Theorems · Theorem · category theory

CategoryTheory.Functor.OplaxMonoidal.associativity_inv_assoc

∀ {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.OplaxMonoidal] (X Y Z : C) {Z_1 : D}
  (h :
    CategoryTheory.MonoidalCategoryStruct.tensorObj
        (CategoryTheory.MonoidalCategoryStruct.tensorObj (F.obj X) (F.obj Y)) (F.obj Z) ⟶
      Z_1),
  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 h)) =
    CategoryTheory.CategoryStruct.comp (F.map (CategoryTheory.MonoidalCategoryStruct.associator X Y Z).inv)
      (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))
          h))

Defined in

Mathlib.CategoryTheory.Monoidal.Functor

Cited by

2 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Functor.OplaxMonoidal