Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.DayConvolution.symmetry

∀ {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.SymmetricCategory C]
  [inst_4 : CategoryTheory.MonoidalCategory V] [inst_5 : CategoryTheory.SymmetricCategory V]
  (F G : CategoryTheory.Functor C V) [inst_6 : CategoryTheory.MonoidalCategory.DayConvolution F G]
  [inst_7 : CategoryTheory.MonoidalCategory.DayConvolution G F],
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategory.DayConvolution.braiding F G).hom
      (CategoryTheory.MonoidalCategory.DayConvolution.braiding G F).hom =
    CategoryTheory.CategoryStruct.id (CategoryTheory.MonoidalCategory.DayConvolution.convolution F G)

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution.Braided

Cited by

0 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.SymmetricCategoryCategoryTheory.MonoidalCategoryCategoryTheory.SymmetricCategoryCategoryTheory.MonoidalCategory.DayConvolutionCategoryTheory.MonoidalCategory.DayConvolution