  Recently, S. Carpi et al. (Comm. Math. Phys., 402:169-212, 2023) proved that
every connected (i.e. haploid) Frobenius algebra in a tensor C$^*$-category is
unitarizable (i.e. isomorphic to a special C$^*$-Frobenius algebra). Building
on this result, we extend it to the non-connected case by showing that an
algebra in a multitensor C$^*$-category is unitarizable if and only if it is
separable.
