Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.DayConvolutionInternalHom.coev_naturality_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 H G : CategoryTheory.Functor C V}
  [inst_5 : CategoryTheory.MonoidalCategory.DayConvolution F G]
  (ℌ :
    CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F
      (CategoryTheory.MonoidalCategory.DayConvolution.convolution F G) H)
  {G' H' : CategoryTheory.Functor C V} [inst_6 : CategoryTheory.MonoidalCategory.DayConvolution F G'] (η : G ⟶ G')
  (ℌ' :
    CategoryTheory.MonoidalCategory.DayConvolutionInternalHom F
      (CategoryTheory.MonoidalCategory.DayConvolution.convolution F G') H'),
  CategoryTheory.CategoryStruct.comp η ℌ'.coev_app =
    CategoryTheory.CategoryStruct.comp ℌ.coev_app
      (ℌ.map (CategoryTheory.MonoidalCategory.DayConvolution.map (CategoryTheory.CategoryStruct.id F) η) ℌ')

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution.Closed

Cited by

0 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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