Theorems · Definition · category theory

CategoryTheory.Enriched.FunctorCategory.enrichedOrdinaryCategory

(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),
                      CategoryTheory.Enriched.FunctorCategory.HasEnrichedHom V F₁ F₂] →
                  CategoryTheory.EnrichedOrdinaryCategory V (CategoryTheory.Functor J C)

If C is a V-enriched ordinary category, and C has suitable limits, then J ⥤ C is also a V-enriched ordinary category.

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.HasEnrichedHom