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Theorems · Definition · category theory

CategoryTheory.Limits.biprod.braiding

{C : Type uC} →
  [inst : CategoryTheory.Category.{uC', uC} C] →
    [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C] →
      [inst_2 : CategoryTheory.Limits.HasBinaryBiproducts C] → (P Q : C) → P ⊞ Q ≅ Q ⊞ P

The braiding isomorphism which swaps a binary biproduct.

Defined in
Mathlib.CategoryTheory.Limits.Shapes.BinaryBiproducts
Cited by
9 results in Mathlib
Foundations
Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasBinaryBiproducts
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Around this declaration

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CategoryTheory.Limits.biprod.braiding_hom · cited by 4biprod.braiding_homCategoryTheory.Limits.biprod.braiding_map_braiding · cited by 1biprod.braiding_map_braid…CategoryTheory.Limits.biprod.symmetry · cited by 1biprod.symmetryCategoryTheory.Limits.biprod.braid_natural · cited by 1biprod.braid_naturalCategoryTheory.Limits.biprod.braiding'_eq_braiding · cited by 0biprod.braiding'_eq_braid…CategoryTheory.Limits.biprod.braiding_inv · cited by 0biprod.braiding_invCategoryTheory.Limits.biprod.braiding_map_braiding_assoc · cited by 0biprod.braiding_map_braid…CategoryTheory.Limits.biprod.symmetry_assoc · cited by 0biprod.symmetry_assocCategoryTheory.Limits.biprod.braid_natural_assoc · cited by 0biprod.braid_natural_assocCategoryTheory.Category · cited by 32673CategoryTheory.CategoryCategoryTheory.Iso · cited by 3963CategoryTheory.IsoCategoryTheory.Limits.HasZeroMorphisms · cited by 3275Limits.HasZeroMorphismsCategoryTheory.Limits.biprod · cited by 312Limits.biprodCategoryTheory.Limits.HasBinaryBiproducts · cited by 165Limits.HasBinaryBiproductsCategoryTheory.Limits.biprod.snd · cited by 132biprod.sndCategoryTheory.Limits.biprod.fst · cited by 121biprod.fstCategoryTheory.Limits.biprod.lift · cited by 79biprod.liftbiprod.braidingCITED BYCITES

Cites8

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Cited by9

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