  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.
