Theorems · Theorem · category theory

CategoryTheory.Presheaf.isSheaf_functorEnrichedHom

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {J : CategoryTheory.GrothendieckTopology C} {A : Type u₃}
  [inst_1 : CategoryTheory.Category.{v₃, u₃} A] [inst_2 : CategoryTheory.MonoidalCategory A]
  [inst_3 : CategoryTheory.MonoidalClosed A] (F G : CategoryTheory.Functor Cᵒᵖ A),
  CategoryTheory.Presheaf.IsSheaf J G →
    ∀ [inst_4 : CategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHom A F G],
      CategoryTheory.Presheaf.IsSheaf J (CategoryTheory.Enriched.FunctorCategory.functorEnrichedHom A F G)

Defined in

Mathlib.CategoryTheory.Sites.Monoidal

Cited by

1 results in Mathlib

Foundations

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

Assumes

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