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.
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