  In arXiv:1910.12059 Liu, Palcoux and Wu proved a remarkable necessary
condition for a fusion ring to admit a unitary categorification, by
constructing invariants of the fusion ring that have to be positive if it is
unitarily categorifiable. The main goal of this note is to provide a somewhat
more direct proof of this result. In the last subsection we discuss integrality
properties of the Liu-Palcoux-Wu invariants.
