Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.hexagon_reverse

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasPushouts C]
  [inst_2 : CategoryTheory.Limits.HasInitial C] [inst_3 : CategoryTheory.CartesianMonoidalCategory C]
  [inst_4 : CategoryTheory.MonoidalClosed C] [inst_5 : CategoryTheory.BraidedCategory C]
  (X Y Z : CategoryTheory.Arrow C),
  CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator X Y Z).inv
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.braiding
            (CategoryTheory.MonoidalCategoryStruct.tensorObj X Y) Z).hom
        (CategoryTheory.MonoidalCategoryStruct.associator Z X Y).inv) =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X
        (CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.braiding Y Z).hom)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator X Z Y).inv
        (CategoryTheory.MonoidalCategoryStruct.whiskerRight
          (CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.braiding X Z).hom Y))

Defined in

Mathlib.CategoryTheory.Monoidal.Arrow

Cited by

0 results in Mathlib

Foundations

Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPushoutsCategoryTheory.Limits.HasInitialCategoryTheory.CartesianMonoidalCategoryCategoryTheory.MonoidalClosedCategoryTheory.BraidedCategory