dominating subset and representation graph on topological spaces

Let a family of monomorphisms in the category A ýTo study mathematical notions in a category Aý, ýsuch as injectivityý, ýtensor productsý, ýflatnessý, ýwith respect to a class M of its (mono)morphismsý, ýone should know some of the categorical properties of the pair (A ý,M ý)ý. ýIn this paper we take A to be theýýcategory Pos-S of S-partially ordered sets and to be a particularý class of monomorphismsý, ýto be called partiallyý ýordered regular pure(po-pure)} monomorphismsý. In this paper we investigateý some categorical properties such as limits and colimits for this classý.