%0 Journal Article
%T Categorical Properties of Down Closed Embeddings
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Shahbaz, Leila
%D 2022
%\ 02/01/2022
%V 19
%N 1
%P 89-99
%! Categorical Properties of Down Closed Embeddings
%K S-poset
%K Down closed embeddings
%K dc-embeddings
%K Limit
%K Colimit
%R 10.22130/scma.2022.545343.1038
%X 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.
%U https://scma.maragheh.ac.ir/article_249406_3d57569204846263835eb8b5bf190414.pdf