Theorems · Definition · category theory

CategoryTheory.Localization.Monoidal.tensorBifunctorIso

{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.Functor.whiskeringLeft₂ D).obj
                                  (CategoryTheory.Localization.Monoidal.toMonoidalCategory L W ε)).obj
                              (CategoryTheory.Localization.Monoidal.toMonoidalCategory L W ε)).obj
                          (CategoryTheory.Localization.Monoidal.tensorBifunctor L W ε) ≅
                        (CategoryTheory.Functor.postcompose₂.obj
                              (CategoryTheory.Localization.Monoidal.toMonoidalCategory L W ε)).obj
                          (CategoryTheory.MonoidalCategory.curriedTensor C)

The bifunctor tensorBifunctor on LocalizedMonoidal L W ε is induced by curriedTensor C.

Defined in

Mathlib.CategoryTheory.Localization.Monoidal.Basic

Cited by

2 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MorphismProperty.IsMonoidalCategoryTheory.Functor.IsLocalization