A category of multiplier bimonoids

Gabriella Böhm*, Stephen Lack

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    Abstract

    The central object studied in this paper is a multiplier bimonoid in a braided monoidal category C, introduced and studied in Böhm and Lack (J. Algebra 423, 853–889 2015). Adapting the philosophy in Janssen and Vercruysse (J. Algebra Appl. 9(2), 275–303 2010), and making some mild assumptions on the category C, we introduce a category ℳ whose objects are certain semigroups in C and whose morphisms A→B can be regarded as suitable multiplicative morphisms from A to the multiplier monoid of B. We equip this category ℳ with a monoidal structure and describe multiplier bimonoids in C (whose structure morphisms belong to a distinguished class of regular epimorphisms) as certain comonoids in ℳ. This provides us with one possible notion of morphism between such multiplier bimonoids.

    Original languageEnglish
    Pages (from-to)279-301
    Number of pages23
    JournalApplied Categorical Structures
    Volume25
    Issue number2
    Early online date24 Mar 2016
    DOIs
    Publication statusPublished - 2017

    Keywords

    • Braided monoidal category
    • Multiplier bimonoid

    Fingerprint Dive into the research topics of 'A category of multiplier bimonoids'. Together they form a unique fingerprint.

    Cite this