Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.W.whiskerLeft

∀ {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]
  [∀ (F₁ F₂ : CategoryTheory.Functor Cᵒᵖ A), CategoryTheory.Enriched.FunctorCategory.HasFunctorEnrichedHom A F₁ F₂]
  [∀ (F₁ F₂ : CategoryTheory.Functor Cᵒᵖ A), CategoryTheory.Enriched.FunctorCategory.HasEnrichedHom A F₁ F₂]
  {G₁ G₂ : CategoryTheory.Functor Cᵒᵖ A} {g : G₁ ⟶ G₂},
  J.W g → ∀ (F : CategoryTheory.Functor Cᵒᵖ A), J.W (CategoryTheory.MonoidalCategoryStruct.whiskerLeft F g)

Defined in

Mathlib.CategoryTheory.Sites.Monoidal

Cited by

1 results in Mathlib

Foundations

Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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