category_theory.limits.shapes.reflexive
⟷
Mathlib.CategoryTheory.Limits.Shapes.Reflexive
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
@@ -43,7 +43,7 @@ variable {D : Type u₂} [Category.{v₂} D]
variable {A B : C} {f g : A ⟶ B}
#print CategoryTheory.IsReflexivePair /-
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`common_section] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`common_section] [] -/
/-- The pair `f g : A ⟶ B` is reflexive if there is a morphism `B ⟶ A` which is a section for both.
-/
class IsReflexivePair (f g : A ⟶ B) : Prop where
@@ -52,7 +52,7 @@ class IsReflexivePair (f g : A ⟶ B) : Prop where
-/
#print CategoryTheory.IsCoreflexivePair /-
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`common_retraction] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`common_retraction] [] -/
/--
The pair `f g : A ⟶ B` is coreflexive if there is a morphism `B ⟶ A` which is a retraction for both.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -43,7 +43,7 @@ variable {D : Type u₂} [Category.{v₂} D]
variable {A B : C} {f g : A ⟶ B}
#print CategoryTheory.IsReflexivePair /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`common_section] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`common_section] [] -/
/-- The pair `f g : A ⟶ B` is reflexive if there is a morphism `B ⟶ A` which is a section for both.
-/
class IsReflexivePair (f g : A ⟶ B) : Prop where
@@ -52,7 +52,7 @@ class IsReflexivePair (f g : A ⟶ B) : Prop where
-/
#print CategoryTheory.IsCoreflexivePair /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`common_retraction] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`common_retraction] [] -/
/--
The pair `f g : A ⟶ B` is coreflexive if there is a morphism `B ⟶ A` which is a retraction for both.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -3,8 +3,8 @@ 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 Mathbin.CategoryTheory.Limits.Shapes.KernelPair
+import CategoryTheory.Limits.Shapes.Equalizers
+import CategoryTheory.Limits.Shapes.KernelPair
#align_import category_theory.limits.shapes.reflexive from "leanprover-community/mathlib"@"97eab48559068f3d6313da387714ef25768fb730"
@@ -43,7 +43,7 @@ variable {D : Type u₂} [Category.{v₂} D]
variable {A B : C} {f g : A ⟶ B}
#print CategoryTheory.IsReflexivePair /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`common_section] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`common_section] [] -/
/-- The pair `f g : A ⟶ B` is reflexive if there is a morphism `B ⟶ A` which is a section for both.
-/
class IsReflexivePair (f g : A ⟶ B) : Prop where
@@ -52,7 +52,7 @@ class IsReflexivePair (f g : A ⟶ B) : Prop where
-/
#print CategoryTheory.IsCoreflexivePair /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`common_retraction] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`common_retraction] [] -/
/--
The pair `f g : A ⟶ B` is coreflexive if there is a morphism `B ⟶ A` which is a retraction for both.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,15 +2,12 @@
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.reflexive
-! leanprover-community/mathlib commit 97eab48559068f3d6313da387714ef25768fb730
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Limits.Shapes.Equalizers
import Mathbin.CategoryTheory.Limits.Shapes.KernelPair
+#align_import category_theory.limits.shapes.reflexive from "leanprover-community/mathlib"@"97eab48559068f3d6313da387714ef25768fb730"
+
/-!
# Reflexive coequalizers
mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423
@@ -46,7 +46,7 @@ variable {D : Type u₂} [Category.{v₂} D]
variable {A B : C} {f g : A ⟶ B}
#print CategoryTheory.IsReflexivePair /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`common_section] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`common_section] [] -/
/-- The pair `f g : A ⟶ B` is reflexive if there is a morphism `B ⟶ A` which is a section for both.
-/
class IsReflexivePair (f g : A ⟶ B) : Prop where
@@ -55,7 +55,7 @@ class IsReflexivePair (f g : A ⟶ B) : Prop where
-/
#print CategoryTheory.IsCoreflexivePair /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`common_retraction] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`common_retraction] [] -/
/--
The pair `f g : A ⟶ B` is coreflexive if there is a morphism `B ⟶ A` which is a retraction for both.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297
@@ -46,7 +46,7 @@ variable {D : Type u₂} [Category.{v₂} D]
variable {A B : C} {f g : A ⟶ B}
#print CategoryTheory.IsReflexivePair /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`common_section] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`common_section] [] -/
/-- The pair `f g : A ⟶ B` is reflexive if there is a morphism `B ⟶ A` which is a section for both.
-/
class IsReflexivePair (f g : A ⟶ B) : Prop where
@@ -55,7 +55,7 @@ class IsReflexivePair (f g : A ⟶ B) : Prop where
-/
#print CategoryTheory.IsCoreflexivePair /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`common_retraction] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`common_retraction] [] -/
/--
The pair `f g : A ⟶ B` is coreflexive if there is a morphism `B ⟶ A` which is a retraction for both.
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -152,9 +152,7 @@ variable {F : C ⥤ D} {G : D ⥤ C} (adj : F ⊣ G)
instance (B : D) :
IsReflexivePair (F.map (G.map (adj.counit.app B))) (adj.counit.app (F.obj (G.obj B))) :=
IsReflexivePair.mk' (F.map (adj.Unit.app (G.obj B)))
- (by
- rw [← F.map_comp, adj.right_triangle_components]
- apply F.map_id)
+ (by rw [← F.map_comp, adj.right_triangle_components]; apply F.map_id)
adj.left_triangle_components
namespace Limits
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -86,14 +86,14 @@ noncomputable def commonSection (f g : A ⟶ B) [IsReflexivePair f g] : B ⟶ A
-/
#print CategoryTheory.section_comp_left /-
-@[simp, reassoc.1]
+@[simp, reassoc]
theorem section_comp_left (f g : A ⟶ B) [IsReflexivePair f g] : commonSection f g ≫ f = 𝟙 B :=
(IsReflexivePair.common_section f g).choose_spec.1
#align category_theory.section_comp_left CategoryTheory.section_comp_left
-/
#print CategoryTheory.section_comp_right /-
-@[simp, reassoc.1]
+@[simp, reassoc]
theorem section_comp_right (f g : A ⟶ B) [IsReflexivePair f g] : commonSection f g ≫ g = 𝟙 B :=
(IsReflexivePair.common_section f g).choose_spec.2
#align category_theory.section_comp_right CategoryTheory.section_comp_right
@@ -107,7 +107,7 @@ noncomputable def commonRetraction (f g : A ⟶ B) [IsCoreflexivePair f g] : B
-/
#print CategoryTheory.left_comp_retraction /-
-@[simp, reassoc.1]
+@[simp, reassoc]
theorem left_comp_retraction (f g : A ⟶ B) [IsCoreflexivePair f g] :
f ≫ commonRetraction f g = 𝟙 A :=
(IsCoreflexivePair.common_retraction f g).choose_spec.1
@@ -115,7 +115,7 @@ theorem left_comp_retraction (f g : A ⟶ B) [IsCoreflexivePair f g] :
-/
#print CategoryTheory.right_comp_retraction /-
-@[simp, reassoc.1]
+@[simp, reassoc]
theorem right_comp_retraction (f g : A ⟶ B) [IsCoreflexivePair f g] :
g ≫ commonRetraction f g = 𝟙 A :=
(IsCoreflexivePair.common_retraction f g).choose_spec.2
mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c
@@ -46,7 +46,7 @@ variable {D : Type u₂} [Category.{v₂} D]
variable {A B : C} {f g : A ⟶ B}
#print CategoryTheory.IsReflexivePair /-
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`common_section] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`common_section] [] -/
/-- The pair `f g : A ⟶ B` is reflexive if there is a morphism `B ⟶ A` which is a section for both.
-/
class IsReflexivePair (f g : A ⟶ B) : Prop where
@@ -55,7 +55,7 @@ class IsReflexivePair (f g : A ⟶ B) : Prop where
-/
#print CategoryTheory.IsCoreflexivePair /-
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`common_retraction] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`common_retraction] [] -/
/--
The pair `f g : A ⟶ B` is coreflexive if there is a morphism `B ⟶ A` which is a retraction for both.
-/
@@ -175,9 +175,9 @@ class HasCoreflexiveEqualizers : Prop where
#align category_theory.limits.has_coreflexive_equalizers CategoryTheory.Limits.HasCoreflexiveEqualizers
-/
-attribute [instance] has_reflexive_coequalizers.has_coeq
+attribute [instance 1] has_reflexive_coequalizers.has_coeq
-attribute [instance] has_coreflexive_equalizers.has_eq
+attribute [instance 1] has_coreflexive_equalizers.has_eq
#print CategoryTheory.Limits.hasCoequalizer_of_common_section /-
theorem hasCoequalizer_of_common_section [HasReflexiveCoequalizers C] {A B : C} {f g : A ⟶ B}
mathlib commit https://github.com/leanprover-community/mathlib/commit/d11893b411025250c8e61ff2f12ccbd7ee35ab15
@@ -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.reflexive
-! leanprover-community/mathlib commit d6814c584384ddf2825ff038e868451a7c956f31
+! leanprover-community/mathlib commit 97eab48559068f3d6313da387714ef25768fb730
! 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.Limits.Shapes.KernelPair
/-!
# Reflexive coequalizers
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
We define reflexive pairs as a pair of morphisms which have a common section. We say a category has
reflexive coequalizers if it has coequalizers of all reflexive pairs.
Reflexive coequalizers often enjoy nicer properties than general coequalizers, and feature heavily
mathlib commit https://github.com/leanprover-community/mathlib/commit/57e09a1296bfb4330ddf6624f1028ba186117d82
@@ -42,13 +42,16 @@ variable {D : Type u₂} [Category.{v₂} D]
variable {A B : C} {f g : A ⟶ B}
+#print CategoryTheory.IsReflexivePair /-
/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`common_section] [] -/
/-- The pair `f g : A ⟶ B` is reflexive if there is a morphism `B ⟶ A` which is a section for both.
-/
class IsReflexivePair (f g : A ⟶ B) : Prop where
common_section : ∃ s : B ⟶ A, s ≫ f = 𝟙 B ∧ s ≫ g = 𝟙 B
#align category_theory.is_reflexive_pair CategoryTheory.IsReflexivePair
+-/
+#print CategoryTheory.IsCoreflexivePair /-
/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`common_retraction] [] -/
/--
The pair `f g : A ⟶ B` is coreflexive if there is a morphism `B ⟶ A` which is a retraction for both.
@@ -56,66 +59,89 @@ The pair `f g : A ⟶ B` is coreflexive if there is a morphism `B ⟶ A` which i
class IsCoreflexivePair (f g : A ⟶ B) : Prop where
common_retraction : ∃ s : B ⟶ A, f ≫ s = 𝟙 A ∧ g ≫ s = 𝟙 A
#align category_theory.is_coreflexive_pair CategoryTheory.IsCoreflexivePair
+-/
+#print CategoryTheory.IsReflexivePair.mk' /-
theorem IsReflexivePair.mk' (s : B ⟶ A) (sf : s ≫ f = 𝟙 B) (sg : s ≫ g = 𝟙 B) :
IsReflexivePair f g :=
⟨⟨s, sf, sg⟩⟩
#align category_theory.is_reflexive_pair.mk' CategoryTheory.IsReflexivePair.mk'
+-/
+#print CategoryTheory.IsCoreflexivePair.mk' /-
theorem IsCoreflexivePair.mk' (s : B ⟶ A) (fs : f ≫ s = 𝟙 A) (gs : g ≫ s = 𝟙 A) :
IsCoreflexivePair f g :=
⟨⟨s, fs, gs⟩⟩
#align category_theory.is_coreflexive_pair.mk' CategoryTheory.IsCoreflexivePair.mk'
+-/
+#print CategoryTheory.commonSection /-
/-- Get the common section for a reflexive pair. -/
noncomputable def commonSection (f g : A ⟶ B) [IsReflexivePair f g] : B ⟶ A :=
(IsReflexivePair.common_section f g).some
#align category_theory.common_section CategoryTheory.commonSection
+-/
+#print CategoryTheory.section_comp_left /-
@[simp, reassoc.1]
theorem section_comp_left (f g : A ⟶ B) [IsReflexivePair f g] : commonSection f g ≫ f = 𝟙 B :=
(IsReflexivePair.common_section f g).choose_spec.1
#align category_theory.section_comp_left CategoryTheory.section_comp_left
+-/
+#print CategoryTheory.section_comp_right /-
@[simp, reassoc.1]
theorem section_comp_right (f g : A ⟶ B) [IsReflexivePair f g] : commonSection f g ≫ g = 𝟙 B :=
(IsReflexivePair.common_section f g).choose_spec.2
#align category_theory.section_comp_right CategoryTheory.section_comp_right
+-/
+#print CategoryTheory.commonRetraction /-
/-- Get the common retraction for a coreflexive pair. -/
noncomputable def commonRetraction (f g : A ⟶ B) [IsCoreflexivePair f g] : B ⟶ A :=
(IsCoreflexivePair.common_retraction f g).some
#align category_theory.common_retraction CategoryTheory.commonRetraction
+-/
+#print CategoryTheory.left_comp_retraction /-
@[simp, reassoc.1]
theorem left_comp_retraction (f g : A ⟶ B) [IsCoreflexivePair f g] :
f ≫ commonRetraction f g = 𝟙 A :=
(IsCoreflexivePair.common_retraction f g).choose_spec.1
#align category_theory.left_comp_retraction CategoryTheory.left_comp_retraction
+-/
+#print CategoryTheory.right_comp_retraction /-
@[simp, reassoc.1]
theorem right_comp_retraction (f g : A ⟶ B) [IsCoreflexivePair f g] :
g ≫ commonRetraction f g = 𝟙 A :=
(IsCoreflexivePair.common_retraction f g).choose_spec.2
#align category_theory.right_comp_retraction CategoryTheory.right_comp_retraction
+-/
+#print CategoryTheory.IsKernelPair.isReflexivePair /-
/-- If `f,g` is a kernel pair for some morphism `q`, then it is reflexive. -/
theorem IsKernelPair.isReflexivePair {R : C} {f g : R ⟶ A} {q : A ⟶ B} (h : IsKernelPair q f g) :
IsReflexivePair f g :=
IsReflexivePair.mk' _ (h.lift' _ _ rfl).2.1 (h.lift' _ _ _).2.2
#align category_theory.is_kernel_pair.is_reflexive_pair CategoryTheory.IsKernelPair.isReflexivePair
+-/
+#print CategoryTheory.IsReflexivePair.swap /-
-- This shouldn't be an instance as it would instantly loop.
/-- If `f,g` is reflexive, then `g,f` is reflexive. -/
theorem IsReflexivePair.swap [IsReflexivePair f g] : IsReflexivePair g f :=
IsReflexivePair.mk' _ (section_comp_right f g) (section_comp_left f g)
#align category_theory.is_reflexive_pair.swap CategoryTheory.IsReflexivePair.swap
+-/
+#print CategoryTheory.IsCoreflexivePair.swap /-
-- This shouldn't be an instance as it would instantly loop.
/-- If `f,g` is coreflexive, then `g,f` is coreflexive. -/
theorem IsCoreflexivePair.swap [IsCoreflexivePair f g] : IsCoreflexivePair g f :=
IsCoreflexivePair.mk' _ (right_comp_retraction f g) (left_comp_retraction f g)
#align category_theory.is_coreflexive_pair.swap CategoryTheory.IsCoreflexivePair.swap
+-/
variable {F : C ⥤ D} {G : D ⥤ C} (adj : F ⊣ G)
@@ -132,43 +158,55 @@ namespace Limits
variable (C)
+#print CategoryTheory.Limits.HasReflexiveCoequalizers /-
/-- `C` has reflexive coequalizers if it has coequalizers for every reflexive pair. -/
class HasReflexiveCoequalizers : Prop where
has_coeq : ∀ ⦃A B : C⦄ (f g : A ⟶ B) [IsReflexivePair f g], HasCoequalizer f g
#align category_theory.limits.has_reflexive_coequalizers CategoryTheory.Limits.HasReflexiveCoequalizers
+-/
+#print CategoryTheory.Limits.HasCoreflexiveEqualizers /-
/-- `C` has coreflexive equalizers if it has equalizers for every coreflexive pair. -/
class HasCoreflexiveEqualizers : Prop where
has_eq : ∀ ⦃A B : C⦄ (f g : A ⟶ B) [IsCoreflexivePair f g], HasEqualizer f g
#align category_theory.limits.has_coreflexive_equalizers CategoryTheory.Limits.HasCoreflexiveEqualizers
+-/
attribute [instance] has_reflexive_coequalizers.has_coeq
attribute [instance] has_coreflexive_equalizers.has_eq
+#print CategoryTheory.Limits.hasCoequalizer_of_common_section /-
theorem hasCoequalizer_of_common_section [HasReflexiveCoequalizers C] {A B : C} {f g : A ⟶ B}
(r : B ⟶ A) (rf : r ≫ f = 𝟙 _) (rg : r ≫ g = 𝟙 _) : HasCoequalizer f g :=
by
letI := is_reflexive_pair.mk' r rf rg
infer_instance
#align category_theory.limits.has_coequalizer_of_common_section CategoryTheory.Limits.hasCoequalizer_of_common_section
+-/
+#print CategoryTheory.Limits.hasEqualizer_of_common_retraction /-
theorem hasEqualizer_of_common_retraction [HasCoreflexiveEqualizers C] {A B : C} {f g : A ⟶ B}
(r : B ⟶ A) (fr : f ≫ r = 𝟙 _) (gr : g ≫ r = 𝟙 _) : HasEqualizer f g :=
by
letI := is_coreflexive_pair.mk' r fr gr
infer_instance
#align category_theory.limits.has_equalizer_of_common_retraction CategoryTheory.Limits.hasEqualizer_of_common_retraction
+-/
+#print CategoryTheory.Limits.hasReflexiveCoequalizers_of_hasCoequalizers /-
/-- If `C` has coequalizers, then it has reflexive coequalizers. -/
instance (priority := 100) hasReflexiveCoequalizers_of_hasCoequalizers [HasCoequalizers C] :
HasReflexiveCoequalizers C where has_coeq A B f g i := by infer_instance
#align category_theory.limits.has_reflexive_coequalizers_of_has_coequalizers CategoryTheory.Limits.hasReflexiveCoequalizers_of_hasCoequalizers
+-/
+#print CategoryTheory.Limits.hasCoreflexiveEqualizers_of_hasEqualizers /-
/-- If `C` has equalizers, then it has coreflexive equalizers. -/
instance (priority := 100) hasCoreflexiveEqualizers_of_hasEqualizers [HasEqualizers C] :
HasCoreflexiveEqualizers C where has_eq A B f g i := by infer_instance
#align category_theory.limits.has_coreflexive_equalizers_of_has_equalizers CategoryTheory.Limits.hasCoreflexiveEqualizers_of_hasEqualizers
+-/
end Limits
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)
@@ -34,9 +34,7 @@ namespace CategoryTheory
universe v v₂ u u₂
variable {C : Type u} [Category.{v} C]
-
variable {D : Type u₂} [Category.{v₂} D]
-
variable {A B : C} {f g : A ⟶ B}
/-- The pair `f g : A ⟶ B` is reflexive if there is a morphism `B ⟶ A` which is a section for both.
@@ -45,7 +45,7 @@ class IsReflexivePair (f g : A ⟶ B) : Prop where
common_section' : ∃ s : B ⟶ A, s ≫ f = 𝟙 B ∧ s ≫ g = 𝟙 B
#align category_theory.is_reflexive_pair CategoryTheory.IsReflexivePair
--- Porting note: added theorem, because of unsupported infer kinds
+-- Porting note (#10756): added theorem, because of unsupported infer kinds
theorem IsReflexivePair.common_section (f g : A ⟶ B) [IsReflexivePair f g] :
∃ s : B ⟶ A, s ≫ f = 𝟙 B ∧ s ≫ g = 𝟙 B := IsReflexivePair.common_section'
@@ -56,7 +56,7 @@ class IsCoreflexivePair (f g : A ⟶ B) : Prop where
common_retraction' : ∃ s : B ⟶ A, f ≫ s = 𝟙 A ∧ g ≫ s = 𝟙 A
#align category_theory.is_coreflexive_pair CategoryTheory.IsCoreflexivePair
--- Porting note: added theorem, because of unsupported infer kinds
+-- Porting note (#10756): added theorem, because of unsupported infer kinds
theorem IsCoreflexivePair.common_retraction (f g : A ⟶ B) [IsCoreflexivePair f g] :
∃ s : B ⟶ A, f ≫ s = 𝟙 A ∧ g ≫ s = 𝟙 A := IsCoreflexivePair.common_retraction'
Homogenises porting notes via capitalisation and addition of whitespace.
It makes the following changes:
@@ -45,7 +45,7 @@ class IsReflexivePair (f g : A ⟶ B) : Prop where
common_section' : ∃ s : B ⟶ A, s ≫ f = 𝟙 B ∧ s ≫ g = 𝟙 B
#align category_theory.is_reflexive_pair CategoryTheory.IsReflexivePair
--- porting note: added theorem, because of unsupported infer kinds
+-- Porting note: added theorem, because of unsupported infer kinds
theorem IsReflexivePair.common_section (f g : A ⟶ B) [IsReflexivePair f g] :
∃ s : B ⟶ A, s ≫ f = 𝟙 B ∧ s ≫ g = 𝟙 B := IsReflexivePair.common_section'
@@ -56,7 +56,7 @@ class IsCoreflexivePair (f g : A ⟶ B) : Prop where
common_retraction' : ∃ s : B ⟶ A, f ≫ s = 𝟙 A ∧ g ≫ s = 𝟙 A
#align category_theory.is_coreflexive_pair CategoryTheory.IsCoreflexivePair
--- porting note: added theorem, because of unsupported infer kinds
+-- Porting note: added theorem, because of unsupported infer kinds
theorem IsCoreflexivePair.common_retraction (f g : A ⟶ B) [IsCoreflexivePair f g] :
∃ s : B ⟶ A, f ≫ s = 𝟙 A ∧ g ≫ s = 𝟙 A := IsCoreflexivePair.common_retraction'
This PR contains various prerequisites in order to show that under suitable assumptions, a localized category of a category that has finite products also has finite products:
(J → C) ≌ (Discrete J ⥤ C)
C ⥤ (J ⥤ C)
.MorphismProperty.IsStableUnderFiniteProducts
@@ -129,7 +129,7 @@ instance (B : D) :
(by
rw [← F.map_comp, adj.right_triangle_components]
apply F.map_id)
- adj.left_triangle_components
+ (adj.left_triangle_components _)
namespace Limits
@@ -47,7 +47,7 @@ class IsReflexivePair (f g : A ⟶ B) : Prop where
-- porting note: added theorem, because of unsupported infer kinds
theorem IsReflexivePair.common_section (f g : A ⟶ B) [IsReflexivePair f g] :
- ∃ s : B ⟶ A, s ≫ f = 𝟙 B ∧ s ≫ g = 𝟙 B := IsReflexivePair.common_section'
+ ∃ s : B ⟶ A, s ≫ f = 𝟙 B ∧ s ≫ g = 𝟙 B := IsReflexivePair.common_section'
/--
The pair `f g : A ⟶ B` is coreflexive if there is a morphism `B ⟶ A` which is a retraction for both.
@@ -58,7 +58,7 @@ class IsCoreflexivePair (f g : A ⟶ B) : Prop where
-- porting note: added theorem, because of unsupported infer kinds
theorem IsCoreflexivePair.common_retraction (f g : A ⟶ B) [IsCoreflexivePair f g] :
- ∃ s : B ⟶ A, f ≫ s = 𝟙 A ∧ g ≫ s = 𝟙 A := IsCoreflexivePair.common_retraction'
+ ∃ s : B ⟶ A, f ≫ s = 𝟙 A ∧ g ≫ s = 𝟙 A := IsCoreflexivePair.common_retraction'
theorem IsReflexivePair.mk' (s : B ⟶ A) (sf : s ≫ f = 𝟙 B) (sg : s ≫ g = 𝟙 B) :
IsReflexivePair f g :=
@@ -2,15 +2,12 @@
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.reflexive
-! leanprover-community/mathlib commit d6814c584384ddf2825ff038e868451a7c956f31
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Limits.Shapes.Equalizers
import Mathlib.CategoryTheory.Limits.Shapes.KernelPair
+#align_import category_theory.limits.shapes.reflexive from "leanprover-community/mathlib"@"d6814c584384ddf2825ff038e868451a7c956f31"
+
/-!
# Reflexive coequalizers
@@ -49,7 +49,7 @@ class IsReflexivePair (f g : A ⟶ B) : Prop where
#align category_theory.is_reflexive_pair CategoryTheory.IsReflexivePair
-- porting note: added theorem, because of unsupported infer kinds
-theorem IsReflexivePair.common_section (f g : A ⟶ B) [IsReflexivePair f g]:
+theorem IsReflexivePair.common_section (f g : A ⟶ B) [IsReflexivePair f g] :
∃ s : B ⟶ A, s ≫ f = 𝟙 B ∧ s ≫ g = 𝟙 B := IsReflexivePair.common_section'
/--
@@ -60,7 +60,7 @@ class IsCoreflexivePair (f g : A ⟶ B) : Prop where
#align category_theory.is_coreflexive_pair CategoryTheory.IsCoreflexivePair
-- porting note: added theorem, because of unsupported infer kinds
-theorem IsCoreflexivePair.common_retraction (f g : A ⟶ B) [IsCoreflexivePair f g]:
+theorem IsCoreflexivePair.common_retraction (f g : A ⟶ B) [IsCoreflexivePair f g] :
∃ s : B ⟶ A, f ≫ s = 𝟙 A ∧ g ≫ s = 𝟙 A := IsCoreflexivePair.common_retraction'
theorem IsReflexivePair.mk' (s : B ⟶ A) (sf : s ≫ f = 𝟙 B) (sg : s ≫ g = 𝟙 B) :
See discussion at https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/mathport.20drops.20priorities.20in.20.60attribute.20.5Binstance.5D.60. mathport
has been dropping the priorities on instances when using the attribute
command.
This PR adds back all the priorities, except for local attribute
, and instances involving coercions, which I didn't want to mess with.
Co-authored-by: Scott Morrison <scott.morrison@gmail.com>
@@ -148,9 +148,9 @@ class HasCoreflexiveEqualizers : Prop where
has_eq : ∀ ⦃A B : C⦄ (f g : A ⟶ B) [IsCoreflexivePair f g], HasEqualizer f g
#align category_theory.limits.has_coreflexive_equalizers CategoryTheory.Limits.HasCoreflexiveEqualizers
-attribute [instance] HasReflexiveCoequalizers.has_coeq
+attribute [instance 1] HasReflexiveCoequalizers.has_coeq
-attribute [instance] HasCoreflexiveEqualizers.has_eq
+attribute [instance 1] HasCoreflexiveEqualizers.has_eq
theorem hasCoequalizer_of_common_section [HasReflexiveCoequalizers C] {A B : C} {f g : A ⟶ B}
(r : B ⟶ A) (rf : r ≫ f = 𝟙 _) (rg : r ≫ g = 𝟙 _) : HasCoequalizer f g := by
The unported dependencies are