No subtopics of Category Theory
- Hopf monoidal comonads
- Coherence for Categorified Operadic Theories
- A skew-duoidal Eckmann-Hilton argument and quantum categories
- Algebraic extensions of an Eilenberg-MacLane spectrum
Weak bimonads and weak Hopf monads
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.
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