Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.pentagon_inv

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

Defined in

Mathlib.CategoryTheory.Monoidal.Category

Cited by

4 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategory