# nLab coherence theorem for braided monoidal bicategories

### Context

#### Monoidal categories

monoidal categories

## In higher category theory

#### Higher category theory

higher category theory

# Contents

## 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
Revised on October 7, 2012 20:42:34 by Mike Shulman (192.16.204.218)