  We define a weak bimonad as a monad T on a monoidal category M with the
property that the Eilenberg-Moore category M^T is monoidal and the forgetful
functor from M^T to M is separable Frobenius. Whenever M is also Cauchy
complete, a simple set of axioms is provided, that characterizes the monoidal
structure of M^T as a weak lifting of the monoidal structure of M . The
relation to bimonads, and the relation to weak bimonoids in a braided monoidal
category are revealed. We also discuss antipodes, obtaining the notion of weak
Hopf monad.
