nLab coherence theorem for braided monoidal bicategories

Contents

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

Last revised on October 7, 2012 at 20:42:34. See the history of this page for a list of all contributions to it.