Leila Shahbaz - Department of Mathematics, University of Maragheh, Maragheh, ۵۵۱۸۱-۸۳۱۱۱, Iran.

Let \mathcal M be a  class of (mono)morphisms in a category \mathcal A. To study mathematical notions, such as injectivity, tensor products, flatness, one needs to have some categorical and algebraic information about the pair ({\mathcal A},{\mathcal M}).In this paper, we take \mathcal A to be the category {\bf Pos}-S of S-posets over a posemigroup S, and {\mathcal M}_{dc} to be the class of down closed embeddings and study the categorical properties, such as limits and colimits, of the  pair ({\mathcal A},{\mathcal M}). Injectivity with respect to this class of monomorphisms have been studied by Shahbaz et al., who used it to obtain  information about regular injectivity.

S-poset, Down closed embeddings, dc-embeddings, Limit, Colimit