On braided and ribbon unitary fusion categories

TL;DR

This paper proves that in the context of unitary fusion categories, all braidings are inherently unitary and that such categories have a unique compatible ribbon structure, clarifying foundational aspects of their structure.

Contribution

It establishes the automatic unitarity of braidings and the uniqueness of ribbon structures in unitary fusion categories, resolving key structural questions.

Findings

Every braiding on a unitary fusion category is automatically unitary.

Every unitary braided fusion category admits a unique unitary ribbon structure.

Clarifies the foundational structure of unitary fusion categories.

Abstract

We prove that every braiding on a unitary fusion category is automatically unitary, and that every unitary braided fusion category admits a unique unitary ribbon structure.