Theorems · Definition · category theory

CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.braiding

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasPushouts C] →
      [inst_2 : CategoryTheory.MonoidalCategory C] →
        [CategoryTheory.BraidedCategory C] → (X₁ X₂ : CategoryTheory.Arrow C) → (X₁ □ X₂) ≅ X₂ □ X₁

The pushout-product is commutative: X₁ □ X₂ ≅ X₂ □ X₁.

Defined in

Mathlib.CategoryTheory.Monoidal.PushoutProduct

Cited by

12 results in Mathlib

Foundations

Depth 43 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPushoutsCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategory