Weak bimonads and weak Hopf monads

Gabriella Böhm*, Stephen Lack, Ross Street

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    12 Citations (Scopus)


    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 languageEnglish
    Pages (from-to)1-30
    Number of pages30
    JournalJournal of Algebra
    Issue number1
    Publication statusPublished - 15 Feb 2011


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