Theorems · Definition · category theory

CategoryTheory.GradedObject.Monoidal.braiding

{I : Type u_1} →
  [inst : AddCommMonoid I] →
    {C : Type u_2} →
      [inst_1 : CategoryTheory.Category.{v_1, u_2} C] →
        [inst_2 : CategoryTheory.MonoidalCategory C] →
          (X Y : CategoryTheory.GradedObject I C) →
            [CategoryTheory.BraidedCategory C] →
              [inst_4 : X.HasTensor Y] →
                [inst_5 : Y.HasTensor X] →
                  CategoryTheory.GradedObject.Monoidal.tensorObj X Y ≅
                    CategoryTheory.GradedObject.Monoidal.tensorObj Y X

The braiding tensorObj X Y ≅ tensorObj Y X when X and Y are graded objects indexed by a commutative additive monoid.

Defined in

Mathlib.CategoryTheory.GradedObject.Braiding

Cited by

6 results in Mathlib

Foundations

Depth 34 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommMonoidCategoryTheory.CategoryCategoryTheory.MonoidalCategoryCategoryTheory.BraidedCategoryCategoryTheory.GradedObject.HasTensorCategoryTheory.GradedObject.HasTensor