reflected in the abstract as well. Without referring to the models directly – only that a model consists of spaces and maps between them – the most readily apparent feature of a multi-model system is its topology. We propose that this topology should be modeled first, and then the spaces and maps of the individual models be specified in accordance with the topology. Axiomatically, this construction leads to *sheaves*. Our overall modeling approach consists of specifying sheaves *of* a certain type *on* a certain kind of topological space. We could aim for complete generality, though this leads to considerable computational and analytic difficulties. We will build our theory on *partial orders* (or *posets*, for short); these lend themselves to a balance between theoretical expressiveness and computational facility. We will specify a multi-model system as a sheaf of smooth, finite-dimensional manifolds on a poset. A sheaf model is a natural way to express the topological relationship among state variables and the equations relating them. Solver algorithms for the set of equations enforce consistency constraints among the state variables, which is precisely the process of computing the space of global sections of a sheaf.

Encoding models as sheaves allows one to realize 