Theorems · Theorem · category theory

CategoryTheory.Functor.Monoidal.map_associator_inv

∀ {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 Y Z : C),
  F.map (CategoryTheory.MonoidalCategoryStruct.associator X Y Z).inv =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Functor.OplaxMonoidal.δ F X (CategoryTheory.MonoidalCategoryStruct.tensorObj Y Z))
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.whiskerLeft (F.obj X) (CategoryTheory.Functor.OplaxMonoidal.δ F Y Z))
        (CategoryTheory.CategoryStruct.comp
          (CategoryTheory.MonoidalCategoryStruct.associator (F.obj X) (F.obj Y) (F.obj Z)).inv
          (CategoryTheory.CategoryStruct.comp
            (CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.Functor.LaxMonoidal.μ F X Y) (F.obj Z))
            (CategoryTheory.Functor.LaxMonoidal.μ F (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y) Z))))

Defined in

Mathlib.CategoryTheory.Monoidal.Functor

Cited by

1 results in Mathlib

Foundations

Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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