Every diagram of constraint 2-cells in a free symmetric 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 permutation, in which case they are uniquely isomorphic.
Every symmetric monoidal bicategory is equivalent to a strict symmetric monoidal bicategory.
Nick Gurski and Angelica Osorno?, “Infinite loop spaces, and coherence for symmetric monoidal bicategories”, arXiv
Despite the terminology, the result by Chris Schommer-Pries explained by Bruce Bartlett goes further than the earlier result of Gurski and Osorno. The result in the n-Cafe post seems to go even further.
Revised on February 21, 2015 23:49:19
by John Baez