A braided monoidal category is a monoidal category equipped with a commutativity constraint which satisfies the hexagon axiom (see below). The term braided comes from the fact that the braid group plays an important role in the theory of braided monoidal categories. Partly for this reason, braided monoidal categories and various related notions are important in the theory of knot invariants.
Alternatively, a braided monoidal category can be seen as a tricategory with one 0-cell and one 1-cell.
Read more about Braided Monoidal Category: The Hexagon Axiom, Variations, Examples, Applications
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