Theorems · Theorem · category theory

CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.braiding_inv_left

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasPushouts C]
  [inst_2 : CategoryTheory.MonoidalCategory C] [inst_3 : CategoryTheory.BraidedCategory C]
  (X₁ X₂ : CategoryTheory.Arrow C),
  (CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.braiding X₁ X₂).inv.left =
    CategoryTheory.CategoryStruct.comp
      (CategoryTheory.Limits.HasColimit.isoOfNatIso
          (CategoryTheory.Limits.spanExt (β_ X₁.left X₂.left) (β_ X₁.left X₂.right) (β_ X₁.right X₂.left) ⋯ ⋯)).inv
      (CategoryTheory.Limits.pushoutSymmetry (CategoryTheory.MonoidalCategoryStruct.whiskerRight X₁.hom X₂.left)
          (CategoryTheory.MonoidalCategoryStruct.whiskerLeft X₁.left X₂.hom)).inv

Defined in

Mathlib.CategoryTheory.Monoidal.PushoutProduct

Cited by

0 results in Mathlib

Foundations

Depth 44 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPushoutsCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory