Physical theories on a space M are usually formulated locally, on an open set U. A global theory is then obtained by taking a cover of M, in terms of open sets U, and relating the theory on overlaps by symmetries of the theory. This may however not be a convenient formulation if one is interested in global properties of the theory. In this talk I will introduce surjective submersions as a generalisation of open covers, show that common concepts such as Cech cohomology, line bundles, etc., can all be reformulated in terms of surjective submersions, and will argue that in fact all of physics should be reformulated in terms of surjective submersions. We will study the example of a torus, where we will elucidate the relation to group cohomology.