category_theory.abelian.images
⟷
Mathlib.CategoryTheory.Abelian.Images
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
@@ -3,7 +3,7 @@ Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-/
-import Mathbin.CategoryTheory.Limits.Shapes.Kernels
+import CategoryTheory.Limits.Shapes.Kernels
#align_import category_theory.abelian.images from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -2,14 +2,11 @@
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.abelian.images
-! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathbin.CategoryTheory.Limits.Shapes.Kernels
+#align_import category_theory.abelian.images from "leanprover-community/mathlib"@"69c6a5a12d8a2b159f20933e60115a4f2de62b58"
+
/-!
# The abelian image and coimage.
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -131,10 +131,7 @@ in which this is always an isomorphism, is abelian.
See <https://stacks.math.columbia.edu/tag/0107>
-/
def coimageImageComparison : Abelian.coimage f ⟶ Abelian.image f :=
- cokernel.desc (kernel.ι f) (kernel.lift (cokernel.π f) f (by simp)) <|
- by
- ext
- simp
+ cokernel.desc (kernel.ι f) (kernel.lift (cokernel.π f) f (by simp)) <| by ext; simp
#align category_theory.abelian.coimage_image_comparison CategoryTheory.Abelian.coimageImageComparison
-/
@@ -142,18 +139,13 @@ def coimageImageComparison : Abelian.coimage f ⟶ Abelian.image f :=
/-- An alternative formulation of the canonical map from the abelian coimage to the abelian image.
-/
def coimageImageComparison' : Abelian.coimage f ⟶ Abelian.image f :=
- kernel.lift (cokernel.π f) (cokernel.desc (kernel.ι f) f (by simp))
- (by
- ext
- simp)
+ kernel.lift (cokernel.π f) (cokernel.desc (kernel.ι f) f (by simp)) (by ext; simp)
#align category_theory.abelian.coimage_image_comparison' CategoryTheory.Abelian.coimageImageComparison'
-/
#print CategoryTheory.Abelian.coimageImageComparison_eq_coimageImageComparison' /-
theorem coimageImageComparison_eq_coimageImageComparison' :
- coimageImageComparison f = coimageImageComparison' f :=
- by
- ext
+ coimageImageComparison f = coimageImageComparison' f := by ext;
simp [coimage_image_comparison, coimage_image_comparison']
#align category_theory.abelian.coimage_image_comparison_eq_coimage_image_comparison' CategoryTheory.Abelian.coimageImageComparison_eq_coimageImageComparison'
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828
@@ -69,7 +69,7 @@ protected abbrev factorThruImage : P ⟶ Abelian.image f :=
#print CategoryTheory.Abelian.image.fac /-
/-- `f` factors through its image via the canonical morphism `p`. -/
-@[simp, reassoc.1]
+@[simp, reassoc]
protected theorem image.fac : Abelian.factorThruImage f ≫ image.ι f = f :=
kernel.lift_ι _ _ _
#align category_theory.abelian.image.fac CategoryTheory.Abelian.image.fac
@@ -159,7 +159,7 @@ theorem coimageImageComparison_eq_coimageImageComparison' :
-/
#print CategoryTheory.Abelian.coimage_image_factorisation /-
-@[simp, reassoc.1]
+@[simp, reassoc]
theorem coimage_image_factorisation : coimage.π f ≫ coimageImageComparison f ≫ image.ι f = f := by
simp [coimage_image_comparison]
#align category_theory.abelian.coimage_image_factorisation CategoryTheory.Abelian.coimage_image_factorisation
mathlib commit https://github.com/leanprover-community/mathlib/commit/2196ab363eb097c008d4497125e0dde23fb36db2
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
! This file was ported from Lean 3 source module category_theory.abelian.images
-! leanprover-community/mathlib commit 9e7c80f638149bfb3504ba8ff48dfdbfc949fb1a
+! leanprover-community/mathlib commit 69c6a5a12d8a2b159f20933e60115a4f2de62b58
! 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.Kernels
/-!
# The abelian image and coimage.
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
In an abelian category we usually want the image of a morphism `f` to be defined as
`kernel (cokernel.π f)`, and the coimage to be defined as `cokernel (kernel.ι f)`.
mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5
@@ -43,61 +43,82 @@ variable {P Q : C} (f : P ⟶ Q)
section Image
+#print CategoryTheory.Abelian.image /-
/-- The kernel of the cokernel of `f` is called the (abelian) image of `f`. -/
protected abbrev image : C :=
kernel (cokernel.π f)
#align category_theory.abelian.image CategoryTheory.Abelian.image
+-/
+#print CategoryTheory.Abelian.image.ι /-
/-- The inclusion of the image into the codomain. -/
protected abbrev image.ι : Abelian.image f ⟶ Q :=
kernel.ι (cokernel.π f)
#align category_theory.abelian.image.ι CategoryTheory.Abelian.image.ι
+-/
+#print CategoryTheory.Abelian.factorThruImage /-
/-- There is a canonical epimorphism `p : P ⟶ image f` for every `f`. -/
protected abbrev factorThruImage : P ⟶ Abelian.image f :=
kernel.lift (cokernel.π f) f <| cokernel.condition f
#align category_theory.abelian.factor_thru_image CategoryTheory.Abelian.factorThruImage
+-/
+#print CategoryTheory.Abelian.image.fac /-
/-- `f` factors through its image via the canonical morphism `p`. -/
@[simp, reassoc.1]
protected theorem image.fac : Abelian.factorThruImage f ≫ image.ι f = f :=
kernel.lift_ι _ _ _
#align category_theory.abelian.image.fac CategoryTheory.Abelian.image.fac
+-/
+#print CategoryTheory.Abelian.mono_factorThruImage /-
instance mono_factorThruImage [Mono f] : Mono (Abelian.factorThruImage f) :=
mono_of_mono_fac <| image.fac f
#align category_theory.abelian.mono_factor_thru_image CategoryTheory.Abelian.mono_factorThruImage
+-/
end Image
section Coimage
+#print CategoryTheory.Abelian.coimage /-
/-- The cokernel of the kernel of `f` is called the (abelian) coimage of `f`. -/
protected abbrev coimage : C :=
cokernel (kernel.ι f)
#align category_theory.abelian.coimage CategoryTheory.Abelian.coimage
+-/
+#print CategoryTheory.Abelian.coimage.π /-
/-- The projection onto the coimage. -/
protected abbrev coimage.π : P ⟶ Abelian.coimage f :=
cokernel.π (kernel.ι f)
#align category_theory.abelian.coimage.π CategoryTheory.Abelian.coimage.π
+-/
+#print CategoryTheory.Abelian.factorThruCoimage /-
/-- There is a canonical monomorphism `i : coimage f ⟶ Q`. -/
protected abbrev factorThruCoimage : Abelian.coimage f ⟶ Q :=
cokernel.desc (kernel.ι f) f <| kernel.condition f
#align category_theory.abelian.factor_thru_coimage CategoryTheory.Abelian.factorThruCoimage
+-/
+#print CategoryTheory.Abelian.coimage.fac /-
/-- `f` factors through its coimage via the canonical morphism `p`. -/
protected theorem coimage.fac : coimage.π f ≫ Abelian.factorThruCoimage f = f :=
cokernel.π_desc _ _ _
#align category_theory.abelian.coimage.fac CategoryTheory.Abelian.coimage.fac
+-/
+#print CategoryTheory.Abelian.epi_factorThruCoimage /-
instance epi_factorThruCoimage [Epi f] : Epi (Abelian.factorThruCoimage f) :=
epi_of_epi_fac <| coimage.fac f
#align category_theory.abelian.epi_factor_thru_coimage CategoryTheory.Abelian.epi_factorThruCoimage
+-/
end Coimage
+#print CategoryTheory.Abelian.coimageImageComparison /-
/-- The canonical map from the abelian coimage to the abelian image.
In any abelian category this is an isomorphism.
@@ -112,7 +133,9 @@ def coimageImageComparison : Abelian.coimage f ⟶ Abelian.image f :=
ext
simp
#align category_theory.abelian.coimage_image_comparison CategoryTheory.Abelian.coimageImageComparison
+-/
+#print CategoryTheory.Abelian.coimageImageComparison' /-
/-- An alternative formulation of the canonical map from the abelian coimage to the abelian image.
-/
def coimageImageComparison' : Abelian.coimage f ⟶ Abelian.image f :=
@@ -121,18 +144,23 @@ def coimageImageComparison' : Abelian.coimage f ⟶ Abelian.image f :=
ext
simp)
#align category_theory.abelian.coimage_image_comparison' CategoryTheory.Abelian.coimageImageComparison'
+-/
+#print CategoryTheory.Abelian.coimageImageComparison_eq_coimageImageComparison' /-
theorem coimageImageComparison_eq_coimageImageComparison' :
coimageImageComparison f = coimageImageComparison' f :=
by
ext
simp [coimage_image_comparison, coimage_image_comparison']
#align category_theory.abelian.coimage_image_comparison_eq_coimage_image_comparison' CategoryTheory.Abelian.coimageImageComparison_eq_coimageImageComparison'
+-/
+#print CategoryTheory.Abelian.coimage_image_factorisation /-
@[simp, reassoc.1]
theorem coimage_image_factorisation : coimage.π f ≫ coimageImageComparison f ≫ image.ι f = f := by
simp [coimage_image_comparison]
#align category_theory.abelian.coimage_image_factorisation CategoryTheory.Abelian.coimage_image_factorisation
+-/
end CategoryTheory.Abelian
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)
@@ -35,7 +35,6 @@ open CategoryTheory.Limits
namespace CategoryTheory.Abelian
variable {C : Type u} [Category.{v} C] [HasZeroMorphisms C] [HasKernels C] [HasCokernels C]
-
variable {P Q : C} (f : P ⟶ Q)
section Image
@@ -55,7 +55,7 @@ protected abbrev factorThruImage : P ⟶ Abelian.image f :=
kernel.lift (cokernel.π f) f <| cokernel.condition f
#align category_theory.abelian.factor_thru_image CategoryTheory.Abelian.factorThruImage
--- Porting note: simp can prove this and reassoc version, removed tags
+-- Porting note (#10618): simp can prove this and reassoc version, removed tags
/-- `f` factors through its image via the canonical morphism `p`. -/
protected theorem image.fac : Abelian.factorThruImage f ≫ image.ι f = f :=
kernel.lift_ι _ _ _
@@ -2,14 +2,11 @@
Copyright (c) 2020 Markus Himmel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Markus Himmel, Scott Morrison
-
-! This file was ported from Lean 3 source module category_theory.abelian.images
-! leanprover-community/mathlib commit 9e7c80f638149bfb3504ba8ff48dfdbfc949fb1a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
-/
import Mathlib.CategoryTheory.Limits.Shapes.Kernels
+#align_import category_theory.abelian.images from "leanprover-community/mathlib"@"9e7c80f638149bfb3504ba8ff48dfdbfc949fb1a"
+
/-!
# The abelian image and coimage.
@@ -107,20 +107,18 @@ in which this is always an isomorphism, is abelian.
See <https://stacks.math.columbia.edu/tag/0107>
-/
def coimageImageComparison : Abelian.coimage f ⟶ Abelian.image f :=
- cokernel.desc (kernel.ι f) (kernel.lift (cokernel.π f) f (by simp)) <|
- by apply equalizer.hom_ext; simp
+ cokernel.desc (kernel.ι f) (kernel.lift (cokernel.π f) f (by simp)) (by ext; simp)
#align category_theory.abelian.coimage_image_comparison CategoryTheory.Abelian.coimageImageComparison
/-- An alternative formulation of the canonical map from the abelian coimage to the abelian image.
-/
def coimageImageComparison' : Abelian.coimage f ⟶ Abelian.image f :=
- kernel.lift (cokernel.π f) (cokernel.desc (kernel.ι f) f (by simp))
- (by apply coequalizer.hom_ext; simp)
+ kernel.lift (cokernel.π f) (cokernel.desc (kernel.ι f) f (by simp)) (by ext; simp)
#align category_theory.abelian.coimage_image_comparison' CategoryTheory.Abelian.coimageImageComparison'
theorem coimageImageComparison_eq_coimageImageComparison' :
coimageImageComparison f = coimageImageComparison' f := by
- apply coequalizer.hom_ext; apply equalizer.hom_ext
+ ext
simp [coimageImageComparison, coimageImageComparison']
#align category_theory.abelian.coimage_image_comparison_eq_coimage_image_comparison' CategoryTheory.Abelian.coimageImageComparison_eq_coimageImageComparison'
@@ -130,4 +128,3 @@ theorem coimage_image_factorisation : coimage.π f ≫ coimageImageComparison f
#align category_theory.abelian.coimage_image_factorisation CategoryTheory.Abelian.coimage_image_factorisation
end CategoryTheory.Abelian
-
All dependencies are ported!