Theorems · Theorem · category theory

CategoryTheory.Functor.OplaxMonoidal.associativity

∀ {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) [self : F.OplaxMonoidal] (X Y Z : C),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Functor.OplaxMonoidal.δ F (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y) Z)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.Functor.OplaxMonoidal.δ F X Y) (F.obj Z))
        (CategoryTheory.MonoidalCategoryStruct.associator (F.obj X) (F.obj Y) (F.obj Z)).hom) =
    CategoryTheory.CategoryStruct.comp (F.map (CategoryTheory.MonoidalCategoryStruct.associator X Y Z).hom)
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.Functor.OplaxMonoidal.δ F X (CategoryTheory.MonoidalCategoryStruct.tensorObj Y Z))
        (CategoryTheory.MonoidalCategoryStruct.whiskerLeft (F.obj X) (CategoryTheory.Functor.OplaxMonoidal.δ F Y Z)))

Alias of CategoryTheory.Functor.OplaxMonoidal.oplax_associativity. associativity of the tensorator

Defined in

Mathlib.CategoryTheory.Monoidal.Functor

Cited by

3 results in Mathlib

Foundations

Depth 5 from the axioms · uses no axioms

Assumes

CategoryTheory.Functor.OplaxMonoidal