On braided and ribbon 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.

In this version, Proposition 3.1, which discussed the equality of the unitary center and the ordinary center, has been removed. While these centers are equivalent as braided fusion categories, the unitary center is generally a non-replete subcategory. The proof of Theorem 3.2 has been revised to avoid reliance on this proposition