University of MaraghehSahand Communications in Mathematical Analysis2322-580719120220201Categorical Properties of Down Closed Embeddings899924940610.22130/scma.2022.545343.1038ENLeilaShahbazDepartment of Mathematics, University of Maragheh, Maragheh,
55181-83111, Iran.0000-0001-6312-6231Journal Article20211222Let $\mathcal M$ 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 (${\mathcal A}$,${\mathcal M}$).<br />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.https://scma.maragheh.ac.ir/article_249406_3d57569204846263835eb8b5bf190414.pdf