symmetric monoidal category (original) (raw)

A monoidal category 𝒞 with tensor productPlanetmathPlanetmath ⊗ is said to be symmetricPlanetmathPlanetmath if for every pair A,B of objects in 𝒞, there is an isomorphismMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath

sA⁢B:A⊗B≅B⊗A

that is natural in both A and B such that the following diagrams are commutativePlanetmathPlanetmathPlanetmath

    1. (unit coherence for s):
      \xymatrix@+=2⁢c⁢m⁢A⊗I⁢\xy@@ix@⁢