category_theory.monoidal.of_chosen_finite_products.symmetric
⟷
Mathlib.CategoryTheory.Monoidal.OfChosenFiniteProducts.Symmetric
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/65a1391a0106c9204fe45bc73a039f056558cb83
@@ -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"
mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451
@@ -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"
mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345
@@ -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.
mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3
@@ -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.
+
-/
mathlib commit https://github.com/leanprover-community/mathlib/commit/13361559d66b84f80b6d5a1c4a26aa5054766725
@@ -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
mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb
@@ -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
mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4
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>
@@ -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
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)
@@ -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
@@ -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"
@@ -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
@@ -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.
All dependencies are ported!