Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.associator_inv_naturality_assoc

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  {X Y Z X' Y' Z' : C} (f : X ⟶ X') (g : Y ⟶ Y') (h : Z ⟶ Z') {Z_1 : C}
  (h_1 :
    CategoryTheory.MonoidalCategoryStruct.tensorObj (CategoryTheory.MonoidalCategoryStruct.tensorObj X' Y') Z' ⟶ Z_1),
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.tensorHom f (CategoryTheory.MonoidalCategoryStruct.tensorHom g h))
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator X' Y' Z').inv h_1) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator X Y Z).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.tensorHom (CategoryTheory.MonoidalCategoryStruct.tensorHom f g) h) h_1)

Defined in

Mathlib.CategoryTheory.Monoidal.Category

Cited by

1 results in Mathlib

Foundations

Depth 9 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategory