Weak bimonads and weak Hopf monads

@article{Bhm2011WeakBA,
  title={Weak bimonads and weak Hopf monads},
  author={G. B{\`o}hm and S. Lack and R. Street},
  journal={Journal of Algebra},
  year={2011},
  volume={328},
  pages={1-30}
}
We define a weak bimonad as a monad T on a monoidal category M with the property that the Eilenberg–Moore category MT is monoidal and the forgetful functor MT→M is separable Frobenius. Whenever M is also Cauchy complete, a simple set of axioms is provided, that characterizes the monoidal structure of MT 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… Expand
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