Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.unit_app_ev_app_app

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {V : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} V]
  [inst_2 : CategoryTheory.MonoidalCategory C] [inst_3 : CategoryTheory.MonoidalCategory V]
  [inst_4 : CategoryTheory.MonoidalClosed V] {F G H : CategoryTheory.Functor C V}
  [inst_5 : CategoryTheory.MonoidalCategory.DayConvolution F H]
  (ℌ : CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F G H) (x y : C),
  CategoryTheory.CategoryStruct.comp ((CategoryTheory.MonoidalCategory.DayConvolution.unit F H).app (x, y))
      (ℌ.ev_app.app (CategoryTheory.MonoidalCategoryStruct.tensorObj x y)) =
    CategoryTheory.MonoidalClosed.uncurry (ℌ.π y x)

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed

Cited by

4 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalCategoryCategoryTheory.MonoidalClosedCategoryTheory.MonoidalCategory.DayConvolution