科研之友
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摘要
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 M-T -> 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 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.
- 出版日期2011-2-15
