category_theory.category.PointedMathlib.CategoryTheory.Category.Pointed

This file has been ported!

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

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -3,7 +3,7 @@ Copyright (c) 2022 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
 -/
-import Mathbin.CategoryTheory.ConcreteCategory.Basic
+import CategoryTheory.ConcreteCategory.Basic
 
 #align_import category_theory.category.Pointed from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
 
Diff
@@ -57,7 +57,7 @@ theorem coe_of {X : Type _} (point : X) : ↥(of point) = X :=
 #align Pointed.coe_of Pointed.coe_of
 -/
 
-alias of ← _root_.prod.Pointed
+alias _root_.prod.Pointed := of
 #align prod.Pointed Prod.Pointed
 
 instance : Inhabited Pointed :=
Diff
@@ -2,14 +2,11 @@
 Copyright (c) 2022 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
-
-! This file was ported from Lean 3 source module category_theory.category.Pointed
-! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.ConcreteCategory.Basic
 
+#align_import category_theory.category.Pointed from "leanprover-community/mathlib"@"10bf4f825ad729c5653adc039dafa3622e7f93c9"
+
 /-!
 # The category of pointed types
 
Diff
@@ -154,16 +154,9 @@ def typeToPointedForgetAdjunction : typeToPointed ⊣ forget Pointed :=
     { homEquiv := fun X Y =>
         { toFun := fun f => f.toFun ∘ Option.some
           invFun := fun f => ⟨fun o => o.elim Y.point f, rfl⟩
-          left_inv := fun f => by
-            ext
-            cases x
-            exact f.map_point.symm
-            rfl
+          left_inv := fun f => by ext; cases x; exact f.map_point.symm; rfl
           right_inv := fun f => funext fun _ => rfl }
-      homEquiv_naturality_left_symm := fun X' X Y f g =>
-        by
-        ext
-        cases x <;> rfl }
+      homEquiv_naturality_left_symm := fun X' X Y f g => by ext; cases x <;> rfl }
 #align Type_to_Pointed_forget_adjunction typeToPointedForgetAdjunction
 -/
 
Diff
@@ -61,7 +61,7 @@ theorem coe_of {X : Type _} (point : X) : ↥(of point) = X :=
 -/
 
 alias of ← _root_.prod.Pointed
-#align prod.Pointed prod.Pointed
+#align prod.Pointed Prod.Pointed
 
 instance : Inhabited Pointed :=
   ⟨of ((), ())⟩
Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
 
 ! This file was ported from Lean 3 source module category_theory.category.Pointed
-! leanprover-community/mathlib commit c8ab806ef73c20cab1d87b5157e43a82c205f28e
+! leanprover-community/mathlib commit 10bf4f825ad729c5653adc039dafa3622e7f93c9
 ! 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.ConcreteCategory.Basic
 /-!
 # The category of pointed types
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This defines `Pointed`, the category of pointed types.
 
 ## TODO
Diff
@@ -28,11 +28,13 @@ universe u
 
 variable {α β : Type _}
 
+#print Pointed /-
 /-- The category of pointed types. -/
 structure Pointed : Type (u + 1) where
   pt : Type u
   point : X
 #align Pointed Pointed
+-/
 
 namespace Pointed
 
@@ -41,48 +43,59 @@ instance : CoeSort Pointed (Type _) :=
 
 attribute [protected] Pointed.X
 
+#print Pointed.of /-
 /-- Turns a point into a pointed type. -/
 def of {X : Type _} (point : X) : Pointed :=
   ⟨X, point⟩
 #align Pointed.of Pointed.of
+-/
 
+#print Pointed.coe_of /-
 @[simp]
 theorem coe_of {X : Type _} (point : X) : ↥(of point) = X :=
   rfl
 #align Pointed.coe_of Pointed.coe_of
+-/
 
 alias of ← _root_.prod.Pointed
-#align prod.Pointed Prod.pointed
+#align prod.Pointed prod.Pointed
 
 instance : Inhabited Pointed :=
   ⟨of ((), ())⟩
 
+#print Pointed.Hom /-
 /-- Morphisms in `Pointed`. -/
 @[ext]
 protected structure Hom (X Y : Pointed.{u}) : Type u where
   toFun : X → Y
   map_point : to_fun X.point = Y.point
 #align Pointed.hom Pointed.Hom
+-/
 
 namespace Hom
 
+#print Pointed.Hom.id /-
 /-- The identity morphism of `X : Pointed`. -/
 @[simps]
 def id (X : Pointed) : Hom X X :=
   ⟨id, rfl⟩
 #align Pointed.hom.id Pointed.Hom.id
+-/
 
 instance (X : Pointed) : Inhabited (Hom X X) :=
   ⟨id X⟩
 
+#print Pointed.Hom.comp /-
 /-- Composition of morphisms of `Pointed`. -/
 @[simps]
 def comp {X Y Z : Pointed.{u}} (f : Hom X Y) (g : Hom Y Z) : Hom X Z :=
   ⟨g.toFun ∘ f.toFun, by rw [Function.comp_apply, f.map_point, g.map_point]⟩
 #align Pointed.hom.comp Pointed.Hom.comp
+-/
 
 end Hom
 
+#print Pointed.largeCategory /-
 instance largeCategory : LargeCategory Pointed
     where
   Hom := Hom
@@ -92,7 +105,9 @@ instance largeCategory : LargeCategory Pointed
   comp_id' _ _ _ := Hom.ext _ _ rfl
   assoc' _ _ _ _ _ _ _ := Hom.ext _ _ rfl
 #align Pointed.large_category Pointed.largeCategory
+-/
 
+#print Pointed.concreteCategory /-
 instance concreteCategory : ConcreteCategory Pointed
     where
   forget :=
@@ -100,7 +115,9 @@ instance concreteCategory : ConcreteCategory Pointed
       map := @Hom.toFun }
   forget_faithful := ⟨@Hom.ext⟩
 #align Pointed.concrete_category Pointed.concreteCategory
+-/
 
+#print Pointed.Iso.mk /-
 /-- Constructs a isomorphism between pointed types from an equivalence that preserves the point
 between them. -/
 @[simps]
@@ -111,9 +128,11 @@ def Iso.mk {α β : Pointed} (e : α ≃ β) (he : e α.point = β.point) : α 
   hom_inv_id' := Pointed.Hom.ext _ _ e.symm_comp_self
   inv_hom_id' := Pointed.Hom.ext _ _ e.self_comp_symm
 #align Pointed.iso.mk Pointed.Iso.mk
+-/
 
 end Pointed
 
+#print typeToPointed /-
 /-- `option` as a functor from types to pointed types. This is the free functor. -/
 @[simps]
 def typeToPointed : Type u ⥤ Pointed.{u}
@@ -123,7 +142,9 @@ def typeToPointed : Type u ⥤ Pointed.{u}
   map_id' X := Pointed.Hom.ext _ _ Option.map_id
   map_comp' X Y Z f g := Pointed.Hom.ext _ _ (Option.map_comp_map _ _).symm
 #align Type_to_Pointed typeToPointed
+-/
 
+#print typeToPointedForgetAdjunction /-
 /-- `Type_to_Pointed` is the free functor. -/
 def typeToPointedForgetAdjunction : typeToPointed ⊣ forget Pointed :=
   Adjunction.mkOfHomEquiv
@@ -141,4 +162,5 @@ def typeToPointedForgetAdjunction : typeToPointed ⊣ forget Pointed :=
         ext
         cases x <;> rfl }
 #align Type_to_Pointed_forget_adjunction typeToPointedForgetAdjunction
+-/
 
Diff
@@ -30,7 +30,7 @@ variable {α β : Type _}
 
 /-- The category of pointed types. -/
 structure Pointed : Type (u + 1) where
-  x : Type u
+  pt : Type u
   point : X
 #align Pointed Pointed
 

Changes in mathlib4

mathlib3
mathlib4
feat: Option {b // b ≠ a} ≃ α (#11095)

Extract from partialFunEquivPointed the equivalence between any type with a distinguished element and an Option type.

Co-authored-by: @YaelDillies <yael.dillies@gmail.com> Co-authored-by: @fpvandoorn <fpvdoorn@gmail.com>

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

Diff
@@ -100,6 +100,11 @@ instance largeCategory : LargeCategory Pointed
 set_option linter.uppercaseLean3 false in
 #align Pointed.large_category Pointed.largeCategory
 
+@[simp] lemma Hom.id_toFun' (X : Pointed.{u}) : (𝟙 X : X ⟶ X).toFun = _root_.id := rfl
+
+@[simp] lemma Hom.comp_toFun' {X Y Z : Pointed.{u}} (f : X ⟶ Y) (g : Y ⟶ Z) :
+    (f ≫ g).toFun = g.toFun ∘ f.toFun := rfl
+
 instance concreteCategory : ConcreteCategory Pointed where
   forget :=
     { obj := Pointed.X
style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

  • converts "--porting note" into "-- Porting note";
  • converts "porting note" into "Porting note".
Diff
@@ -39,7 +39,7 @@ namespace Pointed
 instance : CoeSort Pointed (Type*) :=
   ⟨X⟩
 
--- porting note: protected attribute does not work
+-- Porting note: protected attribute does not work
 --attribute [protected] Pointed.X
 
 /-- Turns a point into a pointed type. -/
feat: patch for new alias command (#6172)
Diff
@@ -54,7 +54,7 @@ theorem coe_of {X : Type*} (point : X) : ↥(of point) = X :=
 set_option linter.uppercaseLean3 false in
 #align Pointed.coe_of Pointed.coe_of
 
-alias of ← _root_.Prod.Pointed
+alias _root_.Prod.Pointed := of
 set_option linter.uppercaseLean3 false in
 #align prod.Pointed Prod.Pointed
 
chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

Diff
@@ -23,7 +23,7 @@ open CategoryTheory
 
 universe u
 
-variable {α β : Type _}
+variable {α β : Type*}
 
 /-- The category of pointed types. -/
 structure Pointed : Type (u + 1) where
@@ -36,20 +36,20 @@ set_option linter.uppercaseLean3 false in
 
 namespace Pointed
 
-instance : CoeSort Pointed (Type _) :=
+instance : CoeSort Pointed (Type*) :=
   ⟨X⟩
 
 -- porting note: protected attribute does not work
 --attribute [protected] Pointed.X
 
 /-- Turns a point into a pointed type. -/
-def of {X : Type _} (point : X) : Pointed :=
+def of {X : Type*} (point : X) : Pointed :=
   ⟨X, point⟩
 set_option linter.uppercaseLean3 false in
 #align Pointed.of Pointed.of
 
 @[simp]
-theorem coe_of {X : Type _} (point : X) : ↥(of point) = X :=
+theorem coe_of {X : Type*} (point : X) : ↥(of point) = X :=
   rfl
 set_option linter.uppercaseLean3 false in
 #align Pointed.coe_of Pointed.coe_of
chore: script to replace headers with #align_import statements (#5979)

Open in Gitpod

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

Diff
@@ -2,14 +2,11 @@
 Copyright (c) 2022 Yaël Dillies. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yaël Dillies
-
-! This file was ported from Lean 3 source module category_theory.category.Pointed
-! leanprover-community/mathlib commit c8ab806ef73c20cab1d87b5157e43a82c205f28e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.ConcreteCategory.Basic
 
+#align_import category_theory.category.Pointed from "leanprover-community/mathlib"@"c8ab806ef73c20cab1d87b5157e43a82c205f28e"
+
 /-!
 # The category of pointed types
 
chore: fix focusing dots (#5708)

This PR is the result of running

find . -type f -name "*.lean" -exec sed -i -E 's/^( +)\. /\1· /' {} \;
find . -type f -name "*.lean" -exec sed -i -E 'N;s/^( +·)\n +(.*)$/\1 \2/;P;D' {} \;

which firstly replaces . focusing dots with · and secondly removes isolated instances of such dots, unifying them with the following line. A new rule is placed in the style linter to verify this.

Diff
@@ -144,8 +144,8 @@ def typeToPointedForgetAdjunction : typeToPointed ⊣ forget Pointed :=
             apply Pointed.Hom.ext
             funext x
             cases x
-            . exact f.map_point.symm
-            . rfl
+            · exact f.map_point.symm
+            · rfl
           right_inv := fun f => funext fun _ => rfl }
       homEquiv_naturality_left_symm := fun f g => by
         apply Pointed.Hom.ext
chore: fix grammar 1/3 (#5001)

All of these are doc fixes

Diff
@@ -111,7 +111,7 @@ instance concreteCategory : ConcreteCategory Pointed where
 set_option linter.uppercaseLean3 false in
 #align Pointed.concrete_category Pointed.concreteCategory
 
-/-- Constructs a isomorphism between pointed types from an equivalence that preserves the point
+/-- Constructs an isomorphism between pointed types from an equivalence that preserves the point
 between them. -/
 @[simps]
 def Iso.mk {α β : Pointed} (e : α ≃ β) (he : e α.point = β.point) : α ≅ β where
chore: fix upper/lowercase in comments (#4360)
  • Run a non-interactive version of fix-comments.py on all files.
  • Go through the diff and manually add/discard/edit chunks.
Diff
@@ -18,7 +18,7 @@ This defines `Pointed`, the category of pointed types.
 ## TODO
 
 * Monoidal structure
-* Upgrade `Type_to_Pointed` to an equivalence
+* Upgrade `typeToPointed` to an equivalence
 -/
 
 
@@ -134,7 +134,7 @@ def typeToPointed : Type u ⥤ Pointed.{u} where
 set_option linter.uppercaseLean3 false in
 #align Type_to_Pointed typeToPointed
 
-/-- `Type_to_Pointed` is the free functor. -/
+/-- `typeToPointed` is the free functor. -/
 def typeToPointedForgetAdjunction : typeToPointed ⊣ forget Pointed :=
   Adjunction.mkOfHomEquiv
     { homEquiv := fun X Y =>
chore: refactor of concrete categories (#3900)

I think the ports

didn't quite get things right, and also have some variation between them. This PR tries to straighten things out.

Major changes:

  • Have the coercion to type be via X.\a, and put attribute @[coe] on this.
  • Make sure the coercion from morphisms to functions means that simp lemmas about the underlying bundled morphisms apply directly.
    • This means we drop lemmas like
    lemma Hom.map_mul {X Y : MonCat} (f : X ⟶ Y) (x y : X) : ((forget MonCat).map f) (x * y) = f x * f y
    
    • But at the expense of adding lemmas like
    lemma coe_comp {X Y Z : MonCat} {f : X ⟶ Y} {g : Y ⟶ Z} : (f ≫ g : X → Z) = g ∘ f := rfl
    

Overall I'm pretty happy, and it allows me to unstick the long stuck https://github.com/leanprover-community/mathlib4/pull/3105.

This is not everything I want to do to refactor these files, but once I was satisfied that I can move forward with RingCat, I want to get this merged so we can unblock porting progress. I'll promise to come back to this soon! :-)

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

Diff
@@ -104,7 +104,7 @@ set_option linter.uppercaseLean3 false in
 #align Pointed.large_category Pointed.largeCategory
 
 instance concreteCategory : ConcreteCategory Pointed where
-  Forget :=
+  forget :=
     { obj := Pointed.X
       map := @Hom.toFun }
   forget_faithful := ⟨@Hom.ext⟩
chore: tidy various files (#2950)
Diff
@@ -57,9 +57,9 @@ theorem coe_of {X : Type _} (point : X) : ↥(of point) = X :=
 set_option linter.uppercaseLean3 false in
 #align Pointed.coe_of Pointed.coe_of
 
-alias of ← _root_.prod.Pointed
+alias of ← _root_.Prod.Pointed
 set_option linter.uppercaseLean3 false in
-#align prod.Pointed prod.Pointed
+#align prod.Pointed Prod.Pointed
 
 instance : Inhabited Pointed :=
   ⟨of ((), ())⟩
@@ -114,8 +114,7 @@ set_option linter.uppercaseLean3 false in
 /-- Constructs a isomorphism between pointed types from an equivalence that preserves the point
 between them. -/
 @[simps]
-def Iso.mk {α β : Pointed} (e : α ≃ β) (he : e α.point = β.point) : α ≅ β
-    where
+def Iso.mk {α β : Pointed} (e : α ≃ β) (he : e α.point = β.point) : α ≅ β where
   hom := ⟨e, he⟩
   inv := ⟨e.symm, e.symm_apply_eq.2 he.symm⟩
   hom_inv_id := Pointed.Hom.ext _ _ e.symm_comp_self
feat: port CategoryTheory.Category.Pointed (#2864)

Dependencies 114

115 files ported (100.0%)
45854 lines ported (100.0%)

All dependencies are ported!