A Category of Multiplier Bimonoids

G. Böhm, Stephen Lack

Research output: Contribution to journalArticle

Abstract

The central object studied in this paper is a multiplier bimonoid in a braided monoidal category(Formula presented.), 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 (Formula presented.), we introduce a category (Formula presented.) whose objects are certain semigroups in (Formula presented.) and whose morphisms A→B can be regarded as suitable multiplicative morphisms from A to the multiplier monoid of B. We equip this category (Formula presented.) with a monoidal structure and describe multiplier bimonoids in (Formula presented.) (whose structure morphisms belong to a distinguished class of regular epimorphisms) as certain comonoids in (Formula presented.). This provides us with one possible notion of morphism between such multiplier bimonoids.

Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalApplied Categorical Structures
DOIs
Publication statusAccepted/In press - Mar 24 2016

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Keywords

  • Braided monoidal category
  • Multiplier bimonoid

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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