  We give an alternative presentation of braided monoidal categories. Instead
of the usual associativity and braiding we have just one constraint (the
b-structure). In the unital case, the coherence conditions for a b-structure
are shown to be equivalent to the usual associativity, unit and braiding
axioms. We also discuss the next dimensional version, that is, b-structures on
bicategories. As an application, we show how special b-categories result in the
Yang-Baxter equation, and how special b-bicategories produce Zamolodchikov's
tetrahedron equation. Finally, we define a cohomology theory (the b-cohomology)
which plays a role analogous to the one abelian group cohomology has for
braided monoidal categories.
