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.
Keywords: multicategories, skew monoidal categories, skew multicategories
2020 MSC: 18M65, 18M05, 18M50, 18M15, 18D15
Theory and Applications of Categories, Vol. 45, 2026, No. 10, pp 332-390.
Published 2026-02-24.
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