On the center of fusion categories (Q363325)

\textit{M. Müger} [J. Pure Appl. Algebra 180, No. 1--2, 159--219 (2003; Zbl 1033.18003)] proved that the centre \(\mathcal{ZC}\) of a spherical fusion category \(\mathcal{C}\) is a modular fusion category with \(\dim\mathcal{ZC} = (\dim\mathcal{C})^2\), provided the dimension of \(\mathcal{C}\) is non-zero and the base commutative ring \(k\) is an algebraically closed field. The present paper removes the proviso: proves the same result for any commutative ring \(k\) and no restriction on \(\dim\mathcal{C}\). The proof uses an explicit description of the coend Hopf algebra of \(\mathcal{ZC}\).