Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.Limits.pushout.associator_naturality_left_condition

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.MonoidalCategory C]
  [inst_2 : CategoryTheory.Limits.HasPushouts C] {A B X Y Z W : C} {f : A ⟶ B} {g : X ⟶ Y}
  {h : CategoryTheory.MonoidalCategoryStruct.tensorObj Z W ⟶ X},
  CategoryTheory.CategoryStruct.comp
      (CategoryTheory.MonoidalCategoryStruct.whiskerRight (CategoryTheory.MonoidalCategoryStruct.whiskerRight f Z) W)
      (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator B Z W).hom
        (CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.whiskerLeft B h)
          (CategoryTheory.Limits.pushout.inl (CategoryTheory.MonoidalCategoryStruct.whiskerRight f X)
            (CategoryTheory.MonoidalCategoryStruct.whiskerLeft A g)))) =
    CategoryTheory.CategoryStruct.comp (CategoryTheory.MonoidalCategoryStruct.associator A Z W).hom
      (CategoryTheory.CategoryStruct.comp
        (CategoryTheory.MonoidalCategoryStruct.whiskerLeft A (CategoryTheory.CategoryStruct.comp h g))
        (CategoryTheory.Limits.pushout.inr (CategoryTheory.MonoidalCategoryStruct.whiskerRight f X)
          (CategoryTheory.MonoidalCategoryStruct.whiskerLeft A g)))

Defined in

Mathlib.CategoryTheory.Monoidal.Limits.Shapes.Pullback

Cited by

1 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.Limits.HasPushouts