Find in Library

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.