Weak bimonads and weak Hopf monads

Details Weak bimonads and weak Hopf monads Weak bimonads and weak Hopf monads

2010-02-24

arxiv.org/abs/1002.4493v2

Journal of Algebra, 28(1):1-30, 2011

Mathematics

Category Theory

29 pages; version 2 minor corrections and added references, also added remark 4.3; title changed from "Weak bimonads" to "Weak

Scientific paper

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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