A categorical approach to loops, neardomains and nearfields
Category Theory
2013-08-13 v1 Group Theory
Abstract
In this paper we study loops, neardomains and nearfields from a categorical point of view. By choosing the right kind of morphisms, we can show that the category of neardomains is equivalent to the category of sharply 2-transitive groups. The other categories are also shown to be equivalent with categories whose objects are sets of permutations with suitable extra properties. Up to now the equivalence between neardomains and sharply 2-transitive groups was only known when both categories were equipped with the obvious isomorphisms as morphisms. We thank Hubert Kiechle for this observation.
Keywords
Cite
@article{arxiv.1207.3600,
title = {A categorical approach to loops, neardomains and nearfields},
author = {Philippe Cara and Rudger Kieboom and Tina Vervloet},
journal= {arXiv preprint arXiv:1207.3600},
year = {2013}
}
Comments
to appear in Bull. Belg. Math. Soc. Simon Stevin