Every diagram of constraint 2-cells in a free braided monoidal bicategory commutes; in other words, any two parallel composites of constraint 2-cells are equal. Moreover, two parallel composites of constraint 1-cells are isomorphic if and only if they have the same underlying braid?, in which case they are uniquely isomorphic.
Every braided monoidal bicategory is equivalent to a strict braided monoidal bicategory.
Nick Gurski, “Loop spaces, and coherence for monoidal and braided monoidal bicategories”. Adv. Math 226(5):4225–4265, 2011
Revised on October 7, 2012 20:42:34
by Mike Shulman