Theorems · Theorem · category theory

CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv_naturality_two_symm

∀ {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 F₂' F₃ : CategoryTheory.Functor J C} (f₂ : F₂ ⟶ F₂')
  (g : F₂' ⟶ CategoryTheory.Enriched.FunctorCategory.functorEnrichedHom C F₁ F₃),
  CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv.symm (CategoryTheory.CategoryStruct.comp f₂ g) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft F₁ f₂)
      (CategoryTheory.MonoidalClosed.FunctorCategory.homEquiv.symm g)

Defined in

Mathlib.CategoryTheory.Monoidal.Closed.FunctorCategory.Basic

Cited by

0 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalClosedCategoryTheory.CategoryCategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHom