category_theory.essential_image | Mathlib porting status

Changes since the initial port

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.

Changes in mathlib3

550b5853

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

c3291da4

bump to nightly-2024-04-14-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

f736ea6b

Diff

@@ -105,7 +105,7 @@ deriving Category
 @[simps]
 def essImageInclusion (F : C ⥤ D) : F.EssImageSubcategory ⥤ D :=
   fullSubcategoryInclusion _
-deriving Full, Faithful
+deriving CategoryTheory.Functor.Full, CategoryTheory.Functor.Faithful
 #align category_theory.functor.ess_image_inclusion CategoryTheory.Functor.essImageInclusion
 -/
 
@@ -132,29 +132,29 @@ def toEssImageCompEssentialImageInclusion (F : C ⥤ D) : F.toEssImage ⋙ F.ess
 
 end Functor
 
-#print CategoryTheory.EssSurj /-
+#print CategoryTheory.Functor.EssSurj /-
 /- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`mem_essImage] [] -/
 /-- A functor `F : C ⥤ D` is essentially surjective if every object of `D` is in the essential image
 of `F`. In other words, for every `Y : D`, there is some `X : C` with `F.obj X ≅ Y`.
 
 See <https://stacks.math.columbia.edu/tag/001C>.
 -/
-class EssSurj (F : C ⥤ D) : Prop where
+class CategoryTheory.Functor.EssSurj (F : C ⥤ D) : Prop where
   mem_essImage (Y : D) : Y ∈ F.essImage
-#align category_theory.ess_surj CategoryTheory.EssSurj
+#align category_theory.ess_surj CategoryTheory.Functor.EssSurj
 -/
 
-instance : EssSurj F.toEssImage
+instance : CategoryTheory.Functor.EssSurj F.toEssImage
     where mem_essImage := fun ⟨Y, hY⟩ => ⟨_, ⟨⟨_, _, hY.getIso.hom_inv_id, hY.getIso.inv_hom_id⟩⟩⟩
 
-variable (F) [EssSurj F]
+variable (F) [CategoryTheory.Functor.EssSurj F]
 
 #print CategoryTheory.Functor.objPreimage /-
 /-- Given an essentially surjective functor, we can find a preimage for every object `Y` in the
     codomain. Applying the functor to this preimage will yield an object isomorphic to `Y`, see
     `obj_obj_preimage_iso`. -/
 def Functor.objPreimage (Y : D) : C :=
-  (EssSurj.mem_essImage F Y).witness
+  (CategoryTheory.Functor.EssSurj.mem_essImage F Y).witness
 #align category_theory.functor.obj_preimage CategoryTheory.Functor.objPreimage
 -/
 
@@ -162,23 +162,25 @@ def Functor.objPreimage (Y : D) : C :=
 /-- Applying an essentially surjective functor to a preimage of `Y` yields an object that is
     isomorphic to `Y`. -/
 def Functor.objObjPreimageIso (Y : D) : F.obj (F.objPreimage Y) ≅ Y :=
-  (EssSurj.mem_essImage F Y).getIso
+  (CategoryTheory.Functor.EssSurj.mem_essImage F Y).getIso
 #align category_theory.functor.obj_obj_preimage_iso CategoryTheory.Functor.objObjPreimageIso
 -/
 
-#print CategoryTheory.Faithful.toEssImage /-
+#print CategoryTheory.Functor.Faithful.toEssImage /-
 /-- The induced functor of a faithful functor is faithful -/
-instance Faithful.toEssImage (F : C ⥤ D) [Faithful F] : Faithful F.toEssImage :=
-  Faithful.of_comp_iso F.toEssImageCompEssentialImageInclusion
-#align category_theory.faithful.to_ess_image CategoryTheory.Faithful.toEssImage
+instance CategoryTheory.Functor.Faithful.toEssImage (F : C ⥤ D)
+    [CategoryTheory.Functor.Faithful F] : CategoryTheory.Functor.Faithful F.toEssImage :=
+  CategoryTheory.Functor.Faithful.of_comp_iso F.toEssImageCompEssentialImageInclusion
+#align category_theory.faithful.to_ess_image CategoryTheory.Functor.Faithful.toEssImage
 -/
 
-#print CategoryTheory.Full.toEssImage /-
+#print CategoryTheory.Functor.Full.toEssImage /-
 /-- The induced functor of a full functor is full -/
-instance Full.toEssImage (F : C ⥤ D) [Full F] : Full F.toEssImage :=
+instance CategoryTheory.Functor.Full.toEssImage (F : C ⥤ D) [CategoryTheory.Functor.Full F] :
+    CategoryTheory.Functor.Full F.toEssImage :=
   haveI := full.of_iso F.to_ess_image_comp_essential_image_inclusion.symm
   full.of_comp_faithful F.to_ess_image F.ess_image_inclusion
-#align category_theory.full.to_ess_image CategoryTheory.Full.toEssImage
+#align category_theory.full.to_ess_image CategoryTheory.Functor.Full.toEssImage
 -/
 
 end CategoryTheory

c3291da4

bump to nightly-2024-04-06-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

e34029c9

Diff

@@ -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 CategoryTheory.NaturalIsomorphism
+import CategoryTheory.NatIso
 import CategoryTheory.FullSubcategory
 
 #align_import category_theory.essential_image from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"

c3291da4

bump to nightly-2024-02-05-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

516c6ec2

Diff

@@ -133,7 +133,7 @@ def toEssImageCompEssentialImageInclusion (F : C ⥤ D) : F.toEssImage ⋙ F.ess
 end Functor
 
 #print CategoryTheory.EssSurj /-
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`mem_essImage] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`mem_essImage] [] -/
 /-- A functor `F : C ⥤ D` is essentially surjective if every object of `D` is in the essential image
 of `F`. In other words, for every `Y : D`, there is some `X : C` with `F.obj X ≅ Y`.

c3291da4

bump to nightly-2023-12-23-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

b8c74971

Diff

@@ -133,7 +133,7 @@ def toEssImageCompEssentialImageInclusion (F : C ⥤ D) : F.toEssImage ⋙ F.ess
 end Functor
 
 #print CategoryTheory.EssSurj /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`mem_essImage] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`mem_essImage] [] -/
 /-- A functor `F : C ⥤ D` is essentially surjective if every object of `D` is in the essential image
 of `F`. In other words, for every `Y : D`, there is some `X : C` with `F.obj X ≅ Y`.

c3291da4

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -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.NaturalIsomorphism
-import Mathbin.CategoryTheory.FullSubcategory
+import CategoryTheory.NaturalIsomorphism
+import CategoryTheory.FullSubcategory
 
 #align_import category_theory.essential_image from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
 
@@ -133,7 +133,7 @@ def toEssImageCompEssentialImageInclusion (F : C ⥤ D) : F.toEssImage ⋙ F.ess
 end Functor
 
 #print CategoryTheory.EssSurj /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`mem_essImage] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`mem_essImage] [] -/
 /-- A functor `F : C ⥤ D` is essentially surjective if every object of `D` is in the essential image
 of `F`. In other words, for every `Y : D`, there is some `X : C` with `F.obj X ≅ Y`.

c3291da4

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -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.essential_image
-! leanprover-community/mathlib commit c3291da49cfa65f0d43b094750541c0731edc932
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.NaturalIsomorphism
 import Mathbin.CategoryTheory.FullSubcategory
 
+#align_import category_theory.essential_image from "leanprover-community/mathlib"@"c3291da49cfa65f0d43b094750541c0731edc932"
+
 /-!
 # Essential image of a functor

c3291da4

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -56,10 +56,12 @@ def essImage.witness {Y : D} (h : Y ∈ F.essImage) : C :=
 #align category_theory.functor.ess_image.witness CategoryTheory.Functor.essImage.witness
 -/
 
+#print CategoryTheory.Functor.essImage.getIso /-
 /-- Extract the isomorphism between `F.obj h.witness` and `Y` itself. -/
 def essImage.getIso {Y : D} (h : Y ∈ F.essImage) : F.obj h.witness ≅ Y :=
   Classical.choice h.choose_spec
 #align category_theory.functor.ess_image.get_iso CategoryTheory.Functor.essImage.getIso
+-/
 
 #print CategoryTheory.Functor.essImage.ofIso /-
 /-- Being in the essential image is a "hygenic" property: it is preserved under isomorphism. -/
@@ -85,10 +87,12 @@ theorem essImage_eq_of_natIso {F' : C ⥤ D} (h : F ≅ F') : essImage F = essIm
 #align category_theory.functor.ess_image_eq_of_nat_iso CategoryTheory.Functor.essImage_eq_of_natIso
 -/
 
+#print CategoryTheory.Functor.obj_mem_essImage /-
 /-- An object in the image is in the essential image. -/
 theorem obj_mem_essImage (F : D ⥤ C) (Y : D) : F.obj Y ∈ essImage F :=
   ⟨Y, ⟨Iso.refl _⟩⟩
 #align category_theory.functor.obj_mem_ess_image CategoryTheory.Functor.obj_mem_essImage
+-/
 
 #print CategoryTheory.Functor.EssImageSubcategory /-
 /-- The essential image of a functor, interpreted of a full subcategory of the target category. -/
@@ -132,7 +136,7 @@ def toEssImageCompEssentialImageInclusion (F : C ⥤ D) : F.toEssImage ⋙ F.ess
 end Functor
 
 #print CategoryTheory.EssSurj /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`mem_essImage] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`mem_essImage] [] -/
 /-- A functor `F : C ⥤ D` is essentially surjective if every object of `D` is in the essential image
 of `F`. In other words, for every `Y : D`, there is some `X : C` with `F.obj X ≅ Y`.
 
@@ -157,11 +161,13 @@ def Functor.objPreimage (Y : D) : C :=
 #align category_theory.functor.obj_preimage CategoryTheory.Functor.objPreimage
 -/
 
+#print CategoryTheory.Functor.objObjPreimageIso /-
 /-- Applying an essentially surjective functor to a preimage of `Y` yields an object that is
     isomorphic to `Y`. -/
 def Functor.objObjPreimageIso (Y : D) : F.obj (F.objPreimage Y) ≅ Y :=
   (EssSurj.mem_essImage F Y).getIso
 #align category_theory.functor.obj_obj_preimage_iso CategoryTheory.Functor.objObjPreimageIso
+-/
 
 #print CategoryTheory.Faithful.toEssImage /-
 /-- The induced functor of a faithful functor is faithful -/

c3291da4

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -132,7 +132,7 @@ def toEssImageCompEssentialImageInclusion (F : C ⥤ D) : F.toEssImage ⋙ F.ess
 end Functor
 
 #print CategoryTheory.EssSurj /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`mem_essImage] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`mem_essImage] [] -/
 /-- A functor `F : C ⥤ D` is essentially surjective if every object of `D` is in the essential image
 of `F`. In other words, for every `Y : D`, there is some `X : C` with `F.obj X ≅ Y`.

c3291da4

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -94,7 +94,8 @@ theorem obj_mem_essImage (F : D ⥤ C) (Y : D) : F.obj Y ∈ essImage F :=
 /-- The essential image of a functor, interpreted of a full subcategory of the target category. -/
 @[nolint has_nonempty_instance]
 def EssImageSubcategory (F : C ⥤ D) :=
-  FullSubcategory F.essImage deriving Category
+  FullSubcategory F.essImage
+deriving Category
 #align category_theory.functor.ess_image_subcategory CategoryTheory.Functor.EssImageSubcategory
 -/
 
@@ -102,7 +103,8 @@ def EssImageSubcategory (F : C ⥤ D) :=
 /-- The essential image as a subcategory has a fully faithful inclusion into the target category. -/
 @[simps]
 def essImageInclusion (F : C ⥤ D) : F.EssImageSubcategory ⥤ D :=
-  fullSubcategoryInclusion _ deriving Full, Faithful
+  fullSubcategoryInclusion _
+deriving Full, Faithful
 #align category_theory.functor.ess_image_inclusion CategoryTheory.Functor.essImageInclusion
 -/

c3291da4

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -56,12 +56,6 @@ def essImage.witness {Y : D} (h : Y ∈ F.essImage) : C :=
 #align category_theory.functor.ess_image.witness CategoryTheory.Functor.essImage.witness
 -/
 
-/- warning: category_theory.functor.ess_image.get_iso -> CategoryTheory.Functor.essImage.getIso is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2} {Y : D} (h : Membership.Mem.{u4, u4} D (Set.{u4} D) (Set.hasMem.{u4} D) Y (CategoryTheory.Functor.essImage.{u1, u2, u3, u4} C D _inst_1 _inst_2 F)), CategoryTheory.Iso.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F (CategoryTheory.Functor.essImage.witness.{u1, u2, u3, u4} C D _inst_1 _inst_2 F Y h)) Y
-but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] {F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2} {Y : D} (h : Membership.mem.{u4, u4} D (Set.{u4} D) (Set.instMembershipSet.{u4} D) Y (CategoryTheory.Functor.essImage.{u1, u2, u3, u4} C D _inst_1 _inst_2 F)), CategoryTheory.Iso.{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) (CategoryTheory.Functor.essImage.witness.{u1, u2, u3, u4} C D _inst_1 _inst_2 F Y h)) Y
-Case conversion may be inaccurate. Consider using '#align category_theory.functor.ess_image.get_iso CategoryTheory.Functor.essImage.getIsoₓ'. -/
 /-- Extract the isomorphism between `F.obj h.witness` and `Y` itself. -/
 def essImage.getIso {Y : D} (h : Y ∈ F.essImage) : F.obj h.witness ≅ Y :=
   Classical.choice h.choose_spec
@@ -91,12 +85,6 @@ theorem essImage_eq_of_natIso {F' : C ⥤ D} (h : F ≅ F') : essImage F = essIm
 #align category_theory.functor.ess_image_eq_of_nat_iso CategoryTheory.Functor.essImage_eq_of_natIso
 -/
 
-/- warning: category_theory.functor.obj_mem_ess_image -> CategoryTheory.Functor.obj_mem_essImage is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1) (Y : D), Membership.Mem.{u3, u3} C (Set.{u3} C) (Set.hasMem.{u3} C) (CategoryTheory.Functor.obj.{u2, u1, u4, u3} D _inst_2 C _inst_1 F Y) (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 F)
-but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u2, u1, u4, u3} D _inst_2 C _inst_1) (Y : D), Membership.mem.{u3, u3} C (Set.{u3} C) (Set.instMembershipSet.{u3} C) (Prefunctor.obj.{succ u2, succ u1, u4, u3} D (CategoryTheory.CategoryStruct.toQuiver.{u2, u4} D (CategoryTheory.Category.toCategoryStruct.{u2, u4} D _inst_2)) C (CategoryTheory.CategoryStruct.toQuiver.{u1, u3} C (CategoryTheory.Category.toCategoryStruct.{u1, u3} C _inst_1)) (CategoryTheory.Functor.toPrefunctor.{u2, u1, u4, u3} D _inst_2 C _inst_1 F) Y) (CategoryTheory.Functor.essImage.{u2, u1, u4, u3} D C _inst_2 _inst_1 F)
-Case conversion may be inaccurate. Consider using '#align category_theory.functor.obj_mem_ess_image CategoryTheory.Functor.obj_mem_essImageₓ'. -/
 /-- An object in the image is in the essential image. -/
 theorem obj_mem_essImage (F : D ⥤ C) (Y : D) : F.obj Y ∈ essImage F :=
   ⟨Y, ⟨Iso.refl _⟩⟩
@@ -167,12 +155,6 @@ def Functor.objPreimage (Y : D) : C :=
 #align category_theory.functor.obj_preimage CategoryTheory.Functor.objPreimage
 -/
 
-/- warning: category_theory.functor.obj_obj_preimage_iso -> CategoryTheory.Functor.objObjPreimageIso is a dubious translation:
-lean 3 declaration is
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) [_inst_3 : CategoryTheory.EssSurj.{u1, u2, u3, u4} C D _inst_1 _inst_2 F] (Y : D), CategoryTheory.Iso.{u2, u4} D _inst_2 (CategoryTheory.Functor.obj.{u1, u2, u3, u4} C _inst_1 D _inst_2 F (CategoryTheory.Functor.objPreimage.{u1, u2, u3, u4} C D _inst_1 _inst_2 F _inst_3 Y)) Y
-but is expected to have type
-  forall {C : Type.{u3}} {D : Type.{u4}} [_inst_1 : CategoryTheory.Category.{u1, u3} C] [_inst_2 : CategoryTheory.Category.{u2, u4} D] (F : CategoryTheory.Functor.{u1, u2, u3, u4} C _inst_1 D _inst_2) [_inst_3 : CategoryTheory.EssSurj.{u1, u2, u3, u4} C D _inst_1 _inst_2 F] (Y : D), CategoryTheory.Iso.{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) (CategoryTheory.Functor.objPreimage.{u1, u2, u3, u4} C D _inst_1 _inst_2 F _inst_3 Y)) Y
-Case conversion may be inaccurate. Consider using '#align category_theory.functor.obj_obj_preimage_iso CategoryTheory.Functor.objObjPreimageIsoₓ'. -/
 /-- Applying an essentially surjective functor to a preimage of `Y` yields an object that is
     isomorphic to `Y`. -/
 def Functor.objObjPreimageIso (Y : D) : F.obj (F.objPreimage Y) ≅ Y :=

c3291da4

bump to nightly-2023-04-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

ff662d55

Diff

@@ -142,7 +142,7 @@ def toEssImageCompEssentialImageInclusion (F : C ⥤ D) : F.toEssImage ⋙ F.ess
 end Functor
 
 #print CategoryTheory.EssSurj /-
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`mem_essImage] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`mem_essImage] [] -/
 /-- A functor `F : C ⥤ D` is essentially surjective if every object of `D` is in the essential image
 of `F`. In other words, for every `Y : D`, there is some `X : C` with `F.obj X ≅ Y`.

c3291da4

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

550b5853

chore(CategoryTheory): make Functor.Full a Prop (#12449)

Before this PR, Functor.Full contained the data of the preimage of maps by a full functor F. This PR makes Functor.Full a proposition. This is to prevent any diamond to appear.

The lemma Functor.image_preimage is also renamed Functor.map_preimage.

Co-authored-by: Joël Riou <37772949+joelriou@users.noreply.github.com>

ce289a0e

Diff

@@ -159,8 +159,7 @@ instance Faithful.toEssImage (F : C ⥤ D) [Faithful F] : Faithful F.toEssImage
 
 /-- The induced functor of a full functor is full. -/
 instance Full.toEssImage (F : C ⥤ D) [Full F] : Full F.toEssImage :=
-  haveI := Full.ofIso F.toEssImageCompEssentialImageInclusion.symm
-  Full.ofCompFaithful F.toEssImage F.essImageInclusion
+  Full.of_comp_faithful_iso F.toEssImageCompEssentialImageInclusion
 #align category_theory.full.to_ess_image CategoryTheory.Functor.Full.toEssImage
 
 instance instEssSurjId : EssSurj (𝟭 C) where

550b5853

chore(CategoryTheory): move Full, Faithful, EssSurj, IsEquivalence and ReflectsIsomorphisms to the Functor namespace (#11985)

These notions on functors are now Functor.Full, Functor.Faithful, Functor.EssSurj, Functor.IsEquivalence, Functor.ReflectsIsomorphisms. Deprecated aliases are introduced for the previous names.

65b7affc

Diff

@@ -122,8 +122,6 @@ def toEssImageCompEssentialImageInclusion (F : C ⥤ D) : F.toEssImage ⋙ F.ess
 #align category_theory.functor.to_ess_image_comp_essential_image_inclusion_hom_app CategoryTheory.Functor.toEssImageCompEssentialImageInclusion_hom_app
 #align category_theory.functor.to_ess_image_comp_essential_image_inclusion_inv_app CategoryTheory.Functor.toEssImageCompEssentialImageInclusion_inv_app
 
-end Functor
-
 /-- A functor `F : C ⥤ D` is essentially surjective if every object of `D` is in the essential
 image of `F`. In other words, for every `Y : D`, there is some `X : C` with `F.obj X ≅ Y`.
 
@@ -132,47 +130,54 @@ See <https://stacks.math.columbia.edu/tag/001C>.
 class EssSurj (F : C ⥤ D) : Prop where
   /-- All the objects of the target category are in the essential image. -/
   mem_essImage (Y : D) : Y ∈ F.essImage
-#align category_theory.ess_surj CategoryTheory.EssSurj
+#align category_theory.ess_surj CategoryTheory.Functor.EssSurj
 
 instance EssSurj.toEssImage : EssSurj F.toEssImage where
   mem_essImage := fun ⟨_, hY⟩ =>
     ⟨_, ⟨⟨_, _, hY.getIso.hom_inv_id, hY.getIso.inv_hom_id⟩⟩⟩
 
-variable (F) [EssSurj F]
+variable (F)
+variable [F.EssSurj]
 
 /-- Given an essentially surjective functor, we can find a preimage for every object `Y` in the
     codomain. Applying the functor to this preimage will yield an object isomorphic to `Y`, see
     `obj_obj_preimage_iso`. -/
-def Functor.objPreimage (Y : D) : C :=
+def objPreimage (Y : D) : C :=
   essImage.witness (@EssSurj.mem_essImage _ _ _ _ F _ Y)
 #align category_theory.functor.obj_preimage CategoryTheory.Functor.objPreimage
 
 /-- Applying an essentially surjective functor to a preimage of `Y` yields an object that is
     isomorphic to `Y`. -/
-def Functor.objObjPreimageIso (Y : D) : F.obj (F.objPreimage Y) ≅ Y :=
+def objObjPreimageIso (Y : D) : F.obj (F.objPreimage Y) ≅ Y :=
   Functor.essImage.getIso _
 #align category_theory.functor.obj_obj_preimage_iso CategoryTheory.Functor.objObjPreimageIso
 
 /-- The induced functor of a faithful functor is faithful. -/
 instance Faithful.toEssImage (F : C ⥤ D) [Faithful F] : Faithful F.toEssImage :=
   Faithful.of_comp_iso F.toEssImageCompEssentialImageInclusion
-#align category_theory.faithful.to_ess_image CategoryTheory.Faithful.toEssImage
+#align category_theory.faithful.to_ess_image CategoryTheory.Functor.Faithful.toEssImage
 
 /-- The induced functor of a full functor is full. -/
 instance Full.toEssImage (F : C ⥤ D) [Full F] : Full F.toEssImage :=
   haveI := Full.ofIso F.toEssImageCompEssentialImageInclusion.symm
   Full.ofCompFaithful F.toEssImage F.essImageInclusion
-#align category_theory.full.to_ess_image CategoryTheory.Full.toEssImage
+#align category_theory.full.to_ess_image CategoryTheory.Functor.Full.toEssImage
 
 instance instEssSurjId : EssSurj (𝟭 C) where
   mem_essImage Y := ⟨Y, ⟨Iso.refl _⟩⟩
 
-theorem Functor.essSurj_of_surj (h : Function.Surjective F.obj) : EssSurj F where
+theorem essSurj_of_surj (h : Function.Surjective F.obj) : EssSurj F where
   mem_essImage Y := by
     obtain ⟨X, rfl⟩ := h Y
     apply obj_mem_essImage
 
-theorem Iso.map_essSurj {F G : C ⥤ D} [EssSurj F] (α : F ≅ G) : EssSurj G where
+lemma essSurj_of_iso {F G : C ⥤ D} [EssSurj F] (α : F ≅ G) : EssSurj G where
   mem_essImage Y := Functor.essImage.ofNatIso α (EssSurj.mem_essImage Y)
 
+end Functor
+
+-- deprecated on 2024-04-06
+@[deprecated] alias EssSurj := Functor.EssSurj
+@[deprecated] alias Iso.map_essSurj := Functor.essSurj_of_iso
+
 end CategoryTheory

550b5853

feat(CategoryTheory/EssentialImage): show that surjective functors are essentially surjective (#11239)

Show that if F.obj is surjective, F is essentially surjective.

c992d17b

Diff

@@ -167,6 +167,11 @@ instance Full.toEssImage (F : C ⥤ D) [Full F] : Full F.toEssImage :=
 instance instEssSurjId : EssSurj (𝟭 C) where
   mem_essImage Y := ⟨Y, ⟨Iso.refl _⟩⟩
 
+theorem Functor.essSurj_of_surj (h : Function.Surjective F.obj) : EssSurj F where
+  mem_essImage Y := by
+    obtain ⟨X, rfl⟩ := h Y
+    apply obj_mem_essImage
+
 theorem Iso.map_essSurj {F G : C ⥤ D} [EssSurj F] (α : F ≅ G) : EssSurj G where
   mem_essImage Y := Functor.essImage.ofNatIso α (EssSurj.mem_essImage Y)

550b5853

docs(CategoryTheory/EssentialImage): typo and punctuation (#6841)

Fix a typo, add two periods.

9c42de5a

Diff

@@ -75,7 +75,7 @@ theorem obj_mem_essImage (F : D ⥤ C) (Y : D) : F.obj Y ∈ essImage F :=
   ⟨Y, ⟨Iso.refl _⟩⟩
 #align category_theory.functor.obj_mem_ess_image CategoryTheory.Functor.obj_mem_essImage
 
-/-- The essential image of a functor, interpreted of a full subcategory of the target category. -/
+/-- The essential image of a functor, interpreted as a full subcategory of the target category. -/
 -- Porting note: no hasNonEmptyInstance linter yet
 def EssImageSubcategory (F : C ⥤ D) :=
   FullSubcategory F.essImage
@@ -153,12 +153,12 @@ def Functor.objObjPreimageIso (Y : D) : F.obj (F.objPreimage Y) ≅ Y :=
   Functor.essImage.getIso _
 #align category_theory.functor.obj_obj_preimage_iso CategoryTheory.Functor.objObjPreimageIso
 
-/-- The induced functor of a faithful functor is faithful -/
+/-- The induced functor of a faithful functor is faithful. -/
 instance Faithful.toEssImage (F : C ⥤ D) [Faithful F] : Faithful F.toEssImage :=
   Faithful.of_comp_iso F.toEssImageCompEssentialImageInclusion
 #align category_theory.faithful.to_ess_image CategoryTheory.Faithful.toEssImage
 
-/-- The induced functor of a full functor is full -/
+/-- The induced functor of a full functor is full. -/
 instance Full.toEssImage (F : C ⥤ D) [Full F] : Full F.toEssImage :=
   haveI := Full.ofIso F.toEssImageCompEssentialImageInclusion.symm
   Full.ofCompFaithful F.toEssImage F.essImageInclusion

550b5853

chore: remove 'Ported by' headers (#6018)

Briefly during the port we were adding "Ported by" headers, but only ~60 / 3000 files ended up with such a header.

I propose deleting them.

We could consider adding these uniformly via a script, as part of the great history rewrite...?

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

e8318a88

Diff

@@ -2,7 +2,6 @@
 Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
-Ported by: Joël Riou
 -/
 import Mathlib.CategoryTheory.NatIso
 import Mathlib.CategoryTheory.FullSubcategory

550b5853

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -3,15 +3,12 @@ Copyright (c) 2020 Bhavik Mehta. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Bhavik Mehta
 Ported by: Joël Riou
-
-! This file was ported from Lean 3 source module category_theory.essential_image
-! leanprover-community/mathlib commit 550b58538991c8977703fdeb7c9d51a5aa27df11
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.NatIso
 import Mathlib.CategoryTheory.FullSubcategory
 
+#align_import category_theory.essential_image from "leanprover-community/mathlib"@"550b58538991c8977703fdeb7c9d51a5aa27df11"
+
 /-!
 # Essential image of a functor

550b5853

feat: easy facts about essentially surjective functors (#5702)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

30a855da

Diff

@@ -168,4 +168,10 @@ instance Full.toEssImage (F : C ⥤ D) [Full F] : Full F.toEssImage :=
   Full.ofCompFaithful F.toEssImage F.essImageInclusion
 #align category_theory.full.to_ess_image CategoryTheory.Full.toEssImage
 
+instance instEssSurjId : EssSurj (𝟭 C) where
+  mem_essImage Y := ⟨Y, ⟨Iso.refl _⟩⟩
+
+theorem Iso.map_essSurj {F G : C ⥤ D} [EssSurj F] (α : F ≅ G) : EssSurj G where
+  mem_essImage Y := Functor.essImage.ofNatIso α (EssSurj.mem_essImage Y)
+
 end CategoryTheory

550b5853

feat: port AlgebraicGeometry.AffineScheme (#5394)

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

a5ab9709

Diff

@@ -138,9 +138,8 @@ class EssSurj (F : C ⥤ D) : Prop where
   mem_essImage (Y : D) : Y ∈ F.essImage
 #align category_theory.ess_surj CategoryTheory.EssSurj
 
-instance :
-    EssSurj
-      F.toEssImage where mem_essImage := fun ⟨_, hY⟩ =>
+instance EssSurj.toEssImage : EssSurj F.toEssImage where
+  mem_essImage := fun ⟨_, hY⟩ =>
     ⟨_, ⟨⟨_, _, hY.getIso.hom_inv_id, hY.getIso.inv_hom_id⟩⟩⟩
 
 variable (F) [EssSurj F]

550b5853

chore: fix grammar 1/3 (#5001)

All of these are doc fixes

d8caa37d

Diff

@@ -22,7 +22,7 @@ functor rather than a subtype, preserving the principle of equivalence. For exam
 define exponential ideals.
 
 The essential image can also be seen as a subcategory of the target category, and witnesses that
-a functor decomposes into a essentially surjective functor and a fully faithful functor.
+a functor decomposes into an essentially surjective functor and a fully faithful functor.
 (TODO: show that this decomposition forms an orthogonal factorisation system).
 -/

550b5853

chore: fix typos (#4518)

I ran codespell Mathlib and got tired halfway through the suggestions.

92beef58

Diff

@@ -56,7 +56,7 @@ def essImage.getIso {Y : D} (h : Y ∈ F.essImage) : F.obj (essImage.witness h)
   Classical.choice h.choose_spec
 #align category_theory.functor.ess_image.get_iso CategoryTheory.Functor.essImage.getIso
 
-/-- Being in the essential image is a "hygenic" property: it is preserved under isomorphism. -/
+/-- Being in the essential image is a "hygienic" property: it is preserved under isomorphism. -/
 theorem essImage.ofIso {Y Y' : D} (h : Y ≅ Y') (hY : Y ∈ essImage F) : Y' ∈ essImage F :=
   hY.imp fun _ => Nonempty.map (· ≪≫ h)
 #align category_theory.functor.ess_image.of_iso CategoryTheory.Functor.essImage.ofIso

550b5853

feat: require @[simps!] if simps runs in expensive mode (#1885)

This does not change the behavior of simps, just raises a linter error if you run simps in a more expensive mode without writing !.
Fixed some incorrect occurrences of to_additive, simps. Will do that systematically in future PR.
Fix port of OmegaCompletePartialOrder.ContinuousHom.ofMono a bit

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

52c04a34

Diff

@@ -90,7 +90,7 @@ instance : Category (EssImageSubcategory F) :=
   (inferInstance : Category.{v₂} (FullSubcategory _))
 
 /-- The essential image as a subcategory has a fully faithful inclusion into the target category. -/
-@[simps]
+@[simps!]
 def essImageInclusion (F : C ⥤ D) : F.EssImageSubcategory ⥤ D :=
   fullSubcategoryInclusion _
 #align category_theory.functor.ess_image_inclusion CategoryTheory.Functor.essImageInclusion
@@ -109,7 +109,7 @@ instance : Faithful (essImageInclusion F) :=
 Given a functor `F : C ⥤ D`, we have an (essentially surjective) functor from `C` to the essential
 image of `F`.
 -/
-@[simps]
+@[simps!]
 def toEssImage (F : C ⥤ D) : C ⥤ F.EssImageSubcategory :=
   FullSubcategory.lift _ F (obj_mem_essImage _)
 #align category_theory.functor.to_ess_image CategoryTheory.Functor.toEssImage
@@ -119,7 +119,7 @@ def toEssImage (F : C ⥤ D) : C ⥤ F.EssImageSubcategory :=
 /-- The functor `F` factorises through its essential image, where the first functor is essentially
 surjective and the second is fully faithful.
 -/
-@[simps]
+@[simps!]
 def toEssImageCompEssentialImageInclusion (F : C ⥤ D) : F.toEssImage ⋙ F.essImageInclusion ≅ F :=
   FullSubcategory.lift_comp_inclusion _ _ _
 #align category_theory.functor.to_ess_image_comp_essential_image_inclusion CategoryTheory.Functor.toEssImageCompEssentialImageInclusion

550b5853

chore: add missing #align statements (#1902)

This PR is the result of a slight variant on the following "algorithm"

take all mathlib 3 names, remove _ and make all uppercase letters into lowercase
take all mathlib 4 names, remove _ and make all uppercase letters into lowercase
look for matches, and create pairs (original_lean3_name, OriginalLean4Name)
for pairs that do not have an align statement:
- use Lean 4 to lookup the file + position of the Lean 4 name
- add an #align statement just before the next empty line
manually fix some tiny mistakes (e.g., empty lines in proofs might cause the #align statement to have been inserted too early)

b72bb858

Diff

@@ -94,6 +94,8 @@ instance : Category (EssImageSubcategory F) :=
 def essImageInclusion (F : C ⥤ D) : F.EssImageSubcategory ⥤ D :=
   fullSubcategoryInclusion _
 #align category_theory.functor.ess_image_inclusion CategoryTheory.Functor.essImageInclusion
+#align category_theory.functor.ess_image_inclusion_obj CategoryTheory.Functor.essImageInclusion_obj
+#align category_theory.functor.ess_image_inclusion_map CategoryTheory.Functor.essImageInclusion_map
 
 -- Porting note: `deriving Full` is not able to derive this instance
 instance : Full (essImageInclusion F) :=
@@ -111,6 +113,8 @@ image of `F`.
 def toEssImage (F : C ⥤ D) : C ⥤ F.EssImageSubcategory :=
   FullSubcategory.lift _ F (obj_mem_essImage _)
 #align category_theory.functor.to_ess_image CategoryTheory.Functor.toEssImage
+#align category_theory.functor.to_ess_image_map CategoryTheory.Functor.toEssImage_map
+#align category_theory.functor.to_ess_image_obj_obj CategoryTheory.Functor.toEssImage_obj_obj
 
 /-- The functor `F` factorises through its essential image, where the first functor is essentially
 surjective and the second is fully faithful.
@@ -119,6 +123,8 @@ surjective and the second is fully faithful.
 def toEssImageCompEssentialImageInclusion (F : C ⥤ D) : F.toEssImage ⋙ F.essImageInclusion ≅ F :=
   FullSubcategory.lift_comp_inclusion _ _ _
 #align category_theory.functor.to_ess_image_comp_essential_image_inclusion CategoryTheory.Functor.toEssImageCompEssentialImageInclusion
+#align category_theory.functor.to_ess_image_comp_essential_image_inclusion_hom_app CategoryTheory.Functor.toEssImageCompEssentialImageInclusion_hom_app
+#align category_theory.functor.to_ess_image_comp_essential_image_inclusion_inv_app CategoryTheory.Functor.toEssImageCompEssentialImageInclusion_inv_app
 
 end Functor

550b5853

chore: the style linter shouldn't complain about long #align lines (#1643)

54af0498

Diff

@@ -72,8 +72,7 @@ theorem essImage.ofNatIso {F' : C ⥤ D} (h : F ≅ F') {Y : D} (hY : Y ∈ essI
 /-- Isomorphic functors have equal essential images. -/
 theorem essImage_eq_of_natIso {F' : C ⥤ D} (h : F ≅ F') : essImage F = essImage F' :=
   funext fun _ => propext ⟨essImage.ofNatIso h, essImage.ofNatIso h.symm⟩
-#align
-  category_theory.functor.ess_image_eq_of_nat_iso CategoryTheory.Functor.essImage_eq_of_natIso
+#align category_theory.functor.ess_image_eq_of_nat_iso CategoryTheory.Functor.essImage_eq_of_natIso
 
 /-- An object in the image is in the essential image. -/
 theorem obj_mem_essImage (F : D ⥤ C) (Y : D) : F.obj Y ∈ essImage F :=
@@ -119,8 +118,7 @@ surjective and the second is fully faithful.
 @[simps]
 def toEssImageCompEssentialImageInclusion (F : C ⥤ D) : F.toEssImage ⋙ F.essImageInclusion ≅ F :=
   FullSubcategory.lift_comp_inclusion _ _ _
-#align category_theory.functor.to_ess_image_comp_essential_image_inclusion
-  CategoryTheory.Functor.toEssImageCompEssentialImageInclusion
+#align category_theory.functor.to_ess_image_comp_essential_image_inclusion CategoryTheory.Functor.toEssImageCompEssentialImageInclusion
 
 end Functor

550b5853

feat: port CategoryTheory.EssentialImage (#1132)

depends on: #1126

Notes:

some instances are not derived automatically by the syntax deriving, https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/deriving.20instances/near/317057641
the dot notation does not seem to work for essImage.witness.

Co-authored-by: Kevin Buzzard <k.buzzard@imperial.ac.uk> Co-authored-by: Chris Hughes <chrishughes24@gmail.com> Co-authored-by: Johan Commelin <johan@commelin.net> Co-authored-by: Scott Morrison <scott@tqft.net> Co-authored-by: Joël Riou <richardosborn@mac.com> Co-authored-by: Joël Riou <joel.riou@universite-paris-saclay.fr>

ba128cbf

`category_theory.essential_image` ⟷ `Mathlib.CategoryTheory.EssentialImage`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 7

category_theory.essential_image ⟷ Mathlib.CategoryTheory.EssentialImage

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 7

`category_theory.essential_image` ⟷ `Mathlib.CategoryTheory.EssentialImage`