algebraic_topology.nerve | 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

841aef25

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

f2b757fc

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 -/
-import Mathbin.AlgebraicTopology.SimplicialSet
+import AlgebraicTopology.SimplicialSet
 
 #align_import algebraic_topology.nerve from "leanprover-community/mathlib"@"f2b757fc5c341d88741b9c4630b1e8ba973c5726"

f2b757fc

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
-
-! This file was ported from Lean 3 source module algebraic_topology.nerve
-! leanprover-community/mathlib commit f2b757fc5c341d88741b9c4630b1e8ba973c5726
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.AlgebraicTopology.SimplicialSet
 
+#align_import algebraic_topology.nerve from "leanprover-community/mathlib"@"f2b757fc5c341d88741b9c4630b1e8ba973c5726"
+
 /-!
 
 # The nerve of a category

f2b757fc

bump to nightly-2023-06-20-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

9b351f8c

Diff

@@ -56,7 +56,7 @@ def nerveFunctor : Cat ⥤ SSet where
   obj C := nerve C
   map C C' F := { app := fun Δ x => x ⋙ F }
   map_id' C := by
-    ext (Δ x)
+    ext Δ x
     apply functor.comp_id
 #align category_theory.nerve_functor CategoryTheory.nerveFunctor
 -/

f2b757fc

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -49,6 +49,7 @@ def nerve (C : Type u) [Category.{v} C] : SSet.{max u v}
 instance {C : Type _} [Category C] {Δ : SimplexCategoryᵒᵖ} : Category ((nerve C).obj Δ) :=
   (inferInstance : Category (SimplexCategory.toCat.obj Δ.unop ⥤ C))
 
+#print CategoryTheory.nerveFunctor /-
 /-- The nerve of a category, as a functor `Cat ⥤ sSet` -/
 @[simps]
 def nerveFunctor : Cat ⥤ SSet where
@@ -58,6 +59,7 @@ def nerveFunctor : Cat ⥤ SSet where
     ext (Δ x)
     apply functor.comp_id
 #align category_theory.nerve_functor CategoryTheory.nerveFunctor
+-/
 
 end CategoryTheory

f2b757fc

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -49,12 +49,6 @@ def nerve (C : Type u) [Category.{v} C] : SSet.{max u v}
 instance {C : Type _} [Category C] {Δ : SimplexCategoryᵒᵖ} : Category ((nerve C).obj Δ) :=
   (inferInstance : Category (SimplexCategory.toCat.obj Δ.unop ⥤ C))
 
-/- warning: category_theory.nerve_functor -> CategoryTheory.nerveFunctor is a dubious translation:
-lean 3 declaration is
-  CategoryTheory.Functor.{max u1 u2, max u2 u1, max (succ u2) u2 (succ u1), succ (max u2 u1)} CategoryTheory.Cat.{u1, u2} CategoryTheory.Cat.category.{u1, u2} SSet.{max u2 u1} SSet.largeCategory.{max u2 u1}
-but is expected to have type
-  CategoryTheory.Functor.{max u1 u2, max u1 u2, max (succ u1) (succ u2), succ (max u1 u2)} CategoryTheory.Cat.{u2, u1} CategoryTheory.Cat.category.{u2, u1} SSet.{max u1 u2} SSet.largeCategory.{max u1 u2}
-Case conversion may be inaccurate. Consider using '#align category_theory.nerve_functor CategoryTheory.nerveFunctorₓ'. -/
 /-- The nerve of a category, as a functor `Cat ⥤ sSet` -/
 @[simps]
 def nerveFunctor : Cat ⥤ SSet where

f2b757fc

bump to nightly-2023-04-30-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/86d04064ca33ee3d3405fbfc497d494fd2dd4796

648ff713

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 
 ! This file was ported from Lean 3 source module algebraic_topology.nerve
-! leanprover-community/mathlib commit 841aef25c9d7a5a5d63a3dcf7bc43386b2c206d6
+! leanprover-community/mathlib commit f2b757fc5c341d88741b9c4630b1e8ba973c5726
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.AlgebraicTopology.SimplicialSet
 
 # The nerve of a category
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file provides the definition of the nerve of a category `C`,
 which is a simplicial set `nerve C` (see [goerss-jardine-2009], Example I.1.4).

841aef25

bump to nightly-2023-04-28-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780

7fdaed52

Diff

@@ -29,6 +29,7 @@ universe v u
 
 namespace CategoryTheory
 
+#print CategoryTheory.nerve /-
 /-- The nerve of a category -/
 @[simps]
 def nerve (C : Type u) [Category.{v} C] : SSet.{max u v}
@@ -40,10 +41,17 @@ def nerve (C : Type u) [Category.{v} C] : SSet.{max u v}
     ext x
     apply functor.id_comp
 #align category_theory.nerve CategoryTheory.nerve
+-/
 
 instance {C : Type _} [Category C] {Δ : SimplexCategoryᵒᵖ} : Category ((nerve C).obj Δ) :=
   (inferInstance : Category (SimplexCategory.toCat.obj Δ.unop ⥤ C))
 
+/- warning: category_theory.nerve_functor -> CategoryTheory.nerveFunctor is a dubious translation:
+lean 3 declaration is
+  CategoryTheory.Functor.{max u1 u2, max u2 u1, max (succ u2) u2 (succ u1), succ (max u2 u1)} CategoryTheory.Cat.{u1, u2} CategoryTheory.Cat.category.{u1, u2} SSet.{max u2 u1} SSet.largeCategory.{max u2 u1}
+but is expected to have type
+  CategoryTheory.Functor.{max u1 u2, max u1 u2, max (succ u1) (succ u2), succ (max u1 u2)} CategoryTheory.Cat.{u2, u1} CategoryTheory.Cat.category.{u2, u1} SSet.{max u1 u2} SSet.largeCategory.{max u1 u2}
+Case conversion may be inaccurate. Consider using '#align category_theory.nerve_functor CategoryTheory.nerveFunctorₓ'. -/
 /-- The nerve of a category, as a functor `Cat ⥤ sSet` -/
 @[simps]
 def nerveFunctor : Cat ⥤ SSet where

841aef25

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

Diff

@@ -18,7 +18,7 @@ By definition, the type of `n`-simplices of `nerve C` is `ComposableArrows C n`,
 which is the category `Fin (n + 1) ⥤ C`.
 
 ## References
-* [Paul G. Goerss, John F. Jardine, *Simplical Homotopy Theory*][goerss-jardine-2009]
+* [Paul G. Goerss, John F. Jardine, *Simplicial Homotopy Theory*][goerss-jardine-2009]
 
 -/

841aef25

feat(CategoryTheory): inductive construction of composable arrows (#8146)

dfb12831

Diff

@@ -4,6 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
 -/
 import Mathlib.AlgebraicTopology.SimplicialSet
+import Mathlib.CategoryTheory.ComposableArrows
 
 #align_import algebraic_topology.nerve from "leanprover-community/mathlib"@"841aef25c9d7a5a5d63a3dcf7bc43386b2c206d6"
 
@@ -13,14 +14,15 @@ import Mathlib.AlgebraicTopology.SimplicialSet
 
 This file provides the definition of the nerve of a category `C`,
 which is a simplicial set `nerve C` (see [goerss-jardine-2009], Example I.1.4).
+By definition, the type of `n`-simplices of `nerve C` is `ComposableArrows C n`,
+which is the category `Fin (n + 1) ⥤ C`.
 
 ## References
 * [Paul G. Goerss, John F. Jardine, *Simplical Homotopy Theory*][goerss-jardine-2009]
 
 -/
 
-
-open CategoryTheory.Category
+open CategoryTheory.Category Simplicial
 
 universe v u
 
@@ -29,18 +31,26 @@ namespace CategoryTheory
 /-- The nerve of a category -/
 @[simps]
 def nerve (C : Type u) [Category.{v} C] : SSet.{max u v} where
-  obj Δ := SimplexCategory.toCat.obj Δ.unop ⥤ C
-  map f x := SimplexCategory.toCat.map f.unop ⋙ x
+  obj Δ := ComposableArrows C (Δ.unop.len)
+  map f x := x.whiskerLeft (SimplexCategory.toCat.map f.unop)
 #align category_theory.nerve CategoryTheory.nerve
 
 instance {C : Type*} [Category C] {Δ : SimplexCategoryᵒᵖ} : Category ((nerve C).obj Δ) :=
-  (inferInstance : Category (SimplexCategory.toCat.obj Δ.unop ⥤ C))
+  (inferInstance : Category (ComposableArrows C (Δ.unop.len)))
 
 /-- The nerve of a category, as a functor `Cat ⥤ SSet` -/
 @[simps]
 def nerveFunctor : Cat ⥤ SSet where
   obj C := nerve C
-  map F := { app := fun Δ x => x ⋙ F }
+  map F := { app := fun Δ => (F.mapComposableArrows _).obj }
 #align category_theory.nerve_functor CategoryTheory.nerveFunctor
 
+namespace Nerve
+
+variable {C : Type*} [Category C] {n : ℕ}
+
+lemma δ₀_eq {x : nerve C _[n + 1]} : (nerve C).δ (0 : Fin (n + 2)) x = x.δ₀ := rfl
+
+end Nerve
+
 end CategoryTheory

841aef25

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.

32de3f67

Diff

@@ -33,7 +33,7 @@ def nerve (C : Type u) [Category.{v} C] : SSet.{max u v} where
   map f x := SimplexCategory.toCat.map f.unop ⋙ x
 #align category_theory.nerve CategoryTheory.nerve
 
-instance {C : Type _} [Category C] {Δ : SimplexCategoryᵒᵖ} : Category ((nerve C).obj Δ) :=
+instance {C : Type*} [Category C] {Δ : SimplexCategoryᵒᵖ} : Category ((nerve C).obj Δ) :=
   (inferInstance : Category (SimplexCategory.toCat.obj Δ.unop ⥤ C))
 
 /-- The nerve of a category, as a functor `Cat ⥤ SSet` -/

841aef25

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

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Joël Riou. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Joël Riou
-
-! This file was ported from Lean 3 source module algebraic_topology.nerve
-! leanprover-community/mathlib commit 841aef25c9d7a5a5d63a3dcf7bc43386b2c206d6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.AlgebraicTopology.SimplicialSet
 
+#align_import algebraic_topology.nerve from "leanprover-community/mathlib"@"841aef25c9d7a5a5d63a3dcf7bc43386b2c206d6"
+
 /-!
 
 # The nerve of a category

841aef25

chore: add @[ext] lemmas for NatTrans synonyms (#5228)

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

5ed7d916

Diff

@@ -34,10 +34,6 @@ namespace CategoryTheory
 def nerve (C : Type u) [Category.{v} C] : SSet.{max u v} where
   obj Δ := SimplexCategory.toCat.obj Δ.unop ⥤ C
   map f x := SimplexCategory.toCat.map f.unop ⋙ x
-  map_id Δ := by
-    simp only [unop_id, id_eq]
-    ext x
-    apply Functor.id_comp
 #align category_theory.nerve CategoryTheory.nerve
 
 instance {C : Type _} [Category C] {Δ : SimplexCategoryᵒᵖ} : Category ((nerve C).obj Δ) :=
@@ -48,10 +44,6 @@ instance {C : Type _} [Category C] {Δ : SimplexCategoryᵒᵖ} : Category ((ner
 def nerveFunctor : Cat ⥤ SSet where
   obj C := nerve C
   map F := { app := fun Δ x => x ⋙ F }
-  map_id C := by
-    apply CategoryTheory.NatTrans.ext
-    funext Δ x
-    apply Functor.comp_id
 #align category_theory.nerve_functor CategoryTheory.nerveFunctor
 
 end CategoryTheory

841aef25

feat: port AlgebraicTopology.Nerve (#3693)

85f0cc50

`algebraic_topology.nerve` ⟷ `Mathlib.AlgebraicTopology.Nerve`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 628

algebraic_topology.nerve ⟷ Mathlib.AlgebraicTopology.Nerve

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 628

`algebraic_topology.nerve` ⟷ `Mathlib.AlgebraicTopology.Nerve`