English

Simple semigroups in finite categories

Category Theory 2022-10-04 v1

Abstract

In this paper, we classify finite categories with two objects such that one of the endomorphism monoids is a group. We prove that having a group on one side affects the structure of the other endomorphism monoid, and we prove that it is going to contain a simple semigroup. We also prove the other direction, that if we have a Rees matrix semigroup we can construct a category with two objects such that one of the objects is a group.

Keywords

Cite

@article{arxiv.2210.00505,
  title  = {Simple semigroups in finite categories},
  author = {Najwa Ghannoum and Carlos Simpson},
  journal= {arXiv preprint arXiv:2210.00505},
  year   = {2022}
}

Comments

12 pages

R2 v1 2026-06-28T02:33:10.038Z