Abstract: The path category P(X) of a space X is an invariant which is defined much like the fundamental groupoid, except that directions of paths are not formally reversed. This construction has applications in theoretical computer science, where it gives, in principle, a description of execution paths in geometric models for the behaviour of parallel processing systems. Path categories have resisted calculational analysis until just recently, in part because standard homotopy theoric methods are not applicable.

We now know that the path category P(K) of a finite simplicial complex K can be computed by an algorithmic method which is based on the existence of a finite 2-categorical resolution.

Methods of implementation and applications of this result will be discussed.