category_theory.monoidal.of_chosen_finite_products.symmetricMathlib.CategoryTheory.Monoidal.OfChosenFiniteProducts.Symmetric

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.

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -3,7 +3,7 @@ Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Simon Hudon
 -/
-import CategoryTheory.Monoidal.Braided
+import CategoryTheory.Monoidal.Braided.Basic
 import CategoryTheory.Monoidal.OfChosenFiniteProducts.Basic
 
 #align_import category_theory.monoidal.of_chosen_finite_products.symmetric from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
Diff
@@ -3,8 +3,8 @@ Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Simon Hudon
 -/
-import Mathbin.CategoryTheory.Monoidal.Braided
-import Mathbin.CategoryTheory.Monoidal.OfChosenFiniteProducts.Basic
+import CategoryTheory.Monoidal.Braided
+import CategoryTheory.Monoidal.OfChosenFiniteProducts.Basic
 
 #align_import category_theory.monoidal.of_chosen_finite_products.symmetric from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
 
Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Simon Hudon
-
-! This file was ported from Lean 3 source module category_theory.monoidal.of_chosen_finite_products.symmetric
-! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.CategoryTheory.Monoidal.Braided
 import Mathbin.CategoryTheory.Monoidal.OfChosenFiniteProducts.Basic
 
+#align_import category_theory.monoidal.of_chosen_finite_products.symmetric from "leanprover-community/mathlib"@"36938f775671ff28bea1c0310f1608e4afbb22e0"
+
 /-!
 # The symmetric monoidal structure on a category with chosen finite products.
 
Diff
@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Simon Hudon
 
 ! This file was ported from Lean 3 source module category_theory.monoidal.of_chosen_finite_products.symmetric
-! leanprover-community/mathlib commit 95a87616d63b3cb49d3fe678d416fbe9c4217bf4
+! leanprover-community/mathlib commit 36938f775671ff28bea1c0310f1608e4afbb22e0
 ! 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.Monoidal.OfChosenFiniteProducts.Basic
 /-!
 # The symmetric monoidal structure on a category with chosen finite products.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 -/
 
 
Diff
@@ -43,6 +43,7 @@ namespace MonoidalOfChosenFiniteProducts
 
 open MonoidalCategory
 
+#print CategoryTheory.MonoidalOfChosenFiniteProducts.braiding_naturality /-
 theorem braiding_naturality {X X' Y Y' : C} (f : X ⟶ Y) (g : X' ⟶ Y') :
     tensorHom ℬ f g ≫ (Limits.BinaryFan.braiding (ℬ Y Y').IsLimit (ℬ Y' Y).IsLimit).Hom =
       (Limits.BinaryFan.braiding (ℬ X X').IsLimit (ℬ X' X).IsLimit).Hom ≫ tensorHom ℬ g f :=
@@ -50,8 +51,10 @@ theorem braiding_naturality {X X' Y Y' : C} (f : X ⟶ Y) (g : X' ⟶ Y') :
   dsimp [tensor_hom, limits.binary_fan.braiding]
   apply (ℬ _ _).IsLimit.hom_ext;
   rintro ⟨⟨⟩⟩ <;> · dsimp [limits.is_limit.cone_point_unique_up_to_iso]; simp
-#align category_theory.monoidal_of_chosen_finite_products.braiding_naturality CategoryTheory.monoidalOfChosenFiniteProducts.braiding_naturality
+#align category_theory.monoidal_of_chosen_finite_products.braiding_naturality CategoryTheory.MonoidalOfChosenFiniteProducts.braiding_naturality
+-/
 
+#print CategoryTheory.MonoidalOfChosenFiniteProducts.hexagon_forward /-
 theorem hexagon_forward (X Y Z : C) :
     (BinaryFan.associatorOfLimitCone ℬ X Y Z).Hom ≫
         (Limits.BinaryFan.braiding (ℬ X (tensorObj ℬ Y Z)).IsLimit
@@ -66,8 +69,10 @@ theorem hexagon_forward (X Y Z : C) :
   · dsimp [limits.is_limit.cone_point_unique_up_to_iso]; simp
   · apply (ℬ _ _).IsLimit.hom_ext;
     rintro ⟨⟨⟩⟩ <;> · dsimp [limits.is_limit.cone_point_unique_up_to_iso]; simp
-#align category_theory.monoidal_of_chosen_finite_products.hexagon_forward CategoryTheory.monoidalOfChosenFiniteProducts.hexagon_forward
+#align category_theory.monoidal_of_chosen_finite_products.hexagon_forward CategoryTheory.MonoidalOfChosenFiniteProducts.hexagon_forward
+-/
 
+#print CategoryTheory.MonoidalOfChosenFiniteProducts.hexagon_reverse /-
 theorem hexagon_reverse (X Y Z : C) :
     (BinaryFan.associatorOfLimitCone ℬ X Y Z).inv ≫
         (Limits.BinaryFan.braiding (ℬ (tensorObj ℬ X Y) Z).IsLimit
@@ -87,8 +92,10 @@ theorem hexagon_reverse (X Y Z : C) :
   · dsimp [binary_fan.associator_of_limit_cone, binary_fan.associator,
       limits.is_limit.cone_point_unique_up_to_iso]
     simp
-#align category_theory.monoidal_of_chosen_finite_products.hexagon_reverse CategoryTheory.monoidalOfChosenFiniteProducts.hexagon_reverse
+#align category_theory.monoidal_of_chosen_finite_products.hexagon_reverse CategoryTheory.MonoidalOfChosenFiniteProducts.hexagon_reverse
+-/
 
+#print CategoryTheory.MonoidalOfChosenFiniteProducts.symmetry /-
 theorem symmetry (X Y : C) :
     (Limits.BinaryFan.braiding (ℬ X Y).IsLimit (ℬ Y X).IsLimit).Hom ≫
         (Limits.BinaryFan.braiding (ℬ Y X).IsLimit (ℬ X Y).IsLimit).Hom =
@@ -97,12 +104,14 @@ theorem symmetry (X Y : C) :
   dsimp [tensor_hom, limits.binary_fan.braiding]
   apply (ℬ _ _).IsLimit.hom_ext;
   rintro ⟨⟨⟩⟩ <;> · dsimp [limits.is_limit.cone_point_unique_up_to_iso]; simp
-#align category_theory.monoidal_of_chosen_finite_products.symmetry CategoryTheory.monoidalOfChosenFiniteProducts.symmetry
+#align category_theory.monoidal_of_chosen_finite_products.symmetry CategoryTheory.MonoidalOfChosenFiniteProducts.symmetry
+-/
 
 end MonoidalOfChosenFiniteProducts
 
 open MonoidalOfChosenFiniteProducts
 
+#print CategoryTheory.symmetricOfChosenFiniteProducts /-
 /-- The monoidal structure coming from finite products is symmetric.
 -/
 def symmetricOfChosenFiniteProducts : SymmetricCategory (MonoidalOfChosenFiniteProductsSynonym 𝒯 ℬ)
@@ -113,6 +122,7 @@ def symmetricOfChosenFiniteProducts : SymmetricCategory (MonoidalOfChosenFiniteP
   hexagon_reverse' X Y Z := hexagon_reverse ℬ X Y Z
   symmetry' X Y := symmetry ℬ X Y
 #align category_theory.symmetric_of_chosen_finite_products CategoryTheory.symmetricOfChosenFiniteProducts
+-/
 
 end
 
Diff
@@ -49,9 +49,7 @@ theorem braiding_naturality {X X' Y Y' : C} (f : X ⟶ Y) (g : X' ⟶ Y') :
   by
   dsimp [tensor_hom, limits.binary_fan.braiding]
   apply (ℬ _ _).IsLimit.hom_ext;
-  rintro ⟨⟨⟩⟩ <;>
-    · dsimp [limits.is_limit.cone_point_unique_up_to_iso]
-      simp
+  rintro ⟨⟨⟩⟩ <;> · dsimp [limits.is_limit.cone_point_unique_up_to_iso]; simp
 #align category_theory.monoidal_of_chosen_finite_products.braiding_naturality CategoryTheory.monoidalOfChosenFiniteProducts.braiding_naturality
 
 theorem hexagon_forward (X Y Z : C) :
@@ -65,12 +63,9 @@ theorem hexagon_forward (X Y Z : C) :
   by
   dsimp [tensor_hom, limits.binary_fan.braiding]
   apply (ℬ _ _).IsLimit.hom_ext; rintro ⟨⟨⟩⟩
-  · dsimp [limits.is_limit.cone_point_unique_up_to_iso]
-    simp
-  · apply (ℬ _ _).IsLimit.hom_ext
-    rintro ⟨⟨⟩⟩ <;>
-      · dsimp [limits.is_limit.cone_point_unique_up_to_iso]
-        simp
+  · dsimp [limits.is_limit.cone_point_unique_up_to_iso]; simp
+  · apply (ℬ _ _).IsLimit.hom_ext;
+    rintro ⟨⟨⟩⟩ <;> · dsimp [limits.is_limit.cone_point_unique_up_to_iso]; simp
 #align category_theory.monoidal_of_chosen_finite_products.hexagon_forward CategoryTheory.monoidalOfChosenFiniteProducts.hexagon_forward
 
 theorem hexagon_reverse (X Y Z : C) :
@@ -84,7 +79,7 @@ theorem hexagon_reverse (X Y Z : C) :
   by
   dsimp [tensor_hom, limits.binary_fan.braiding]
   apply (ℬ _ _).IsLimit.hom_ext; rintro ⟨⟨⟩⟩
-  · apply (ℬ _ _).IsLimit.hom_ext
+  · apply (ℬ _ _).IsLimit.hom_ext;
     rintro ⟨⟨⟩⟩ <;>
       · dsimp [binary_fan.associator_of_limit_cone, binary_fan.associator,
           limits.is_limit.cone_point_unique_up_to_iso]
@@ -101,9 +96,7 @@ theorem symmetry (X Y : C) :
   by
   dsimp [tensor_hom, limits.binary_fan.braiding]
   apply (ℬ _ _).IsLimit.hom_ext;
-  rintro ⟨⟨⟩⟩ <;>
-    · dsimp [limits.is_limit.cone_point_unique_up_to_iso]
-      simp
+  rintro ⟨⟨⟩⟩ <;> · dsimp [limits.is_limit.cone_point_unique_up_to_iso]; simp
 #align category_theory.monoidal_of_chosen_finite_products.symmetry CategoryTheory.monoidalOfChosenFiniteProducts.symmetry
 
 end MonoidalOfChosenFiniteProducts

Changes in mathlib4

mathlib3
mathlib4
feat(AlgebraicTopology): the monoidal category structure on simplicial sets (#11396)

If a category C has chosen finite products, then the functor category J ⥤ C also. In particular, the category of simplicial sets is endowed with the monoidal category given by the explicit terminal object and binary products.

Simplifications lemmas have also been added in the context of categories with chosen finite products. For terminal objects in such categories, the terminal object is given as a limit cone of Functor.empty.{0} C rather than Functor.empty.{v} C so as to be consistent with the limits API for terminal objects.

Co-authored-by: Jack McKoen <mckoen@ualberta.ca>

Diff
@@ -22,7 +22,7 @@ variable {C : Type u} [Category.{v} C] {X Y : C}
 
 open CategoryTheory.Limits
 
-variable (𝒯 : LimitCone (Functor.empty.{v} C))
+variable (𝒯 : LimitCone (Functor.empty.{0} C))
 variable (ℬ : ∀ X Y : C, LimitCone (pair X Y))
 
 open MonoidalOfChosenFiniteProducts
chore(*): remove empty lines between variable statements (#11418)

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)
Diff
@@ -23,7 +23,6 @@ variable {C : Type u} [Category.{v} C] {X Y : C}
 open CategoryTheory.Limits
 
 variable (𝒯 : LimitCone (Functor.empty.{v} C))
-
 variable (ℬ : ∀ X Y : C, LimitCone (pair X Y))
 
 open MonoidalOfChosenFiniteProducts
feat: the opposite of a braided category is braided (#10095)

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

Diff
@@ -3,7 +3,7 @@ Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Simon Hudon
 -/
-import Mathlib.CategoryTheory.Monoidal.Braided
+import Mathlib.CategoryTheory.Monoidal.Braided.Basic
 import Mathlib.CategoryTheory.Monoidal.OfChosenFiniteProducts.Basic
 
 #align_import category_theory.monoidal.of_chosen_finite_products.symmetric from "leanprover-community/mathlib"@"95a87616d63b3cb49d3fe678d416fbe9c4217bf4"
refactor(CategoryTheory/Monoidal): replace axioms with those more suitable for the whiskerings (#9991)

Extracted from #6307. We replace some axioms by those more preferable when using the whiskerings instead of the tensor of morphisms.

Diff
@@ -93,7 +93,8 @@ open MonoidalOfChosenFiniteProducts
 def symmetricOfChosenFiniteProducts : SymmetricCategory (MonoidalOfChosenFiniteProductsSynonym 𝒯 ℬ)
     where
   braiding _ _ := Limits.BinaryFan.braiding (ℬ _ _).isLimit (ℬ _ _).isLimit
-  braiding_naturality f g := braiding_naturality ℬ f g
+  braiding_naturality_left f X := braiding_naturality ℬ f (𝟙 X)
+  braiding_naturality_right X _ _ f := braiding_naturality ℬ (𝟙 X) f
   hexagon_forward X Y Z := hexagon_forward ℬ X Y Z
   hexagon_reverse X Y Z := hexagon_reverse ℬ X Y Z
   symmetry X Y := symmetry ℬ X Y
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
@@ -2,15 +2,12 @@
 Copyright (c) 2019 Scott Morrison. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Scott Morrison, Simon Hudon
-
-! This file was ported from Lean 3 source module category_theory.monoidal.of_chosen_finite_products.symmetric
-! leanprover-community/mathlib commit 95a87616d63b3cb49d3fe678d416fbe9c4217bf4
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.CategoryTheory.Monoidal.Braided
 import Mathlib.CategoryTheory.Monoidal.OfChosenFiniteProducts.Basic
 
+#align_import category_theory.monoidal.of_chosen_finite_products.symmetric from "leanprover-community/mathlib"@"95a87616d63b3cb49d3fe678d416fbe9c4217bf4"
+
 /-!
 # The symmetric monoidal structure on a category with chosen finite products.
 
feat: port CategoryTheory.Monoidal.OfChosenFiniteProducts.Symmetric (#4658)

Dependencies 130

131 files ported (100.0%)
50074 lines ported (100.0%)

All dependencies are ported!