Infinite loop spaces, and coherence for symmetric monoidal bicategories

Understand

This paper proves three different coherence theorems for symmetric monoidal bicategories.

• First, we show that in a free symmetric monoidal bicategory every diagram of 2-cells commutes.
• Second, we show that this implies that the free symmetric monoidal bicategory on one object is equivalent, as a symmetric monoidal bicategory, to the discrete symmetric monoidal bicategory given by the disjoint union of the symmetric groups.
• Third, we show that every symmetric monoidal bicategory is equivalent to a strict one.