Theorems · Definition · category theory

CategoryTheory.BraidedCategory.braiding

{C : Type u} →
  {inst : CategoryTheory.Category.{v, u} C} →
    {inst_1 : CategoryTheory.MonoidalCategory C} →
      [self : CategoryTheory.BraidedCategory C] →
        (X Y : C) →
          CategoryTheory.MonoidalCategoryStruct.tensorObj X Y ≅ CategoryTheory.MonoidalCategoryStruct.tensorObj Y X

The braiding natural isomorphism.

Defined in: Mathlib.CategoryTheory.Monoidal.Braided.Basic
Cited by: 257 results in Mathlib
Foundations: Depth 3 from the axioms, rests on 8 definitions · uses no axioms
Assumes: CategoryTheory.BraidedCategory

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Cites5

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Isostatement · cited by 3,963
CategoryTheory.MonoidalCategoryStruct.tensorObjstatement · cited by 3,106
CategoryTheory.MonoidalCategorystatement and proof · cited by 3,095
CategoryTheory.BraidedCategorystatement and proof · cited by 779

Cited by303

Results whose statement or proof uses this declaration.

CategoryTheory.MonoidalCategory.tensorμproof · cited by 71
TopCat.Homotopy.hproof · cited by 15
CategoryTheory.BraidedCategory.braiding_tensor_right_homstatement and proof · cited by 14
CategoryTheory.MonoidalCategory.tensorδproof · cited by 13
CategoryTheory.BraidedCategory.braiding_tensor_left_homstatement and proof · cited by 13
CategoryTheory.MonoidalCategory.Arrow.PushoutProduct.braidingproof · cited by 12
CategoryTheory.SymmetricCategory.symmetry_assocstatement and proof · cited by 11
CategoryTheory.BraidedCategory.braiding_naturalitystatement and proof · cited by 8
CategoryTheory.BraidedCategory.braiding_naturality_leftstatement · cited by 8
CategoryTheory.BraidedCategory.braiding_naturality_rightstatement · cited by 8
CategoryTheory.CartesianMonoidalCategory.braiding_hom_fststatement and proof · cited by 7
CategoryTheory.CartesianMonoidalCategory.braiding_hom_sndstatement and proof · cited by 7

Showing the 200 most cited of 303.