category_theory.isomorphism_classes
⟷
Mathlib.CategoryTheory.IsomorphismClasses
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
@@ -3,9 +3,9 @@ Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
-import Mathbin.CategoryTheory.Category.Cat
-import Mathbin.CategoryTheory.Groupoid
-import Mathbin.CategoryTheory.Types
+import CategoryTheory.Category.Cat
+import CategoryTheory.Groupoid
+import CategoryTheory.Types
#align_import category_theory.isomorphism_classes from "leanprover-community/mathlib"@"3dadefa3f544b1db6214777fe47910739b54c66a"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,16 +2,13 @@
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module category_theory.isomorphism_classes
-! leanprover-community/mathlib commit 3dadefa3f544b1db6214777fe47910739b54c66a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Category.Cat
import Mathbin.CategoryTheory.Groupoid
import Mathbin.CategoryTheory.Types
+#align_import category_theory.isomorphism_classes from "leanprover-community/mathlib"@"3dadefa3f544b1db6214777fe47910739b54c66a"
+
/-!
# Objects of a category up to an isomorphism
mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
! This file was ported from Lean 3 source module category_theory.isomorphism_classes
-! leanprover-community/mathlib commit d6814c584384ddf2825ff038e868451a7c956f31
+! leanprover-community/mathlib commit 3dadefa3f544b1db6214777fe47910739b54c66a
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -15,6 +15,9 @@ import Mathbin.CategoryTheory.Types
/-!
# Objects of a category up to an isomorphism
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
`is_isomorphic X Y := nonempty (X ≅ Y)` is an equivalence relation on the objects of a category.
The quotient with respect to this relation defines a functor from our category to `Type`.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -28,20 +28,25 @@ section Category
variable {C : Type u} [Category.{v} C]
+#print CategoryTheory.IsIsomorphic /-
/-- An object `X` is isomorphic to an object `Y`, if `X ≅ Y` is not empty. -/
def IsIsomorphic : C → C → Prop := fun X Y => Nonempty (X ≅ Y)
#align category_theory.is_isomorphic CategoryTheory.IsIsomorphic
+-/
variable (C)
+#print CategoryTheory.isIsomorphicSetoid /-
/-- `is_isomorphic` defines a setoid. -/
def isIsomorphicSetoid : Setoid C where
R := IsIsomorphic
iseqv := ⟨fun X => ⟨Iso.refl X⟩, fun X Y ⟨α⟩ => ⟨α.symm⟩, fun X Y Z ⟨α⟩ ⟨β⟩ => ⟨α.trans β⟩⟩
#align category_theory.is_isomorphic_setoid CategoryTheory.isIsomorphicSetoid
+-/
end Category
+#print CategoryTheory.isomorphismClasses /-
/-- The functor that sends each category to the quotient space of its objects up to an isomorphism.
-/
def isomorphismClasses : Cat.{v, u} ⥤ Type u
@@ -49,11 +54,14 @@ def isomorphismClasses : Cat.{v, u} ⥤ Type u
obj C := Quotient (isIsomorphicSetoid C.α)
map C D F := Quot.map F.obj fun X Y ⟨f⟩ => ⟨F.mapIso f⟩
#align category_theory.isomorphism_classes CategoryTheory.isomorphismClasses
+-/
+#print CategoryTheory.Groupoid.isIsomorphic_iff_nonempty_hom /-
theorem Groupoid.isIsomorphic_iff_nonempty_hom {C : Type u} [Groupoid.{v} C] {X Y : C} :
IsIsomorphic X Y ↔ Nonempty (X ⟶ Y) :=
(Groupoid.isoEquivHom X Y).nonempty_congr
#align category_theory.groupoid.is_isomorphic_iff_nonempty_hom CategoryTheory.Groupoid.isIsomorphic_iff_nonempty_hom
+-/
-- PROJECT: define `skeletal`, and show every category is equivalent to a skeletal category,
-- using the axiom of choice to pick a representative of every isomorphism class.
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
@@ -2,16 +2,13 @@
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module category_theory.isomorphism_classes
-! leanprover-community/mathlib commit 28aa996fc6fb4317f0083c4e6daf79878d81be33
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Category.Cat
import Mathlib.CategoryTheory.Groupoid
import Mathlib.CategoryTheory.Types
+#align_import category_theory.isomorphism_classes from "leanprover-community/mathlib"@"28aa996fc6fb4317f0083c4e6daf79878d81be33"
+
/-!
# Objects of a category up to an isomorphism
@@ -34,7 +34,7 @@ def IsIsomorphic : C → C → Prop := fun X Y => Nonempty (X ≅ Y)
variable (C)
-/-- `is_isomorphic` defines a setoid. -/
+/-- `IsIsomorphic` defines a setoid. -/
def isIsomorphicSetoid : Setoid C where
r := IsIsomorphic
iseqv := ⟨fun X => ⟨Iso.refl X⟩, fun ⟨α⟩ => ⟨α.symm⟩, fun ⟨α⟩ ⟨β⟩ => ⟨α.trans β⟩⟩
@@ -46,21 +46,21 @@ end Category
-/
def isomorphismClasses : Cat.{v, u} ⥤ Type u where
obj C := Quotient (isIsomorphicSetoid C.α)
- map {C} {D} F := Quot.map F.obj fun X Y ⟨f⟩ => ⟨F.mapIso f⟩
+ map {C D} F := Quot.map F.obj fun X Y ⟨f⟩ => ⟨F.mapIso f⟩
map_id {C} := by -- Porting note: this used to be `tidy`
dsimp; apply funext; intro x
- apply x.recOn -- Porting note: `induction x` not working yet
- · intro _ _ p
+ apply x.recOn -- Porting note: `induction x` not working yet
+ · intro _ _ p
simp only [types_id_apply]
- · intro _
- rfl
- map_comp {C} {D} {E} f g := by -- Porting note(s): idem
+ · intro _
+ rfl
+ map_comp {C D E} f g := by -- Porting note(s): idem
dsimp; apply funext; intro x
- apply x.recOn
- · intro _ _ _
+ apply x.recOn
+ · intro _ _ _
simp only [types_id_apply]
· intro _
- rfl
+ rfl
#align category_theory.isomorphism_classes CategoryTheory.isomorphismClasses
theorem Groupoid.isIsomorphic_iff_nonempty_hom {C : Type u} [Groupoid.{v} C] {X Y : C} :
@@ -69,4 +69,3 @@ theorem Groupoid.isIsomorphic_iff_nonempty_hom {C : Type u} [Groupoid.{v} C] {X
#align category_theory.groupoid.is_isomorphic_iff_nonempty_hom CategoryTheory.Groupoid.isIsomorphic_iff_nonempty_hom
end CategoryTheory
-
All dependencies are ported!