Quantum double of Hopf monads and categorical centers (Q2880681)

The paper under reviews sets out to develop a theory of the double of a Hopf monad. The motivation comes from the necessity to compute the Reshetikhin-Turaev invariant of the center of a spherical fusion category. For a modular category, the construction of the RT invariant uses simple objects, but for the center of a spherical fusion category this is impractical because, in that case, no workable description of simples is available. Instead, the authors rely on an alternative construction, due to Lyubashenko, of the RT invariant by means of the coend of the category, which is a Hopf algebra in that category. The theory of Hopf monads developed in this paper provides an explicit description (in terms of the original category) of the coend of the center and its algebraic structure.