ORDERED CATEGORIES AND ORDERED SEMIGROUPS
Jean-Éric Pin, Arnaud Pinguet, Pascal Weil · Communications in Algebra · 2002
We use ordered categories to study semidirect decompositions of finite ordered semigroups. We obtain ordered analogues of the derived category theorem and of the delay theorem. Next we prove that the ordered analogues of semilattices and of -trivial monoids constitute local varieties, and we derive some decomposition theorems from these results.