Components of directed spaces

A directed space is a topological space with a distinguished family ofpaths . Directed spaces are used in computer science as models of concurrent programs. Unfortunately, no satisfactory analogues of classical homotopy invariants of topological spaces are known. I will present a construction of a category of components of a directed space, which is intended to be a directed analogue of the set of path-connected components of topological spaces. It has some advantages over the construction of Goubault et al.: it works in a greater generality and the component category is enriched in the homotopy category. Thus, it carries also information about higher homotopies.