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 $S$-...
