On split extensions of preordered groups (Q6062711)

Summary: We investigate the behaviour of split extensions in the category \(\mathsf{OrdGrp}\) of (pre)ordered groups. Namely we show that the lexicographic order plays a key role on the existence of compatible orders for semidirect products, establishing necessary and sufficient conditions for such existence; we prove that the Split Short Five Lemma holds for (stably) strong split extensions, and identify classes of split extensions which admit a classifier.