Symmetric monoidal categories obtained as quotients

Hallo! Given a braided monoidal category B, one could consider the monoidal congruence generated by setting the braid equal to its inverse, for every pair of objects. Similarly, given a balanced monoidal category B', one could consider the monoidal congruence generated by setting the balance equal to the identity, for every object. In both cases, taking the quotient should produce a symmetric monoidal category. Has anybody studied such quotients? Cheers, Micah [For admin and other information see: http://www.mta.ca/~cat-dist/ ]