Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.DayConvolution.braiding_naturality_right_assoc

∀ {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.BraidedCategory C]
  [inst_4 : CategoryTheory.MonoidalCategory V] [inst_5 : CategoryTheory.BraidedCategory V]
  {F G : CategoryTheory.Functor C V} (H : CategoryTheory.Functor C V) (η : F ⟶ G)
  [inst_6 : CategoryTheory.MonoidalCategory.DayConvolution F H]
  [inst_7 : CategoryTheory.MonoidalCategory.DayConvolution H F]
  [inst_8 : CategoryTheory.MonoidalCategory.DayConvolution G H]
  [inst_9 : CategoryTheory.MonoidalCategory.DayConvolution H G] {Z : CategoryTheory.Functor C V}
  (h : CategoryTheory.MonoidalCategory.DayConvolution.convolution G H ⟶ Z),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategory.DayConvolution.map (CategoryTheory.CategoryStruct.id H) η)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.DayConvolution.braiding H G).hom h) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.DayConvolution.braiding H F).hom
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategory.DayConvolution.map η (CategoryTheory.CategoryStruct.id H)) h)

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution.Braided

Cited by

0 results in Mathlib

Foundations

Depth 46 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.MonoidalCategory.DayConvolutionCategoryTheory.MonoidalCategory.DayConvolutionCategoryTheory.MonoidalCategory.DayConvolutionCategoryTheory.MonoidalCategory.DayConvolution