Weak bimonads and weak Hopf monads

Gabriella Böhm, Stephen Lack, Ross Street

Research output: Contribution to journalArticle

11 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 - Feb 15 2011


  • Monads
  • Monoidal categories
  • Weak Hopf monads
  • Weak bimonads
  • Weak liftings

ASJC Scopus subject areas

  • Algebra and Number Theory

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