Theorems · Theorem · category theory

CategoryTheory.Monoidal.InducingFunctorData.whiskerRight_eq

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] [inst_1 : CategoryTheory.MonoidalCategory C] {D : Type u₂}
  [inst_2 : CategoryTheory.Category.{v₂, u₂} D] [inst_3 : CategoryTheory.MonoidalCategoryStruct D]
  {F : CategoryTheory.Functor D C} (self : CategoryTheory.Monoidal.InducingFunctorData F) {X₁ X₂ : D} (f : X₁ ⟶ X₂)
  (Y : D),
  F.map (CategoryTheory.MonoidalCategoryStruct.whiskerRight f Y) =
    CategoryTheory.CategoryStruct.comp (self.μIso X₁ Y).inv
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerRight (F.map f) (F.obj Y))
        (self.μIso X₂ Y).hom)

Defined in

Mathlib.CategoryTheory.Monoidal.Transport

Cited by

0 results in Mathlib

Foundations

Depth 4 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryStruct