A finite approach to representable multicategories and related structures
Abstract
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.
Cite
@article{arxiv.2312.06237,
title = {A finite approach to representable multicategories and related structures},
author = {Gabriele Lobbia},
journal= {arXiv preprint arXiv:2312.06237},
year = {2025}
}
Comments
40 pages (plus Appendix 7 pages), all comments are welcome! (Second version: fixed some typos and added some remarks.)