Quantum categories, star autonomy, and quantum groupoids

Brian Day, Ross Street

    Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

    Abstract

    A useful general concept of bialgebroid seems to be resolving itself in recent publications; we give a treatment in terms of modules and enriched categories. We define the term "quantum category". The definition of antipode for a bialgebroid is less resolved in the literature. Our suggestion is that the kind of dualization occurring in Barr's star-autonomous categories is more suitable than autonomy (= compactness = rigidity). This leads to our definition of quantum groupoid intended as a "Hopf algebra with several objects".
    Original languageEnglish
    Title of host publicationGalois theory, Hopf algebras, and semiabelian categories
    EditorsGeorge Janelidze, Bodo Pareigis, Walter Tholen
    Place of PublicationProvidence, RI
    PublisherAmerican Mathematical Society
    Pages187-226
    Number of pages40
    ISBN (Print)0821832905
    Publication statusPublished - 2004
    EventWorkshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras, and Semiabelian Categories - Toronto, Canada
    Duration: 23 Sep 200228 Sep 2002

    Publication series

    NameFields Institute communications
    PublisherAmerican Mathematical Society
    Volume43

    Workshop

    WorkshopWorkshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras, and Semiabelian Categories
    CityToronto, Canada
    Period23/09/0228/09/02

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