A theory of bundles over posets

This paper is motivated by Quantum Field Theory. Whilst the pseudo-Riemannian spacetime manifold enters directly into the formulation of Classical Field Theory, it enters into Quantum Field Theory only through a suitable base for its topology ordered under inclusion. This raises the question as to what extent the topological data of the spacetime manifold are still encoded in the partially ordered set. Positive answers have been given as far as connectivity [9] and the fundamental group go [9, 12] and we shall see in this paper that the same applies to the first locally constant cohomology group. Perhaps the most important open question in Quantum Field Theory concerns gauge theories. There is no formulation of gauge theories which