category_theory.abelian.subobject
⟷
Mathlib.CategoryTheory.Abelian.Subobject
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
@@ -3,8 +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.Subobject.Limits
-import Mathbin.CategoryTheory.Abelian.Basic
+import CategoryTheory.Subobject.Limits
+import CategoryTheory.Abelian.Basic
#align_import category_theory.abelian.subobject 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.abelian.subobject
-! 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.Subobject.Limits
import Mathbin.CategoryTheory.Abelian.Basic
+#align_import category_theory.abelian.subobject from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+
/-!
# Equivalence between subobjects and quotients in an abelian category
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -30,6 +30,7 @@ namespace CategoryTheory.Abelian
variable {C : Type u} [Category.{v} C]
+#print CategoryTheory.Abelian.subobjectIsoSubobjectOp /-
/-- In an abelian category, the subobjects and quotient objects of an object `X` are
order-isomorphic via taking kernels and cokernels.
Implemented here using subobjects in the opposite category,
@@ -69,6 +70,7 @@ def subobjectIsoSubobjectOp [Abelian C] (X : C) : Subobject X ≃o (Subobject (o
autoParam_eq]
· simp only [mono_lift_comp]
#align category_theory.abelian.subobject_iso_subobject_op CategoryTheory.Abelian.subobjectIsoSubobjectOp
+-/
#print CategoryTheory.Abelian.wellPowered_opposite /-
/-- A well-powered abelian category is also well-copowered. -/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -30,12 +30,6 @@ namespace CategoryTheory.Abelian
variable {C : Type u} [Category.{v} C]
-/- warning: category_theory.abelian.subobject_iso_subobject_op -> CategoryTheory.Abelian.subobjectIsoSubobjectOp 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] (X : C), OrderIso.{max u2 u1, max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (OrderDual.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X))) (Preorder.toHasLe.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (CategoryTheory.Subobject.partialOrder.{u2, u1} C _inst_1 X))) (OrderDual.hasLe.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X)) (Preorder.toHasLe.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X)) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X)) (CategoryTheory.Subobject.partialOrder.{u2, u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X)))))
-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] (X : C), OrderIso.{max u2 u1, max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (OrderDual.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X))) (Preorder.toLE.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (CategoryTheory.instPartialOrderSubobject.{u1, u2} C _inst_1 X))) (OrderDual.instLEOrderDual.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X)) (Preorder.toLE.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X)) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X)) (CategoryTheory.instPartialOrderSubobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X)))))
-Case conversion may be inaccurate. Consider using '#align category_theory.abelian.subobject_iso_subobject_op CategoryTheory.Abelian.subobjectIsoSubobjectOpₓ'. -/
/-- In an abelian category, the subobjects and quotient objects of an object `X` are
order-isomorphic via taking kernels and cokernels.
Implemented here using subobjects in the opposite category,
mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
@@ -30,7 +30,12 @@ namespace CategoryTheory.Abelian
variable {C : Type u} [Category.{v} C]
-#print CategoryTheory.Abelian.subobjectIsoSubobjectOp /-
+/- warning: category_theory.abelian.subobject_iso_subobject_op -> CategoryTheory.Abelian.subobjectIsoSubobjectOp 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] (X : C), OrderIso.{max u2 u1, max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (OrderDual.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X))) (Preorder.toHasLe.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (CategoryTheory.Subobject.partialOrder.{u2, u1} C _inst_1 X))) (OrderDual.hasLe.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X)) (Preorder.toHasLe.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X)) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X)) (CategoryTheory.Subobject.partialOrder.{u2, u1} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X)))))
+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] (X : C), OrderIso.{max u2 u1, max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (OrderDual.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X))) (Preorder.toLE.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} C _inst_1 X) (CategoryTheory.instPartialOrderSubobject.{u1, u2} C _inst_1 X))) (OrderDual.instLEOrderDual.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X)) (Preorder.toLE.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X)) (PartialOrder.toPreorder.{max u2 u1} (CategoryTheory.Subobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X)) (CategoryTheory.instPartialOrderSubobject.{u1, u2} (Opposite.{succ u2} C) (CategoryTheory.Category.opposite.{u1, u2} C _inst_1) (Opposite.op.{succ u2} C X)))))
+Case conversion may be inaccurate. Consider using '#align category_theory.abelian.subobject_iso_subobject_op CategoryTheory.Abelian.subobjectIsoSubobjectOpₓ'. -/
/-- In an abelian category, the subobjects and quotient objects of an object `X` are
order-isomorphic via taking kernels and cokernels.
Implemented here using subobjects in the opposite category,
@@ -70,7 +75,6 @@ def subobjectIsoSubobjectOp [Abelian C] (X : C) : Subobject X ≃o (Subobject (o
autoParam_eq]
· simp only [mono_lift_comp]
#align category_theory.abelian.subobject_iso_subobject_op CategoryTheory.Abelian.subobjectIsoSubobjectOp
--/
#print CategoryTheory.Abelian.wellPowered_opposite /-
/-- A well-powered abelian category is also well-copowered. -/
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.abelian.subobject
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
+! 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.Abelian.Basic
/-!
# Equivalence between subobjects and quotients in an abelian category
+> 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/7e281deff072232a3c5b3e90034bd65dde396312
@@ -27,6 +27,7 @@ namespace CategoryTheory.Abelian
variable {C : Type u} [Category.{v} C]
+#print CategoryTheory.Abelian.subobjectIsoSubobjectOp /-
/-- In an abelian category, the subobjects and quotient objects of an object `X` are
order-isomorphic via taking kernels and cokernels.
Implemented here using subobjects in the opposite category,
@@ -66,12 +67,15 @@ def subobjectIsoSubobjectOp [Abelian C] (X : C) : Subobject X ≃o (Subobject (o
autoParam_eq]
· simp only [mono_lift_comp]
#align category_theory.abelian.subobject_iso_subobject_op CategoryTheory.Abelian.subobjectIsoSubobjectOp
+-/
+#print CategoryTheory.Abelian.wellPowered_opposite /-
/-- A well-powered abelian category is also well-copowered. -/
instance wellPowered_opposite [Abelian C] [WellPowered C] : WellPowered Cᵒᵖ
where subobject_small X :=
(small_congr (subobjectIsoSubobjectOp (unop X)).toEquiv).1 inferInstance
#align category_theory.abelian.well_powered_opposite CategoryTheory.Abelian.wellPowered_opposite
+-/
end CategoryTheory.Abelian
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -35,7 +35,7 @@ def subobjectIsoSubobjectOp [Abelian C] (X : C) : Subobject X ≃o (Subobject (o
refine' OrderHom.ext _ _ (funext (Subobject.ind _ _))
intro A f hf
dsimp only [OrderHom.comp_coe, Function.comp_apply, kernelOrderHom_coe, Subobject.lift_mk,
- cokernelOrderHom_coe, OrderHom.id_coe, id.def]
+ cokernelOrderHom_coe, OrderHom.id_coe, id]
refine' Subobject.mk_eq_mk_of_comm _ _ ⟨_, _, Quiver.Hom.unop_inj _, Quiver.Hom.unop_inj _⟩ _
· exact (Abelian.epiDesc f.unop _ (cokernel.condition (kernel.ι f.unop))).op
· exact (cokernel.desc _ _ (kernel.condition f.unop)).op
@@ -49,7 +49,7 @@ def subobjectIsoSubobjectOp [Abelian C] (X : C) : Subobject X ≃o (Subobject (o
refine' OrderHom.ext _ _ (funext (Subobject.ind _ _))
intro A f hf
dsimp only [OrderHom.comp_coe, Function.comp_apply, cokernelOrderHom_coe, Subobject.lift_mk,
- kernelOrderHom_coe, OrderHom.id_coe, id.def, unop_op, Quiver.Hom.unop_op]
+ kernelOrderHom_coe, OrderHom.id_coe, id, unop_op, Quiver.Hom.unop_op]
refine' Subobject.mk_eq_mk_of_comm _ _ ⟨_, _, _, _⟩ _
· exact Abelian.monoLift f _ (kernel.condition (cokernel.π f))
· exact kernel.lift _ _ (cokernel.condition f)
@@ -60,8 +60,8 @@ def subobjectIsoSubobjectOp [Abelian C] (X : C) : Subobject X ≃o (Subobject (o
#align category_theory.abelian.subobject_iso_subobject_op CategoryTheory.Abelian.subobjectIsoSubobjectOp
/-- A well-powered abelian category is also well-copowered. -/
-instance wellPowered_opposite [Abelian C] [WellPowered C] : WellPowered Cᵒᵖ
- where subobject_small X :=
+instance wellPowered_opposite [Abelian C] [WellPowered C] : WellPowered Cᵒᵖ where
+ subobject_small X :=
(small_congr (subobjectIsoSubobjectOp (unop X)).toEquiv).1 inferInstance
#align category_theory.abelian.well_powered_opposite CategoryTheory.Abelian.wellPowered_opposite
@@ -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.abelian.subobject
-! leanprover-community/mathlib commit 70fd9563a21e7b963887c9360bd29b2393e6225a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Subobject.Limits
import Mathlib.CategoryTheory.Abelian.Basic
+#align_import category_theory.abelian.subobject from "leanprover-community/mathlib"@"70fd9563a21e7b963887c9360bd29b2393e6225a"
+
/-!
# Equivalence between subobjects and quotients in an abelian category
The unported dependencies are