  The central object studied in this paper is a multiplier bimonoid in a
braided monoidal category C. Adapting the philosophy of Janssen and Vercruysse,
and making some mild assumptions on the category C, we consider a category M
whose objects are certain semigroups in C and whose morphisms from A to 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.
