(Hopf) bimonoids in duoidal categories

Research output: Chapter in Book/Report/Conference proceedingChapter


This chapter deals with unspecified duoidal —so in particular braided monoidal –categories; at which level of generality there is no bijection between the morphisms in the category and all natural transformations between the induced functors. Those monads are identified which correspond to monoids; and those opmonoidal functors are identified which correspond to comonoids. This leads to an equivalence between bimonoids in a duoidal category and bimonads on it of a certain kind. A characterization of those bimonoids is given whose induced bimonad is a Hopf monad. Examples include Hopf monoids in braided monoidal categories—such as classical Hopf algebras and Hopf group algebras—small categories, Hopf algebroids over commutative (but not arbitrary) base algebras, weak Hopf algebras of Chap. 6, Hopf monads of Chap. 3 and certain coalgebra-enriched categories called Hopf categories.

Original languageEnglish
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Number of pages25
Publication statusPublished - Jan 1 2018

Publication series

NameLecture Notes in Mathematics
ISSN (Print)0075-8434


ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Böhm, G. (2018). (Hopf) bimonoids in duoidal categories. In Lecture Notes in Mathematics (pp. 99-123). (Lecture Notes in Mathematics; Vol. 2226). Springer Verlag. https://doi.org/10.1007/978-3-319-98137-6_7