Theorems · Theorem · category theory

CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost_hom_app_app

∀ {C : Type u_1} {D : Type u_2} {E : Type u_3} [inst : CategoryTheory.Category.{v_1, u_1} C]
  [inst_1 : CategoryTheory.Category.{v_2, u_2} D] [inst_2 : CategoryTheory.Category.{v_3, u_3} E]
  [inst_3 : CategoryTheory.MonoidalCategory C] [inst_4 : CategoryTheory.MonoidalCategory D]
  [inst_5 : CategoryTheory.MonoidalCategory E] (L : CategoryTheory.Functor C D) (W : CategoryTheory.MorphismProperty C)
  [inst_6 : L.IsLocalization W] [inst_7 : L.Monoidal] (F : CategoryTheory.Functor D E) (G : CategoryTheory.Functor C E)
  [inst_8 : G.Monoidal] [inst_9 : W.ContainsIdentities] [inst_10 : CategoryTheory.Localization.Lifting L W G F]
  (X₁ X₂ : C),
  ((CategoryTheory.Localization.Monoidal.curriedTensorPreIsoPost L W F G).hom.app (L.obj X₁)).app (L.obj X₂) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.tensorHom ((CategoryTheory.Localization.Lifting.iso L W G F).hom.app X₁)
        ((CategoryTheory.Localization.Lifting.iso L W G F).hom.app X₂))
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.LaxMonoidal.μ G X₁ X₂)
        (CategoryTheory.CategoryStruct.comp
          ((CategoryTheory.Localization.Lifting.iso L W G F).inv.app
            (CategoryTheory.MonoidalCategoryStruct.tensorObj X₁ X₂))
          (F.map (CategoryTheory.Functor.OplaxMonoidal.δ L X₁ X₂))))

Defined in

Mathlib.CategoryTheory.Localization.Monoidal.Functor

Cited by

3 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.IsLocalizationCategoryTheory.Functor.MonoidalCategoryTheory.Functor.MonoidalCategoryTheory.MorphismProperty.ContainsIdentitiesCategoryTheory.Localization.Lifting