Theorems · Theorem · category theory

CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_three

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.MonoidalClosed C] {J : Type u₂} [inst_3 : CategoryTheory.Category.{v₂, u₂} J]
  [inst_4 :
    ∀ (F₁ F₂ : CategoryTheory.Functor J C), CategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHom C F₁ F₂]
  {F₁ F₂ F₃ F₃' : CategoryTheory.Functor J C}
  [inst_5 : ∀ (F₁ F₂ : CategoryTheory.Functor J C), CategoryTheory.Enriched.FunctorCategory.HasEnrichedHom C F₁ F₂]
  (f : CategoryTheory.MonoidalCategoryStruct.tensorObj F₁ F₂ ⟶ F₃) (f₃ : F₃ ⟶ F₃'),
  CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv (CategoryTheory.CategoryStruct.comp f f₃) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv f)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.rightUnitor
            (CategoryTheory.Enriched.FunctorCategory.functorEnrichedHom C F₁ F₃)).inv
        (CategoryTheory.CategoryStruct.comp
          (CategoryTheory.MonoidalCategoryStruct.whiskerLeft
            (CategoryTheory.Enriched.FunctorCategory.functorEnrichedHom C F₁ F₃)
            ((CategoryTheory.Enriched.FunctorCategory.functorHomEquiv C) f₃))
          (CategoryTheory.Enriched.FunctorCategory.functorEnrichedComp C F₁ F₃ F₃')))

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Basic

Cited by

0 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalClosedCategoryTheory.CategoryCategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHomCategoryTheory.Enriched.FunctorCategory.HasEnrichedHom