Theorems · Theorem · category theory

CategoryTheory.Enriched.FunctorCategory.functorEnrichedComp_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 F₃ : CategoryTheory.Functor J C)
  [inst_5 : CategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHom V F₁ F₂]
  [inst_6 : CategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHom V F₂ F₃]
  [inst_7 : CategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHom V F₁ F₃] (j : J),
  (CategoryTheory.Enriched.FunctorCategory.functorEnrichedComp V F₁ F₂ F₃).app j =
    CategoryTheory.Enriched.FunctorCategory.enrichedComp V ((CategoryTheory.Under.forget j).comp F₁)
      ((CategoryTheory.Under.forget j).comp F₂) ((CategoryTheory.Under.forget j).comp F₃)

Defined in

Mathlib.CategoryTheory.Enriched.FunctorCategory

Cited by

0 results in Mathlib

Foundations

Depth 41 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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