Theorems · Theorem · category theory

CategoryTheory.Functor.Monoidal.map_whiskerLeft

∀ {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.MonoidalCategory D]
  (F : CategoryTheory.Functor C D) [inst_4 : F.Monoidal] (X : C) {Y Z : C} (f : Y ⟶ Z),
  F.map (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X f) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Functor.OplaxMonoidal.δ F X Y)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft (F.obj X) (F.map f))
        (CategoryTheory.Functor.LaxMonoidal.μ F X Z))

Defined in

Mathlib.CategoryTheory.Monoidal.Functor

Cited by

3 results in Mathlib

Foundations

Depth 7 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.Monoidal