Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.DayConvolution.whiskerRight_comp_unit_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]
  (F G : CategoryTheory.Functor C V) [inst_4 : CategoryTheory.MonoidalCategory.DayConvolution F G] {x x' : C} (y : C)
  (f : x ⟶ x'),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight (F.map f) (G.obj y))
      ((CategoryTheory.MonoidalCategory.DayConvolution.unit F G).app (x', y)) =
    CategoryTheory.CategoryStruct.comp ((CategoryTheory.MonoidalCategory.DayConvolution.unit F G).app (x, y))
      ((CategoryTheory.MonoidalCategory.DayConvolution.convolution F G).map
        (CategoryTheory.MonoidalCategoryStruct.whiskerRight f y))

Defined in

Mathlib.CategoryTheory.Monoidal.DayConvolution

Cited by

2 results in Mathlib

Foundations

Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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