  Although multiplier bimonoids in general are not known to correspond to
comonoids in any monoidal category, we classify them in terms of maps from the
Catalan simplicial set to another suitable simplicial set; thus they can be
regarded as (co)monoids in something more general than a monoidal category
(namely, the simplicial set itself). We analyze the particular simplicial maps
corresponding to that class of multiplier bimonoids which can be regarded as
comonoids.
