Theorems · Theorem · category theory

CategoryTheory.Enriched.FunctorCategory.functorHomEquiv_apply_app

∀ (V : Type u₁) [inst : CategoryTheory.Category.{v₁, u₁} V] [inst_1 : CategoryTheory.MonoidalCategory V] {C : Type u₂}
  [inst_2 : CategoryTheory.Category.{v₂, u₂} C] {J : Type u₃} [inst_3 : CategoryTheory.Category.{v₃, u₃} J]
  [inst_4 : CategoryTheory.EnrichedOrdinaryCategory V C] {F₁ F₂ : CategoryTheory.Functor J C}
  [inst_5 : CategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHom V F₁ F₂]
  [inst_6 : CategoryTheory.Enriched.FunctorCategory.HasEnrichedHom V F₁ F₂] (a : F₁ ⟶ F₂) (X : J),
  ((CategoryTheory.Enriched.FunctorCategory.functorHomEquiv V) a).app X =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.Enriched.FunctorCategory.homEquiv V) a)
      (CategoryTheory.Enriched.FunctorCategory.precompEnrichedHom V F₁ F₂ (CategoryTheory.Under.forget X))

Defined in

Mathlib.CategoryTheory.Enriched.FunctorCategory

Cited by

0 results in Mathlib

Foundations

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

Assumes

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