Po-S-Dense Monomorphism

Document Type: Research Paper


1 Department of Mathematics, Tafresh university, Tafresh, ‎Iran.‎

2 Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, ‎Iran.‎


‎In this paper we take $\mathcal A$ to be the category {\bf Pos-S}‎ ‎of $S$-posets‎, ‎for a posemigroup $S$‎, ${\mathcal M}_{pd}$ to‎ ‎be the class of partially ordered sequantially-dense‎ ‎monomorphisms and study the categorical properties‎, ‎such as‎ ‎limits and colimits‎, ‎of this class‎. ‎These properties are usually‎ ‎needed to study the homological notions‎, ‎such as injectivity‎, ‎of‎ ‎$S$-posets‎.