English

Right-preordered groups from a categorical perspective

Category Theory 2024-06-17 v1

Abstract

We study the categorical properties of right-preordered groups, giving an explicit description of limits and colimits in this category, and studying some exactness properties. We show that, from an algebraic point of view, the category of right-preordered groups shares several properties with the one of monoids. Moreover, we describe split extensions of right-preordered groups, showing in particular that semidirect products of ordered groups have always a natural right-preorder.

Keywords

Cite

@article{arxiv.2406.10071,
  title  = {Right-preordered groups from a categorical perspective},
  author = {Maria Manuel Clementino and Andrea Montoli},
  journal= {arXiv preprint arXiv:2406.10071},
  year   = {2024}
}
R2 v1 2026-06-28T17:06:05.099Z