Locally partial-ordered spaces (local po-spaces) have been used to model concurrent systems. We provide equivalences for these spaces by constructing a model category containing the category of local po-spaces. We show that the category of simplicial presheaves on local po-spaces can be given Jardine's model structure, in which we identify the weak equivalences between local po-spaces. In the process, we give an equivalence between the category of sheaves on a local po-space and the category of étale bundles over a local po-space. Finally, we describe a localization that should provide a good framework for studying concurrent systems.
Homology, Homotopy and Applications, Vol. 8 (2006), No. 1, pp.263-292.