nLab coherence theorem for braided monoidal bicategories

Idea

The coherence theorem for braided monoidal bicategories, like many coherence theorems, has several forms (or, alternatively, refers to several different theorems):

1. 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.

2. Every braided monoidal bicategory is equivalent to a strict braided monoidal bicategory.

References

• Nick Gurski, “Loop spaces, and coherence for monoidal and braided monoidal bicategories”. Adv. Math 226(5):4225–4265, 2011