Hopf monads

Hopf monads generalize Hopf algebras to a non-braided setting, that is,
to arbitrary monoidal categories. The initial motivation to introduce
the notion of Hopf monad was to understand the Drinfeld-Joyal-Street
categorical center in Hopf algebraic terms. Such a description is useful
in quantum topology for comparing the Turaev-Viro and Reshetikhin-Turaev
invariants of 3-manifolds.