Theorems · Definition · category theory

CategoryTheory.Localization.Monoidal.braidingNatIso

{C : Type u_1} →
  {D : Type u_2} →
    [inst : CategoryTheory.Category.{v_1, u_1} C] →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} D] →
        (L : CategoryTheory.Functor C D) →
          (W : CategoryTheory.MorphismProperty C) →
            [inst_2 : CategoryTheory.MonoidalCategory C] →
              [inst_3 : W.IsMonoidal] →
                [inst_4 : L.IsLocalization W] →
                  {unit : D} →
                    (ε : L.obj (CategoryTheory.MonoidalCategoryStruct.tensorUnit C) ≅ unit) →
                      [CategoryTheory.BraidedCategory C] →
                        CategoryTheory.Localization.Monoidal.tensorBifunctor L W ε ≅
                          (CategoryTheory.Localization.Monoidal.tensorBifunctor L W ε).flip

The braiding on the localized category as a natural isomorphism of bifunctors.

Defined in

Mathlib.CategoryTheory.Localization.Monoidal.Braided

Cited by

9 results in Mathlib

Foundations

Depth 91 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MorphismProperty.IsMonoidalCategoryTheory.Functor.IsLocalizationCategoryTheory.BraidedCategory