Categorical properties of regular monomorphisms of $S$-posets
Hamid Rasouli · European Journal of Pure and Applied Mathematics · 2014
Recall that monomorphisms in some categories such as the category of posets, and the cat- egory of topological spaces, are not necessarily embeddings. The notion of regular monomorphism, solves this problem in these two categories. We have the same situation in the category S-Pos of S- posets; that is posets with an action of a pomonoid S which preserves the order. In this category, regular monomorphisms exactly determine sub S-posets. In this paper, we study some categorical properties of regular monomorphisms in the category of S- posets with action-preserving monotone maps.