Loop spaces, and coherence for monoidal and braided monoidal bicategories

TL;DR

This paper establishes a coherence theorem for braided monoidal bicategories, linking it to the monoidal case, and interprets coherence topologically via operad actions and surface braid classifications.

Contribution

It provides a new coherence theorem for braided monoidal bicategories and connects it to topological and algebraic frameworks.

Findings

Proves a coherence theorem for braided monoidal bicategories

Relates coherence to the theorem for monoidal bicategories

Interprets coherence topologically using operad actions and surface braids

Abstract

We prove a coherence theorem for braided monoidal bicategories and relate it to the coherence theorem for monoidal bicategories. We show how coherence for these structures can be interpretted topologically using up-to-homotopy operad actions and the algebraic classification of surface braids.