THE CATEGORY OF MONOID ACTIONS IN CPO

In this paper, some categorical properties of the category Cpo Act−S of all {cpo S -acts}, cpo's equipped with actions of a monoid S on them, and strict ontinuous action-preserving maps between them is considered. In particular, we describe products and coproducts in this category, and consider monomorphisms and epimorphisms. Also, we show that the forgetful functor from Cpo Act−S to the category of cpo's has both a left and a right adjoint.