On the category Q-Mod

In this paper we consider the category Q-Mod of modules over a given quantale Q. The paper is motivated by constructions and results from the category of modules over a ring. We show that the category Q-Mod is monadic, consider its relation to the category Q-Top of Q-topological spaces and generalize a method of completion of partially ordered sets. Received December 20, 2005; accepted in final form December 4, 2006.