Actions of a separately strict cpo-monoid on pointed directed complete posets

Abstract

‎ In the present article‎, ‎we study some categorical properties of the category {$bf‎ Cpo_{Sep}$-$S$} of all {separately strict $S$-cpo's}; cpo's equipped with‎ a compatible right action of a separately strict cpo-monoid $S$ which is‎ strict continuous in each component‎. ‎In particular‎, we show that this category is reflective and coreflective in the‎ category of $S$-cpo's‎, ‎find the free and cofree functors‎, characterize products and coproducts‎. ‎Furthermore‎, ‎epimorphisms and‎ monomorphisms in {$bf Cpo_{Sep}$-$S$} are studied‎, ‎and show that‎ {$bf Cpo_{Sep}$-$S$} is not cartesian closed‎.