  It is known that monoidal categories have a finite definition, whereas
multicategories have an infinite (albeit finitary) definition. Since monoidal
categories correspond to representable multicategories, it goes without saying
that representable multicategories should also admit a finite description. With
this in mind, we give a new finite definition of a structure called a short
multicategory, which only has multimaps of dimension at most four, and show
that under certain representability conditions short multicategories correspond
to various flavours of representable multicategories. This is done in both the
classical and skew settings.
