A Category of Multiplier Bimonoids

摘要

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