(Hopf) bimonads

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This chapter continues the survey of the theoretical background, turning to more specific topics. Monoidal categories are introduced and monads on them are studied. The general theory of lifting (explained in Chap. 2) is applied to the functors and natural transformations constituting the monoidal structure of the base category. A bijection is proven between the liftings of the monoidal structure of the base category to the Eilenberg-Moore category of a monad; and opmonoidal structures on the monad. An opmonoidal monad is termed a bimonad. If the base category is closed monoidal, then a sufficient and necessary condition is obtained for the lifting of the closed structure as well, in the form of the invertibility of a canonical natural transformation. A Hopf monad is defined as a bimonad for which this natural transformation is invertible.

Original languageEnglish
Title of host publicationLecture Notes in Mathematics
PublisherSpringer Verlag
Pages29-46
Number of pages18
DOIs
Publication statusPublished - Jan 1 2018

Publication series

NameLecture Notes in Mathematics
Volume2226
ISSN (Print)0075-8434

Fingerprint

Monads
Closed
Monoidal Category
Invertibility
Bijection
Invertible
Functor
Continue
Necessary Conditions
Sufficient Conditions

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Böhm, G. (2018). (Hopf) bimonads. In Lecture Notes in Mathematics (pp. 29-46). (Lecture Notes in Mathematics; Vol. 2226). Springer Verlag. https://doi.org/10.1007/978-3-319-98137-6_3

(Hopf) bimonads. / Böhm, G.

Lecture Notes in Mathematics. Springer Verlag, 2018. p. 29-46 (Lecture Notes in Mathematics; Vol. 2226).

Research output: Chapter in Book/Report/Conference proceedingChapter

Böhm, G 2018, (Hopf) bimonads. in Lecture Notes in Mathematics. Lecture Notes in Mathematics, vol. 2226, Springer Verlag, pp. 29-46. https://doi.org/10.1007/978-3-319-98137-6_3
Böhm G. (Hopf) bimonads. In Lecture Notes in Mathematics. Springer Verlag. 2018. p. 29-46. (Lecture Notes in Mathematics). https://doi.org/10.1007/978-3-319-98137-6_3
Böhm, G. / (Hopf) bimonads. Lecture Notes in Mathematics. Springer Verlag, 2018. pp. 29-46 (Lecture Notes in Mathematics).
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