Theorems · Theorem · category theory

CategoryTheory.Enriched.FunctorCategory.enriched_id_comp

∀ (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.HasEnrichedHom V F₁ F₁]
  [inst_6 : CategoryTheory.Enriched.FunctorCategory.HasEnrichedHom V F₁ F₂],
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.leftUnitor
          (CategoryTheory.Enriched.FunctorCategory.enrichedHom V F₁ F₂)).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.Enriched.FunctorCategory.enrichedId V F₁)
          (CategoryTheory.Enriched.FunctorCategory.enrichedHom V F₁ F₂))
        (CategoryTheory.Enriched.FunctorCategory.enrichedComp V F₁ F₁ F₂)) =
    CategoryTheory.CategoryStruct.id (CategoryTheory.Enriched.FunctorCategory.enrichedHom V F₁ F₂)

Defined in

Mathlib.CategoryTheory.Enriched.FunctorCategory

Cited by

2 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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