category_theory.limits.shapes.split_coequalizer
⟷
Mathlib.CategoryTheory.Limits.Shapes.SplitCoequalizer
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
@@ -138,7 +138,7 @@ end
variable (f g)
#print CategoryTheory.HasSplitCoequalizer /-
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`splittable] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`splittable] [] -/
/--
The pair `f,g` is a split pair if there is a `h : Y ⟶ Z` so that `f, g, h` forms a split coequalizer
in `C`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -138,7 +138,7 @@ end
variable (f g)
#print CategoryTheory.HasSplitCoequalizer /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`splittable] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`splittable] [] -/
/--
The pair `f,g` is a split pair if there is a `h : Y ⟶ Z` so that `f, g, h` forms a split coequalizer
in `C`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,7 +3,7 @@ Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
-import Mathbin.CategoryTheory.Limits.Shapes.Equalizers
+import CategoryTheory.Limits.Shapes.Equalizers
#align_import category_theory.limits.shapes.split_coequalizer from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
@@ -138,7 +138,7 @@ end
variable (f g)
#print CategoryTheory.HasSplitCoequalizer /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`splittable] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`splittable] [] -/
/--
The pair `f,g` is a split pair if there is a `h : Y ⟶ Z` so that `f, g, h` forms a split coequalizer
in `C`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.limits.shapes.split_coequalizer
-! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Limits.Shapes.Equalizers
+#align_import category_theory.limits.shapes.split_coequalizer from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
+
/-!
# Split coequalizers
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -87,6 +87,7 @@ attribute [simp, reassoc] right_section_π left_section_bottom left_section_top
variable {f g}
+#print CategoryTheory.IsSplitCoequalizer.map /-
/-- Split coequalizers are absolute: they are preserved by any functor. -/
@[simps]
def IsSplitCoequalizer.map {Z : C} {π : Y ⟶ Z} (q : IsSplitCoequalizer f g π) (F : C ⥤ D) :
@@ -99,6 +100,7 @@ def IsSplitCoequalizer.map {Z : C} {π : Y ⟶ Z} (q : IsSplitCoequalizer f g π
leftSection_bottom := by rw [← F.map_comp, q.left_section_bottom, F.map_id]
leftSection_top := by rw [← F.map_comp, q.left_section_top, F.map_comp]
#align category_theory.is_split_coequalizer.map CategoryTheory.IsSplitCoequalizer.map
+-/
section
@@ -112,11 +114,13 @@ def IsSplitCoequalizer.asCofork {Z : C} {h : Y ⟶ Z} (t : IsSplitCoequalizer f
#align category_theory.is_split_coequalizer.as_cofork CategoryTheory.IsSplitCoequalizer.asCofork
-/
+#print CategoryTheory.IsSplitCoequalizer.asCofork_π /-
@[simp]
theorem IsSplitCoequalizer.asCofork_π {Z : C} {h : Y ⟶ Z} (t : IsSplitCoequalizer f g h) :
t.asCofork.π = h :=
rfl
#align category_theory.is_split_coequalizer.as_cofork_π CategoryTheory.IsSplitCoequalizer.asCofork_π
+-/
#print CategoryTheory.IsSplitCoequalizer.isCoequalizer /-
/--
@@ -137,7 +141,7 @@ end
variable (f g)
#print CategoryTheory.HasSplitCoequalizer /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`splittable] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`splittable] [] -/
/--
The pair `f,g` is a split pair if there is a `h : Y ⟶ Z` so that `f, g, h` forms a split coequalizer
in `C`.
@@ -180,11 +184,13 @@ noncomputable def HasSplitCoequalizer.isSplitCoequalizer [HasSplitCoequalizer f
#align category_theory.has_split_coequalizer.is_split_coequalizer CategoryTheory.HasSplitCoequalizer.isSplitCoequalizer
-/
+#print CategoryTheory.map_is_split_pair /-
/-- If `f, g` is split, then `G f, G g` is split. -/
instance map_is_split_pair [HasSplitCoequalizer f g] : HasSplitCoequalizer (G.map f) (G.map g)
where splittable :=
⟨_, _, ⟨IsSplitCoequalizer.map (HasSplitCoequalizer.isSplitCoequalizer f g) _⟩⟩
#align category_theory.map_is_split_pair CategoryTheory.map_is_split_pair
+-/
namespace Limits
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -137,7 +137,7 @@ end
variable (f g)
#print CategoryTheory.HasSplitCoequalizer /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`splittable] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`splittable] [] -/
/--
The pair `f,g` is a split pair if there is a `h : Y ⟶ Z` so that `f, g, h` forms a split coequalizer
in `C`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb
@@ -143,7 +143,7 @@ The pair `f,g` is a split pair if there is a `h : Y ⟶ Z` so that `f, g, h` for
in `C`.
-/
class HasSplitCoequalizer : Prop where
- splittable : ∃ (Z : C)(h : Y ⟶ Z), Nonempty (IsSplitCoequalizer f g h)
+ splittable : ∃ (Z : C) (h : Y ⟶ Z), Nonempty (IsSplitCoequalizer f g h)
#align category_theory.has_split_coequalizer CategoryTheory.HasSplitCoequalizer
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -87,12 +87,6 @@ attribute [simp, reassoc] right_section_π left_section_bottom left_section_top
variable {f g}
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-Case conversion may be inaccurate. Consider using '#align category_theory.is_split_coequalizer.map CategoryTheory.IsSplitCoequalizer.mapₓ'. -/
/-- Split coequalizers are absolute: they are preserved by any functor. -/
@[simps]
def IsSplitCoequalizer.map {Z : C} {π : Y ⟶ Z} (q : IsSplitCoequalizer f g π) (F : C ⥤ D) :
@@ -118,12 +112,6 @@ def IsSplitCoequalizer.asCofork {Z : C} {h : Y ⟶ Z} (t : IsSplitCoequalizer f
#align category_theory.is_split_coequalizer.as_cofork CategoryTheory.IsSplitCoequalizer.asCofork
-/
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-Case conversion may be inaccurate. Consider using '#align category_theory.is_split_coequalizer.as_cofork_π CategoryTheory.IsSplitCoequalizer.asCofork_πₓ'. -/
@[simp]
theorem IsSplitCoequalizer.asCofork_π {Z : C} {h : Y ⟶ Z} (t : IsSplitCoequalizer f g h) :
t.asCofork.π = h :=
@@ -192,12 +180,6 @@ noncomputable def HasSplitCoequalizer.isSplitCoequalizer [HasSplitCoequalizer f
#align category_theory.has_split_coequalizer.is_split_coequalizer CategoryTheory.HasSplitCoequalizer.isSplitCoequalizer
-/
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-Case conversion may be inaccurate. Consider using '#align category_theory.map_is_split_pair CategoryTheory.map_is_split_pairₓ'. -/
/-- If `f, g` is split, then `G f, G g` is split. -/
instance map_is_split_pair [HasSplitCoequalizer f g] : HasSplitCoequalizer (G.map f) (G.map g)
where splittable :=
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -138,8 +138,7 @@ is more convenient to show a given cofork is a coequalizer by showing it is spli
def IsSplitCoequalizer.isCoequalizer {Z : C} {h : Y ⟶ Z} (t : IsSplitCoequalizer f g h) :
IsColimit t.asCofork :=
Cofork.IsColimit.mk' _ fun s =>
- ⟨t.rightSection ≫ s.π, by
- dsimp
+ ⟨t.rightSection ≫ s.π, by dsimp;
rw [← t.left_section_top_assoc, s.condition, t.left_section_bottom_assoc], fun m hm => by
simp [← hm]⟩
#align category_theory.is_split_coequalizer.is_coequalizer CategoryTheory.IsSplitCoequalizer.isCoequalizer
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -81,9 +81,9 @@ instance {X : C} : Inhabited (IsSplitCoequalizer (𝟙 X) (𝟙 X) (𝟙 X)) :=
open IsSplitCoequalizer
-attribute [reassoc.1] condition
+attribute [reassoc] condition
-attribute [simp, reassoc.1] right_section_π left_section_bottom left_section_top
+attribute [simp, reassoc] right_section_π left_section_bottom left_section_top
variable {f g}
mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c
@@ -150,7 +150,7 @@ end
variable (f g)
#print CategoryTheory.HasSplitCoequalizer /-
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`splittable] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`splittable] [] -/
/--
The pair `f,g` is a split pair if there is a `h : Y ⟶ Z` so that `f, g, h` forms a split coequalizer
in `C`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
! This file was ported from Lean 3 source module category_theory.limits.shapes.split_coequalizer
-! leanprover-community/mathlib commit 024a4231815538ac739f52d08dd20a55da0d6b23
+! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
! Please do not edit these lines, except to modify the commit id
! if you have ported upstream changes.
-/
@@ -13,6 +13,9 @@ import Mathbin.CategoryTheory.Limits.Shapes.Equalizers
/-!
# Split coequalizers
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
We define what it means for a triple of morphisms `f g : X ⟶ Y`, `π : Y ⟶ Z` to be a split
coequalizer: there is a section `s` of `π` and a section `t` of `g`, which additionally satisfy
`t ≫ f = π ≫ s`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/3b267e70a936eebb21ab546f49a8df34dd300b25
@@ -45,6 +45,7 @@ variable (G : C ⥤ D)
variable {X Y : C} (f g : X ⟶ Y)
+#print CategoryTheory.IsSplitCoequalizer /-
/-- A split coequalizer diagram consists of morphisms
f π
@@ -70,6 +71,7 @@ structure IsSplitCoequalizer {Z : C} (π : Y ⟶ Z) where
leftSection_bottom : left_section ≫ g = 𝟙 Y
leftSection_top : left_section ≫ f = π ≫ right_section
#align category_theory.is_split_coequalizer CategoryTheory.IsSplitCoequalizer
+-/
instance {X : C} : Inhabited (IsSplitCoequalizer (𝟙 X) (𝟙 X) (𝟙 X)) :=
⟨⟨𝟙 _, 𝟙 _, rfl, Category.id_comp _, Category.id_comp _, rfl⟩⟩
@@ -82,6 +84,12 @@ attribute [simp, reassoc.1] right_section_π left_section_bottom left_section_to
variable {f g}
+/- warning: category_theory.is_split_coequalizer.map -> CategoryTheory.IsSplitCoequalizer.map is a dubious translation:
+lean 3 declaration is
+ forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] {X : C} {Y : C} {f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y} {g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y} {Z : C} {π : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) Y Z}, (CategoryTheory.IsSplitCoequalizer.{u1, u3} C _inst_1 X Y f g Z π) -> (forall (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2), CategoryTheory.IsSplitCoequalizer.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X Y f) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 F X Y g) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Z) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 F Y Z π))
+but is expected to have type
+ forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] {X : C} {Y : C} {f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y} {g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y} {Z : C} {π : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) Y Z}, (CategoryTheory.IsSplitCoequalizer.{u1, u3} C _inst_1 X Y f g Z π) -> (forall (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2), CategoryTheory.IsSplitCoequalizer.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X Y f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) X Y g) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) Z) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 F) Y Z π))
+Case conversion may be inaccurate. Consider using '#align category_theory.is_split_coequalizer.map CategoryTheory.IsSplitCoequalizer.mapₓ'. -/
/-- Split coequalizers are absolute: they are preserved by any functor. -/
@[simps]
def IsSplitCoequalizer.map {Z : C} {π : Y ⟶ Z} (q : IsSplitCoequalizer f g π) (F : C ⥤ D) :
@@ -99,18 +107,27 @@ section
open Limits
+#print CategoryTheory.IsSplitCoequalizer.asCofork /-
/-- A split coequalizer clearly induces a cofork. -/
@[simps pt]
def IsSplitCoequalizer.asCofork {Z : C} {h : Y ⟶ Z} (t : IsSplitCoequalizer f g h) : Cofork f g :=
Cofork.ofπ h t.condition
#align category_theory.is_split_coequalizer.as_cofork CategoryTheory.IsSplitCoequalizer.asCofork
+-/
+/- warning: category_theory.is_split_coequalizer.as_cofork_π -> CategoryTheory.IsSplitCoequalizer.asCofork_π is a dubious translation:
+lean 3 declaration is
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} {f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y} {g : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y} {Z : C} {h : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y Z} (t : CategoryTheory.IsSplitCoequalizer.{u1, u2} C _inst_1 X Y f g Z h), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.obj.{0, u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory C _inst_1 (CategoryTheory.Limits.parallelPair.{u1, u2} C _inst_1 X Y f g) CategoryTheory.Limits.WalkingParallelPair.one) (CategoryTheory.Functor.obj.{0, u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory C _inst_1 (CategoryTheory.Functor.obj.{u1, u1, u2, max u1 u2} C _inst_1 (CategoryTheory.Functor.{0, u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory C _inst_1) (CategoryTheory.Functor.category.{0, u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory C _inst_1) (CategoryTheory.Functor.const.{0, u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory C _inst_1) (CategoryTheory.Limits.Cocone.pt.{0, u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory C _inst_1 (CategoryTheory.Limits.parallelPair.{u1, u2} C _inst_1 X Y f g) (CategoryTheory.IsSplitCoequalizer.asCofork.{u1, u2} C _inst_1 X Y f g Z h t))) CategoryTheory.Limits.WalkingParallelPair.one)) (CategoryTheory.Limits.Cofork.π.{u1, u2} C _inst_1 X Y f g (CategoryTheory.IsSplitCoequalizer.asCofork.{u1, u2} C _inst_1 X Y f g Z h t)) h
+but is expected to have type
+ forall {C : Type.{u2}} [_inst_1 : CategoryTheory.Category.{u1, u2} C] {X : C} {Y : C} {f : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y} {g : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) X Y} {Z : C} {h : Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) Y Z} (t : CategoryTheory.IsSplitCoequalizer.{u1, u2} C _inst_1 X Y f g Z h), Eq.{succ u1} (Quiver.Hom.{succ u1, u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (Prefunctor.obj.{1, succ u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair (CategoryTheory.CategoryStruct.toQuiver.{0, 0} CategoryTheory.Limits.WalkingParallelPair (CategoryTheory.Category.toCategoryStruct.{0, 0} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory C _inst_1 (CategoryTheory.Limits.parallelPair.{u1, u2} C _inst_1 X Y f g)) CategoryTheory.Limits.WalkingParallelPair.one) (Prefunctor.obj.{1, succ u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair (CategoryTheory.CategoryStruct.toQuiver.{0, 0} CategoryTheory.Limits.WalkingParallelPair (CategoryTheory.Category.toCategoryStruct.{0, 0} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{0, u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory C _inst_1 (Prefunctor.obj.{succ u1, succ u1, u2, max u1 u2} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u2} C (CategoryTheory.Category.toCategoryStruct.{u1, u2} C _inst_1)) (CategoryTheory.Functor.{0, u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory C _inst_1) (CategoryTheory.CategoryStruct.toQuiver.{u1, max u2 u1} (CategoryTheory.Functor.{0, u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory C _inst_1) (CategoryTheory.Category.toCategoryStruct.{u1, max u2 u1} (CategoryTheory.Functor.{0, u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory C _inst_1) (CategoryTheory.Functor.category.{0, u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory C _inst_1))) (CategoryTheory.Functor.toPrefunctor.{u1, u1, u2, max u2 u1} C _inst_1 (CategoryTheory.Functor.{0, u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory C _inst_1) (CategoryTheory.Functor.category.{0, u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory C _inst_1) (CategoryTheory.Functor.const.{0, u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory C _inst_1)) (CategoryTheory.Limits.Cocone.pt.{0, u1, 0, u2} CategoryTheory.Limits.WalkingParallelPair CategoryTheory.Limits.walkingParallelPairHomCategory C _inst_1 (CategoryTheory.Limits.parallelPair.{u1, u2} C _inst_1 X Y f g) (CategoryTheory.IsSplitCoequalizer.asCofork.{u1, u2} C _inst_1 X Y f g Z h t)))) CategoryTheory.Limits.WalkingParallelPair.one)) (CategoryTheory.Limits.Cofork.π.{u1, u2} C _inst_1 X Y f g (CategoryTheory.IsSplitCoequalizer.asCofork.{u1, u2} C _inst_1 X Y f g Z h t)) h
+Case conversion may be inaccurate. Consider using '#align category_theory.is_split_coequalizer.as_cofork_π CategoryTheory.IsSplitCoequalizer.asCofork_πₓ'. -/
@[simp]
theorem IsSplitCoequalizer.asCofork_π {Z : C} {h : Y ⟶ Z} (t : IsSplitCoequalizer f g h) :
t.asCofork.π = h :=
rfl
#align category_theory.is_split_coequalizer.as_cofork_π CategoryTheory.IsSplitCoequalizer.asCofork_π
+#print CategoryTheory.IsSplitCoequalizer.isCoequalizer /-
/--
The cofork induced by a split coequalizer is a coequalizer, justifying the name. In some cases it
is more convenient to show a given cofork is a coequalizer by showing it is split.
@@ -123,11 +140,13 @@ def IsSplitCoequalizer.isCoequalizer {Z : C} {h : Y ⟶ Z} (t : IsSplitCoequaliz
rw [← t.left_section_top_assoc, s.condition, t.left_section_bottom_assoc], fun m hm => by
simp [← hm]⟩
#align category_theory.is_split_coequalizer.is_coequalizer CategoryTheory.IsSplitCoequalizer.isCoequalizer
+-/
end
variable (f g)
+#print CategoryTheory.HasSplitCoequalizer /-
/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`splittable] [] -/
/--
The pair `f,g` is a split pair if there is a `h : Y ⟶ Z` so that `f, g, h` forms a split coequalizer
@@ -136,7 +155,9 @@ in `C`.
class HasSplitCoequalizer : Prop where
splittable : ∃ (Z : C)(h : Y ⟶ Z), Nonempty (IsSplitCoequalizer f g h)
#align category_theory.has_split_coequalizer CategoryTheory.HasSplitCoequalizer
+-/
+#print CategoryTheory.Functor.IsSplitPair /-
/--
The pair `f,g` is a `G`-split pair if there is a `h : G Y ⟶ Z` so that `G f, G g, h` forms a split
coequalizer in `D`.
@@ -144,24 +165,37 @@ coequalizer in `D`.
abbrev Functor.IsSplitPair : Prop :=
HasSplitCoequalizer (G.map f) (G.map g)
#align category_theory.functor.is_split_pair CategoryTheory.Functor.IsSplitPair
+-/
+#print CategoryTheory.HasSplitCoequalizer.coequalizerOfSplit /-
/-- Get the coequalizer object from the typeclass `is_split_pair`. -/
noncomputable def HasSplitCoequalizer.coequalizerOfSplit [HasSplitCoequalizer f g] : C :=
(HasSplitCoequalizer.splittable f g).some
#align category_theory.has_split_coequalizer.coequalizer_of_split CategoryTheory.HasSplitCoequalizer.coequalizerOfSplit
+-/
+#print CategoryTheory.HasSplitCoequalizer.coequalizerπ /-
/-- Get the coequalizer morphism from the typeclass `is_split_pair`. -/
noncomputable def HasSplitCoequalizer.coequalizerπ [HasSplitCoequalizer f g] :
Y ⟶ HasSplitCoequalizer.coequalizerOfSplit f g :=
(HasSplitCoequalizer.splittable f g).choose_spec.some
#align category_theory.has_split_coequalizer.coequalizer_π CategoryTheory.HasSplitCoequalizer.coequalizerπ
+-/
+#print CategoryTheory.HasSplitCoequalizer.isSplitCoequalizer /-
/-- The coequalizer morphism `coequalizer_ι` gives a split coequalizer on `f,g`. -/
noncomputable def HasSplitCoequalizer.isSplitCoequalizer [HasSplitCoequalizer f g] :
IsSplitCoequalizer f g (HasSplitCoequalizer.coequalizerπ f g) :=
Classical.choice (HasSplitCoequalizer.splittable f g).choose_spec.choose_spec
#align category_theory.has_split_coequalizer.is_split_coequalizer CategoryTheory.HasSplitCoequalizer.isSplitCoequalizer
+-/
+/- warning: category_theory.map_is_split_pair -> CategoryTheory.map_is_split_pair is a dubious translation:
+lean 3 declaration is
+ forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) [_inst_3 : CategoryTheory.HasSplitCoequalizer.{u1, u3} C _inst_1 X Y f g], CategoryTheory.HasSplitCoequalizer.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X) (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 G Y) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X Y f) (CategoryTheory.Functor.map.{u1, u2, u3, u4} C _inst_1 D _inst_2 G X Y g)
+but is expected to have type
+ forall {C : Type.{u3}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] {D : Type.{u4}} [_inst_2 : CategoryTheory.Category.{u2, u4} D] (G : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) {X : C} {Y : C} (f : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) (g : Quiver.Hom.{succ u1, u3} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) X Y) [_inst_3 : CategoryTheory.HasSplitCoequalizer.{u1, u3} C _inst_1 X Y f g], CategoryTheory.HasSplitCoequalizer.{u2, u4} D _inst_2 (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X) (Prefunctor.obj.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) Y) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X Y f) (Prefunctor.map.{succ u1, succ u2, u3, u4} C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) (CategoryTheory.Functor.toPrefunctor.{u1, u2, u3, u4} C _inst_1 D _inst_2 G) X Y g)
+Case conversion may be inaccurate. Consider using '#align category_theory.map_is_split_pair CategoryTheory.map_is_split_pairₓ'. -/
/-- If `f, g` is split, then `G f, G g` is split. -/
instance map_is_split_pair [HasSplitCoequalizer f g] : HasSplitCoequalizer (G.map f) (G.map g)
where splittable :=
@@ -170,11 +204,13 @@ instance map_is_split_pair [HasSplitCoequalizer f g] : HasSplitCoequalizer (G.ma
namespace Limits
+#print CategoryTheory.Limits.hasCoequalizer_of_hasSplitCoequalizer /-
/-- If a pair has a split coequalizer, it has a coequalizer. -/
instance (priority := 1) hasCoequalizer_of_hasSplitCoequalizer [HasSplitCoequalizer f g] :
HasCoequalizer f g :=
HasColimit.mk ⟨_, (HasSplitCoequalizer.isSplitCoequalizer f g).isCoequalizer⟩
#align category_theory.limits.has_coequalizer_of_has_split_coequalizer CategoryTheory.Limits.hasCoequalizer_of_hasSplitCoequalizer
+-/
end Limits
mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211
@@ -100,7 +100,7 @@ section
open Limits
/-- A split coequalizer clearly induces a cofork. -/
-@[simps x]
+@[simps pt]
def IsSplitCoequalizer.asCofork {Z : C} {h : Y ⟶ Z} (t : IsSplitCoequalizer f g h) : Cofork f g :=
Cofork.ofπ h t.condition
#align category_theory.is_split_coequalizer.as_cofork CategoryTheory.IsSplitCoequalizer.asCofork
mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc
Empty lines were removed by executing the following Python script twice
import os
import re
# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
for filename in files:
if filename.endswith('.lean'):
file_path = os.path.join(dir_path, filename)
# Open the file and read its contents
with open(file_path, 'r') as file:
content = file.read()
# Use a regular expression to replace sequences of "variable" lines separated by empty lines
# with sequences without empty lines
modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)
# Write the modified content back to the file
with open(file_path, 'w') as file:
file.write(modified_content)
@@ -35,11 +35,8 @@ namespace CategoryTheory
universe v v₂ u u₂
variable {C : Type u} [Category.{v} C]
-
variable {D : Type u₂} [Category.{v₂} D]
-
variable (G : C ⥤ D)
-
variable {X Y : C} (f g : X ⟶ Y)
/-- A split coequalizer diagram consists of morphisms
@@ -170,8 +170,8 @@ noncomputable def HasSplitCoequalizer.isSplitCoequalizer [HasSplitCoequalizer f
#align category_theory.has_split_coequalizer.is_split_coequalizer CategoryTheory.HasSplitCoequalizer.isSplitCoequalizer
/-- If `f, g` is split, then `G f, G g` is split. -/
-instance map_is_split_pair [HasSplitCoequalizer f g] : HasSplitCoequalizer (G.map f) (G.map g)
- where splittable :=
+instance map_is_split_pair [HasSplitCoequalizer f g] : HasSplitCoequalizer (G.map f) (G.map g) where
+ splittable :=
⟨_, _, ⟨IsSplitCoequalizer.map (HasSplitCoequalizer.isSplitCoequalizer f g) _⟩⟩
#align category_theory.map_is_split_pair CategoryTheory.map_is_split_pair
@@ -2,14 +2,11 @@
Copyright (c) 2020 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-
-! This file was ported from Lean 3 source module category_theory.limits.shapes.split_coequalizer
-! leanprover-community/mathlib commit 024a4231815538ac739f52d08dd20a55da0d6b23
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
+#align_import category_theory.limits.shapes.split_coequalizer from "leanprover-community/mathlib"@"024a4231815538ac739f52d08dd20a55da0d6b23"
+
/-!
# Split coequalizers
@@ -139,8 +139,8 @@ end
variable (f g)
/--
-The pair `f,g` is a split pair if there is a `h : Y ⟶ Z` so that `f, g, h` forms a split coequalizer
-in `C`.
+The pair `f,g` is a split pair if there is an `h : Y ⟶ Z` so that `f, g, h` forms a split
+coequalizer in `C`.
-/
class HasSplitCoequalizer : Prop where
/-- There is some split coequalizer -/
@@ -148,7 +148,7 @@ class HasSplitCoequalizer : Prop where
#align category_theory.has_split_coequalizer CategoryTheory.HasSplitCoequalizer
/--
-The pair `f,g` is a `G`-split pair if there is a `h : G Y ⟶ Z` so that `G f, G g, h` forms a split
+The pair `f,g` is a `G`-split pair if there is an `h : G Y ⟶ Z` so that `G f, G g, h` forms a split
coequalizer in `D`.
-/
abbrev Functor.IsSplitPair : Prop :=
@@ -144,7 +144,7 @@ in `C`.
-/
class HasSplitCoequalizer : Prop where
/-- There is some split coequalizer -/
- splittable : ∃ (Z : C)(h : Y ⟶ Z), Nonempty (IsSplitCoequalizer f g h)
+ splittable : ∃ (Z : C) (h : Y ⟶ Z), Nonempty (IsSplitCoequalizer f g h)
#align category_theory.has_split_coequalizer CategoryTheory.HasSplitCoequalizer
/--
vscode is already configured by .vscode/settings.json
to trim these on save. It's not clear how they've managed to stick around.
By doing this all in one PR now, it avoids getting random whitespace diffs in PRs later.
This was done with a regex search in vscode,
@@ -112,7 +112,7 @@ open Limits
/-- A split coequalizer clearly induces a cofork. -/
@[simps! pt]
-def IsSplitCoequalizer.asCofork {Z : C} {h : Y ⟶ Z} (t : IsSplitCoequalizer f g h) :
+def IsSplitCoequalizer.asCofork {Z : C} {h : Y ⟶ Z} (t : IsSplitCoequalizer f g h) :
Cofork f g := Cofork.ofπ h t.condition
#align category_theory.is_split_coequalizer.as_cofork CategoryTheory.IsSplitCoequalizer.asCofork
@@ -189,4 +189,3 @@ instance (priority := 1) hasCoequalizer_of_hasSplitCoequalizer [HasSplitCoequali
end Limits
end CategoryTheory
-
All dependencies are ported!