nLab
coherence theorem for braided monoidal bicategories

Contents

Context

Monoidal categories

monoidal categories

With symmetry

With duals for objects

With duals for morphisms

With traces

Closed structure

Special sorts of products

Semisimplicity

Morphisms

Internal monoids

Examples

Theorems

In higher category theory

Higher category theory

higher category theory

Basic concepts

Basic theorems

Applications

Models

Morphisms

Functors

Universal constructions

Extra properties and structure

1-categorical presentations

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.