Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.whiskerLeftIso_inv_right

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasPushouts C]
  [inst_2 : CategoryTheory.MonoidalCategory C] (X₁ X₂ : CategoryTheory.Arrow C) {W : C}
  [inst_3 :
    CategoryTheory.Limits.PreservesColimit
      (CategoryTheory.Limits.span (CategoryTheory.MonoidalCategoryStruct.whiskerRight X₁.hom X₂.left)
        (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X₁.left X₂.hom))
      (CategoryTheory.MonoidalCategory.tensorLeft W)],
  (CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.whiskerLeftIso X₁ X₂).inv.right =
    (CategoryTheory.MonoidalCategoryStruct.associator W X₁.right X₂.right).hom

Defined in

Mathlib.CategoryTheory.Monoidal.PushoutProduct

Cited by

0 results in Mathlib

Foundations

Depth 45 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPushoutsCategoryTheory.MonoidalCategoryCategoryTheory.Limits.PreservesColimit