1
Professor of Mathematics of Shahid Beheshti University
2
PhD student at the Department of Mathematics of Shahid Beheshti University
Abstract
In this paper, some categorical properties of the category ${bf Cpo}_{{bf Act}text{-}S}$ of all {cpo $S$-acts}, cpo's equipped with actions of a monoid $S$ on them, and strict continuous 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 ${bf Cpo}_{{bf Act}text{-}S}$ to the category of cpo's has both a left and a right adjoint.
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