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

‎ 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.     

کلیدواژه ها:

Directed complete partially ordered set ، Product ، coproduct ، cartesian closed