We study categorical properties of right-preordered groups, giving an explicit description of limits and colimits in this category, studying some exactness properties, and showing that it is a quasivariety. 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 always have a natural right-preorder.
Right-preordered groups from a categorical perspective / M.M. Clementino, A. Montoli. - In: ALGEBRA UNIVERSALIS. - ISSN 0002-5240. - 86:2(2025), pp. 8.1-8.17. [10.1007/s00012-025-00886-8]
Right-preordered groups from a categorical perspective
A. Montoli
Ultimo
2025
Abstract
We study categorical properties of right-preordered groups, giving an explicit description of limits and colimits in this category, studying some exactness properties, and showing that it is a quasivariety. 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 always have a natural right-preorder.
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