Theorems · Theorem · category theory

CategoryTheory.Monoidal.InducingFunctorData.associator_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) (X Y Z : D),
  F.map (CategoryTheory.MonoidalCategoryStruct.associator X Y Z).hom =
    (((self.μIso (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y) Z).symm ≪≫
          CategoryTheory.MonoidalCategory.tensorIso (self.μIso X Y).symm (CategoryTheory.Iso.refl (F.obj Z))) ≪≫
        CategoryTheory.MonoidalCategoryStruct.associator (F.obj X) (F.obj Y) (F.obj Z) ≪≫
          CategoryTheory.MonoidalCategory.tensorIso (CategoryTheory.Iso.refl (F.obj X)) (self.μIso Y Z) ≪≫
            self.μIso X (CategoryTheory.MonoidalCategoryStruct.tensorObj Y Z)).hom

Defined in

Mathlib.CategoryTheory.Monoidal.Transport

Cited by

0 results in Mathlib

Foundations

Depth 16 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryStruct