithful.of_comp _ (forget₂ _ AddCommGroupCat.{v}), fun h => faithful.comp _ _⟩
#align category_theory.is_separator_iff_faithful_preadditive_coyoneda_obj CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObj
+-/
+#print CategoryTheory.isCoseparator_iff_faithful_preadditiveYoneda /-
theorem isCoseparator_iff_faithful_preadditiveYoneda (G : C) :
IsCoseparator G ↔ Faithful (preadditiveYoneda.obj G) :=
by
@@ -87,13 +92,16 @@ theorem isCoseparator_iff_faithful_preadditiveYoneda (G : C) :
whiskering_right_obj_obj]
exact ⟨fun h => faithful.of_comp _ (forget AddCommGroupCat), fun h => faithful.comp _ _⟩
#align category_theory.is_coseparator_iff_faithful_preadditive_yoneda CategoryTheory.isCoseparator_iff_faithful_preadditiveYoneda
+-/
+#print CategoryTheory.isCoseparator_iff_faithful_preadditiveYonedaObj /-
theorem isCoseparator_iff_faithful_preadditiveYonedaObj (G : C) :
IsCoseparator G ↔ Faithful (preadditiveYonedaObj G) :=
by
rw [is_coseparator_iff_faithful_preadditive_yoneda, preadditive_yoneda_obj_2]
exact ⟨fun h => faithful.of_comp _ (forget₂ _ AddCommGroupCat.{v}), fun h => faithful.comp _ _⟩
#align category_theory.is_coseparator_iff_faithful_preadditive_yoneda_obj CategoryTheory.isCoseparator_iff_faithful_preadditiveYonedaObj
+-/
end CategoryTheory
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -65,12 +65,6 @@ theorem Preadditive.isCoseparator_iff (G : C) :
#align category_theory.preadditive.is_coseparator_iff CategoryTheory.Preadditive.isCoseparator_iff
-/
-/- warning: category_theory.is_separator_iff_faithful_preadditive_coyoneda -> CategoryTheory.isSeparator_iff_faithful_preadditiveCoyoneda 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] (G : C), Iff (CategoryTheory.IsSeparator.{u1, u2} C _inst_1 G) (CategoryTheory.Faithful.{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 G)))
-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] (G : C), Iff (CategoryTheory.IsSeparator.{u1, u2} C _inst_1 G) (CategoryTheory.Faithful.{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 G)))
-Case conversion may be inaccurate. Consider using '#align category_theory.is_separator_iff_faithful_preadditive_coyoneda CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaₓ'. -/
theorem isSeparator_iff_faithful_preadditiveCoyoneda (G : C) :
IsSeparator G ↔ Faithful (preadditiveCoyoneda.obj (op G)) :=
by
@@ -79,12 +73,6 @@ theorem isSeparator_iff_faithful_preadditiveCoyoneda (G : C) :
exact ⟨fun h => faithful.of_comp _ (forget AddCommGroupCat), fun h => faithful.comp _ _⟩
#align category_theory.is_separator_iff_faithful_preadditive_coyoneda CategoryTheory.isSeparator_iff_faithful_preadditiveCoyoneda
-/- warning: category_theory.is_separator_iff_faithful_preadditive_coyoneda_obj -> CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObj is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align category_theory.is_separator_iff_faithful_preadditive_coyoneda_obj CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObjₓ'. -/
theorem isSeparator_iff_faithful_preadditiveCoyonedaObj (G : C) :
IsSeparator G ↔ Faithful (preadditiveCoyonedaObj (op G)) :=
by
@@ -92,12 +80,6 @@ theorem isSeparator_iff_faithful_preadditiveCoyonedaObj (G : C) :
exact ⟨fun h => faithful.of_comp _ (forget₂ _ AddCommGroupCat.{v}), fun h => faithful.comp _ _⟩
#align category_theory.is_separator_iff_faithful_preadditive_coyoneda_obj CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObj
-/- warning: category_theory.is_coseparator_iff_faithful_preadditive_yoneda -> CategoryTheory.isCoseparator_iff_faithful_preadditiveYoneda is a dubious translation:
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- forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (G : C), Iff (CategoryTheory.IsCoseparator.{u1, u2} C _inst_1 G) (CategoryTheory.Faithful.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (CategoryTheory.Functor.obj.{u1, max u2 u1, u2, max u1 u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.preadditiveYoneda.{u1, u2} C _inst_1 _inst_2) G))
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-Case conversion may be inaccurate. Consider using '#align category_theory.is_coseparator_iff_faithful_preadditive_yoneda CategoryTheory.isCoseparator_iff_faithful_preadditiveYonedaₓ'. -/
theorem isCoseparator_iff_faithful_preadditiveYoneda (G : C) :
IsCoseparator G ↔ Faithful (preadditiveYoneda.obj G) :=
by
@@ -106,12 +88,6 @@ theorem isCoseparator_iff_faithful_preadditiveYoneda (G : C) :
exact ⟨fun h => faithful.of_comp _ (forget AddCommGroupCat), fun h => faithful.comp _ _⟩
#align category_theory.is_coseparator_iff_faithful_preadditive_yoneda CategoryTheory.isCoseparator_iff_faithful_preadditiveYoneda
-/- warning: category_theory.is_coseparator_iff_faithful_preadditive_yoneda_obj -> CategoryTheory.isCoseparator_iff_faithful_preadditiveYonedaObj is a dubious translation:
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theorem isCoseparator_iff_faithful_preadditiveYonedaObj (G : C) :
IsCoseparator G ↔ Faithful (preadditiveYonedaObj G) :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740
@@ -69,7 +69,7 @@ theorem Preadditive.isCoseparator_iff (G : 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] (G : C), Iff (CategoryTheory.IsSeparator.{u1, u2} C _inst_1 G) (CategoryTheory.Faithful.{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 G)))
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] (G : C), Iff (CategoryTheory.IsSeparator.{u1, u2} C _inst_1 G) (CategoryTheory.Faithful.{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 G)))
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (G : C), Iff (CategoryTheory.IsSeparator.{u1, u2} C _inst_1 G) (CategoryTheory.Faithful.{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 G)))
Case conversion may be inaccurate. Consider using '#align category_theory.is_separator_iff_faithful_preadditive_coyoneda CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaₓ'. -/
theorem isSeparator_iff_faithful_preadditiveCoyoneda (G : C) :
IsSeparator G ↔ Faithful (preadditiveCoyoneda.obj (op G)) :=
@@ -96,7 +96,7 @@ theorem isSeparator_iff_faithful_preadditiveCoyonedaObj (G : 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] (G : C), Iff (CategoryTheory.IsCoseparator.{u1, u2} C _inst_1 G) (CategoryTheory.Faithful.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (CategoryTheory.Functor.obj.{u1, max u2 u1, u2, max u1 u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.preadditiveYoneda.{u1, u2} C _inst_1 _inst_2) G))
but is expected to have type
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+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] [_inst_2 : CategoryTheory.Preadditive.{u1, u2} C _inst_1] (G : C), Iff (CategoryTheory.IsCoseparator.{u1, u2} C _inst_1 G) (CategoryTheory.Faithful.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1} (Prefunctor.obj.{succ u1, max (succ u1) (succ u2), u2, max (succ u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.CategoryStruct.toQuiver.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Category.toCategoryStruct.{max u2 u1, max u2 (succ u1)} (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} instAddCommGroupCatLargeCategory.{u1}) (CategoryTheory.preadditiveYoneda.{u1, u2} C _inst_1 _inst_2)) G))
Case conversion may be inaccurate. Consider using '#align category_theory.is_coseparator_iff_faithful_preadditive_yoneda CategoryTheory.isCoseparator_iff_faithful_preadditiveYonedaₓ'. -/
theorem isCoseparator_iff_faithful_preadditiveYoneda (G : C) :
IsCoseparator G ↔ Faithful (preadditiveYoneda.obj G) :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780
@@ -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.preadditive.generator
-! leanprover-community/mathlib commit 09f981f72d43749f1fa072deade828d9c1e185bb
+! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -14,6 +14,9 @@ import Mathbin.CategoryTheory.Preadditive.Yoneda.Basic
/-!
# Separators in preadditive categories
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
This file contains characterizations of separating sets and objects that are valid in all
preadditive categories.
mathlib commit https://github.com/leanprover-community/mathlib/commit/2651125b48fc5c170ab1111afd0817c903b1fc6c
@@ -28,32 +28,46 @@ namespace CategoryTheory
variable {C : Type u} [Category.{v} C] [Preadditive C]
+#print CategoryTheory.Preadditive.isSeparating_iff /-
theorem Preadditive.isSeparating_iff (𝒢 : Set C) :
IsSeparating 𝒢 ↔ ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ G ∈ 𝒢, ∀ (h : G ⟶ X), h ≫ f = 0) → f = 0 :=
⟨fun h𝒢 X Y f hf => h𝒢 _ _ (by simpa only [limits.comp_zero] using hf), fun h𝒢 X Y f g hfg =>
sub_eq_zero.1 <| h𝒢 _ (by simpa only [preadditive.comp_sub, sub_eq_zero] using hfg)⟩
#align category_theory.preadditive.is_separating_iff CategoryTheory.Preadditive.isSeparating_iff
+-/
+#print CategoryTheory.Preadditive.isCoseparating_iff /-
theorem Preadditive.isCoseparating_iff (𝒢 : Set C) :
IsCoseparating 𝒢 ↔ ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ G ∈ 𝒢, ∀ (h : Y ⟶ G), f ≫ h = 0) → f = 0 :=
⟨fun h𝒢 X Y f hf => h𝒢 _ _ (by simpa only [limits.zero_comp] using hf), fun h𝒢 X Y f g hfg =>
sub_eq_zero.1 <| h𝒢 _ (by simpa only [preadditive.sub_comp, sub_eq_zero] using hfg)⟩
#align category_theory.preadditive.is_coseparating_iff CategoryTheory.Preadditive.isCoseparating_iff
+-/
+#print CategoryTheory.Preadditive.isSeparator_iff /-
theorem Preadditive.isSeparator_iff (G : C) :
IsSeparator G ↔ ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ h : G ⟶ X, h ≫ f = 0) → f = 0 :=
⟨fun hG X Y f hf => hG.def _ _ (by simpa only [limits.comp_zero] using hf), fun hG =>
(isSeparator_def _).2 fun X Y f g hfg =>
sub_eq_zero.1 <| hG _ (by simpa only [preadditive.comp_sub, sub_eq_zero] using hfg)⟩
#align category_theory.preadditive.is_separator_iff CategoryTheory.Preadditive.isSeparator_iff
+-/
+#print CategoryTheory.Preadditive.isCoseparator_iff /-
theorem Preadditive.isCoseparator_iff (G : C) :
IsCoseparator G ↔ ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ h : Y ⟶ G, f ≫ h = 0) → f = 0 :=
⟨fun hG X Y f hf => hG.def _ _ (by simpa only [limits.zero_comp] using hf), fun hG =>
(isCoseparator_def _).2 fun X Y f g hfg =>
sub_eq_zero.1 <| hG _ (by simpa only [preadditive.sub_comp, sub_eq_zero] using hfg)⟩
#align category_theory.preadditive.is_coseparator_iff CategoryTheory.Preadditive.isCoseparator_iff
+-/
+/- warning: category_theory.is_separator_iff_faithful_preadditive_coyoneda -> CategoryTheory.isSeparator_iff_faithful_preadditiveCoyoneda 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] (G : C), Iff (CategoryTheory.IsSeparator.{u1, u2} C _inst_1 G) (CategoryTheory.Faithful.{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 G)))
+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] (G : C), Iff (CategoryTheory.IsSeparator.{u1, u2} C _inst_1 G) (CategoryTheory.Faithful.{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 G)))
+Case conversion may be inaccurate. Consider using '#align category_theory.is_separator_iff_faithful_preadditive_coyoneda CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaₓ'. -/
theorem isSeparator_iff_faithful_preadditiveCoyoneda (G : C) :
IsSeparator G ↔ Faithful (preadditiveCoyoneda.obj (op G)) :=
by
@@ -62,6 +76,12 @@ theorem isSeparator_iff_faithful_preadditiveCoyoneda (G : C) :
exact ⟨fun h => faithful.of_comp _ (forget AddCommGroupCat), fun h => faithful.comp _ _⟩
#align category_theory.is_separator_iff_faithful_preadditive_coyoneda CategoryTheory.isSeparator_iff_faithful_preadditiveCoyoneda
+/- warning: category_theory.is_separator_iff_faithful_preadditive_coyoneda_obj -> CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObj 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] (G : C), Iff (CategoryTheory.IsSeparator.{u1, u2} C _inst_1 G) (CategoryTheory.Faithful.{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 G)) (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 G))) (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 G)) (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 G))) (CategoryTheory.preadditiveCoyonedaObj.{u1, u2} C _inst_1 _inst_2 (Opposite.op.{succ u2} C G)))
+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] (G : C), Iff (CategoryTheory.IsSeparator.{u1, u2} C _inst_1 G) (CategoryTheory.Faithful.{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 G)) (CategoryTheory.Preadditive.instRingEndToCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.instPreadditiveOppositeOpposite.{u2, u1} C _inst_1 _inst_2) (Opposite.op.{succ u2} C G))) (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 G)) (CategoryTheory.Preadditive.instRingEndToCategoryStruct.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (CategoryTheory.instPreadditiveOppositeOpposite.{u2, u1} C _inst_1 _inst_2) (Opposite.op.{succ u2} C G))) (CategoryTheory.preadditiveCoyonedaObj.{u1, u2} C _inst_1 _inst_2 (Opposite.op.{succ u2} C G)))
+Case conversion may be inaccurate. Consider using '#align category_theory.is_separator_iff_faithful_preadditive_coyoneda_obj CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObjₓ'. -/
theorem isSeparator_iff_faithful_preadditiveCoyonedaObj (G : C) :
IsSeparator G ↔ Faithful (preadditiveCoyonedaObj (op G)) :=
by
@@ -69,6 +89,12 @@ theorem isSeparator_iff_faithful_preadditiveCoyonedaObj (G : C) :
exact ⟨fun h => faithful.of_comp _ (forget₂ _ AddCommGroupCat.{v}), fun h => faithful.comp _ _⟩
#align category_theory.is_separator_iff_faithful_preadditive_coyoneda_obj CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObj
+/- warning: category_theory.is_coseparator_iff_faithful_preadditive_yoneda -> CategoryTheory.isCoseparator_iff_faithful_preadditiveYoneda 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] (G : C), Iff (CategoryTheory.IsCoseparator.{u1, u2} C _inst_1 G) (CategoryTheory.Faithful.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (CategoryTheory.Functor.obj.{u1, max u2 u1, u2, max u1 u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.preadditiveYoneda.{u1, u2} C _inst_1 _inst_2) G))
+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] (G : C), Iff (CategoryTheory.IsCoseparator.{u1, u2} C _inst_1 G) (CategoryTheory.Faithful.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1} (Prefunctor.obj.{succ u1, max (succ u1) (succ u2), u2, max (succ u1) u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} 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} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} 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} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}))) (CategoryTheory.Functor.toPrefunctor.{u1, max u2 u1, u2, max u2 (succ u1)} C _inst_1 (CategoryTheory.Functor.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.Functor.category.{u1, u1, u2, succ u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) AddCommGroupCat.{u1} AddCommGroupCat.largeCategory.{u1}) (CategoryTheory.preadditiveYoneda.{u1, u2} C _inst_1 _inst_2)) G))
+Case conversion may be inaccurate. Consider using '#align category_theory.is_coseparator_iff_faithful_preadditive_yoneda CategoryTheory.isCoseparator_iff_faithful_preadditiveYonedaₓ'. -/
theorem isCoseparator_iff_faithful_preadditiveYoneda (G : C) :
IsCoseparator G ↔ Faithful (preadditiveYoneda.obj G) :=
by
@@ -77,6 +103,12 @@ theorem isCoseparator_iff_faithful_preadditiveYoneda (G : C) :
exact ⟨fun h => faithful.of_comp _ (forget AddCommGroupCat), fun h => faithful.comp _ _⟩
#align category_theory.is_coseparator_iff_faithful_preadditive_yoneda CategoryTheory.isCoseparator_iff_faithful_preadditiveYoneda
+/- warning: category_theory.is_coseparator_iff_faithful_preadditive_yoneda_obj -> CategoryTheory.isCoseparator_iff_faithful_preadditiveYonedaObj 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] (G : C), Iff (CategoryTheory.IsCoseparator.{u1, u2} C _inst_1 G) (CategoryTheory.Faithful.{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) G) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} C _inst_1 _inst_2 G)) (ModuleCat.moduleCategory.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) G) (CategoryTheory.Preadditive.CategoryTheory.End.ring.{u1, u2} C _inst_1 _inst_2 G)) (CategoryTheory.preadditiveYonedaObj.{u1, u2} C _inst_1 _inst_2 G))
+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] (G : C), Iff (CategoryTheory.IsCoseparator.{u1, u2} C _inst_1 G) (CategoryTheory.Faithful.{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) G) (CategoryTheory.Preadditive.instRingEndToCategoryStruct.{u1, u2} C _inst_1 _inst_2 G)) (ModuleCat.moduleCategory.{u1, u1} (CategoryTheory.End.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1) G) (CategoryTheory.Preadditive.instRingEndToCategoryStruct.{u1, u2} C _inst_1 _inst_2 G)) (CategoryTheory.preadditiveYonedaObj.{u1, u2} C _inst_1 _inst_2 G))
+Case conversion may be inaccurate. Consider using '#align category_theory.is_coseparator_iff_faithful_preadditive_yoneda_obj CategoryTheory.isCoseparator_iff_faithful_preadditiveYonedaObjₓ'. -/
theorem isCoseparator_iff_faithful_preadditiveYonedaObj (G : C) :
IsCoseparator G ↔ Faithful (preadditiveYonedaObj G) :=
by
mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936
@@ -4,12 +4,12 @@ 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.preadditive.generator
-! leanprover-community/mathlib commit 6db15773a59381c4102a41d7dbad8ec1b1609482
+! 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.Generator
-import Mathbin.CategoryTheory.Preadditive.Yoneda
+import Mathbin.CategoryTheory.Preadditive.Yoneda.Basic
/-!
# Separators in preadditive categories
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
These notions on functors are now Functor.Full
, Functor.Faithful
, Functor.EssSurj
, Functor.IsEquivalence
, Functor.ReflectsIsomorphisms
. Deprecated aliases are introduced for the previous names.
@@ -52,29 +52,33 @@ theorem Preadditive.isCoseparator_iff (G : C) :
#align category_theory.preadditive.is_coseparator_iff CategoryTheory.Preadditive.isCoseparator_iff
theorem isSeparator_iff_faithful_preadditiveCoyoneda (G : C) :
- IsSeparator G ↔ Faithful (preadditiveCoyoneda.obj (op G)) := by
+ IsSeparator G ↔ (preadditiveCoyoneda.obj (op G)).Faithful := by
rw [isSeparator_iff_faithful_coyoneda_obj, ← whiskering_preadditiveCoyoneda, Functor.comp_obj,
whiskeringRight_obj_obj]
- exact ⟨fun h => Faithful.of_comp _ (forget AddCommGroupCat), fun h => Faithful.comp _ _⟩
+ exact ⟨fun h => Functor.Faithful.of_comp _ (forget AddCommGroupCat),
+ fun h => Functor.Faithful.comp _ _⟩
#align category_theory.is_separator_iff_faithful_preadditive_coyoneda CategoryTheory.isSeparator_iff_faithful_preadditiveCoyoneda
theorem isSeparator_iff_faithful_preadditiveCoyonedaObj (G : C) :
- IsSeparator G ↔ Faithful (preadditiveCoyonedaObj (op G)) := by
+ IsSeparator G ↔ (preadditiveCoyonedaObj (op G)).Faithful := by
rw [isSeparator_iff_faithful_preadditiveCoyoneda, preadditiveCoyoneda_obj]
- exact ⟨fun h => Faithful.of_comp _ (forget₂ _ AddCommGroupCat.{v}), fun h => Faithful.comp _ _⟩
+ exact ⟨fun h => Functor.Faithful.of_comp _ (forget₂ _ AddCommGroupCat.{v}),
+ fun h => Functor.Faithful.comp _ _⟩
#align category_theory.is_separator_iff_faithful_preadditive_coyoneda_obj CategoryTheory.isSeparator_iff_faithful_preadditiveCoyonedaObj
theorem isCoseparator_iff_faithful_preadditiveYoneda (G : C) :
- IsCoseparator G ↔ Faithful (preadditiveYoneda.obj G) := by
+ IsCoseparator G ↔ (preadditiveYoneda.obj G).Faithful := by
rw [isCoseparator_iff_faithful_yoneda_obj, ← whiskering_preadditiveYoneda, Functor.comp_obj,
whiskeringRight_obj_obj]
- exact ⟨fun h => Faithful.of_comp _ (forget AddCommGroupCat), fun h => Faithful.comp _ _⟩
+ exact ⟨fun h => Functor.Faithful.of_comp _ (forget AddCommGroupCat),
+ fun h => Functor.Faithful.comp _ _⟩
#align category_theory.is_coseparator_iff_faithful_preadditive_yoneda CategoryTheory.isCoseparator_iff_faithful_preadditiveYoneda
theorem isCoseparator_iff_faithful_preadditiveYonedaObj (G : C) :
- IsCoseparator G ↔ Faithful (preadditiveYonedaObj G) := by
+ IsCoseparator G ↔ (preadditiveYonedaObj G).Faithful := by
rw [isCoseparator_iff_faithful_preadditiveYoneda, preadditiveYoneda_obj]
- exact ⟨fun h => Faithful.of_comp _ (forget₂ _ AddCommGroupCat.{v}), fun h => Faithful.comp _ _⟩
+ exact ⟨fun h => Functor.Faithful.of_comp _ (forget₂ _ AddCommGroupCat.{v}),
+ fun h => Functor.Faithful.comp _ _⟩
#align category_theory.is_coseparator_iff_faithful_preadditive_yoneda_obj CategoryTheory.isCoseparator_iff_faithful_preadditiveYonedaObj
end CategoryTheory
@@ -39,14 +39,14 @@ theorem Preadditive.isCoseparating_iff (𝒢 : Set C) :
theorem Preadditive.isSeparator_iff (G : C) :
IsSeparator G ↔ ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ h : G ⟶ X, h ≫ f = 0) → f = 0 :=
- ⟨fun hG X Y f hf => hG.def' _ _ (by simpa only [Limits.comp_zero] using hf), fun hG =>
+ ⟨fun hG X Y f hf => hG.def _ _ (by simpa only [Limits.comp_zero] using hf), fun hG =>
(isSeparator_def _).2 fun X Y f g hfg =>
sub_eq_zero.1 <| hG _ (by simpa only [Preadditive.comp_sub, sub_eq_zero] using hfg)⟩
#align category_theory.preadditive.is_separator_iff CategoryTheory.Preadditive.isSeparator_iff
theorem Preadditive.isCoseparator_iff (G : C) :
IsCoseparator G ↔ ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ h : Y ⟶ G, f ≫ h = 0) → f = 0 :=
- ⟨fun hG X Y f hf => hG.def' _ _ (by simpa only [Limits.zero_comp] using hf), fun hG =>
+ ⟨fun hG X Y f hf => hG.def _ _ (by simpa only [Limits.zero_comp] using hf), fun hG =>
(isCoseparator_def _).2 fun X Y f g hfg =>
sub_eq_zero.1 <| hG _ (by simpa only [Preadditive.sub_comp, sub_eq_zero] using hfg)⟩
#align category_theory.preadditive.is_coseparator_iff CategoryTheory.Preadditive.isCoseparator_iff
@@ -39,14 +39,14 @@ theorem Preadditive.isCoseparating_iff (𝒢 : Set C) :
theorem Preadditive.isSeparator_iff (G : C) :
IsSeparator G ↔ ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ h : G ⟶ X, h ≫ f = 0) → f = 0 :=
- ⟨fun hG X Y f hf => hG.def _ _ (by simpa only [Limits.comp_zero] using hf), fun hG =>
+ ⟨fun hG X Y f hf => hG.def' _ _ (by simpa only [Limits.comp_zero] using hf), fun hG =>
(isSeparator_def _).2 fun X Y f g hfg =>
sub_eq_zero.1 <| hG _ (by simpa only [Preadditive.comp_sub, sub_eq_zero] using hfg)⟩
#align category_theory.preadditive.is_separator_iff CategoryTheory.Preadditive.isSeparator_iff
theorem Preadditive.isCoseparator_iff (G : C) :
IsCoseparator G ↔ ∀ ⦃X Y : C⦄ (f : X ⟶ Y), (∀ h : Y ⟶ G, f ≫ h = 0) → f = 0 :=
- ⟨fun hG X Y f hf => hG.def _ _ (by simpa only [Limits.zero_comp] using hf), fun hG =>
+ ⟨fun hG X Y f hf => hG.def' _ _ (by simpa only [Limits.zero_comp] using hf), fun hG =>
(isCoseparator_def _).2 fun X Y f g hfg =>
sub_eq_zero.1 <| hG _ (by simpa only [Preadditive.sub_comp, sub_eq_zero] using hfg)⟩
#align category_theory.preadditive.is_coseparator_iff CategoryTheory.Preadditive.isCoseparator_iff
@@ -2,15 +2,12 @@
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.preadditive.generator
-! leanprover-community/mathlib commit 09f981f72d43749f1fa072deade828d9c1e185bb
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Generator
import Mathlib.CategoryTheory.Preadditive.Yoneda.Basic
+#align_import category_theory.preadditive.generator from "leanprover-community/mathlib"@"09f981f72d43749f1fa072deade828d9c1e185bb"
+
/-!
# Separators in preadditive categories
The unported dependencies are