Weak bimonads and weak Hopf monads

Gabriella Böhm; Stephen Lack; Ross Street

doi:10.1016/j.jalgebra.2010.07.032

Weak bimonads and weak Hopf monads

Gabriella Böhm^*, Stephen Lack, Ross Street

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

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 the notion of weak Hopf monad.

Original language	English
Pages (from-to)	1-30
Number of pages	30
Journal	Journal of Algebra
Volume	328
Issue number	1
DOIs	https://doi.org/10.1016/j.jalgebra.2010.07.032
Publication status	Published - 15 Feb 2011

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AU - Lack, Stephen

AU - Street, Ross

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AB - 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 the notion of weak Hopf monad.

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Weak bimonads and weak Hopf monads

Abstract

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