Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.associator_inv_naturality_right_assoc

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

Defined in

Mathlib.CategoryTheory.Monoidal.Category

Cited by

11 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategory