The category of monoid actions in Cpo

Abstract

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