COGENERATOR AND SUBDIRECTLY IRREDUCIBLE IN THE CATEGORY OF S-POSETS

Abstract

In this paper we study the notions of cogenerator and subdirectlyirreducible in the category of S-poset. First we give somenecessary and sufficient conditions for a cogenerator $S$-posets.Then we see that under some conditions, regular injectivityimplies generator and cogenerator. Recalling Birkhoff'sRepresentation Theorem for algebra, we study subdirectlyirreducible S-posets and give this theorem for the category ofordered right acts over an ordered monoid. Among other things, wegive the relations between cogenerators and subdirectlyirreducible S-posets.

Keywords

• S-poset
• cogenerator
• regular injective
• subdirectly irreducible