relationships. Although the study of sheaves over general topological spaces can be quite technical, sheaves over partially ordered sets are much more tractable. Sheaves have a number of useful invariants that provide descriptive power for systems of equations, and often the mere act of encoding a system as a sheaf is illuminating. For instance, writing differential equations along a stratified manifold requires delicate management of boundary conditions of various sorts. The sheaf encoding described in this chapter makes specifying the correct kind of boundary conditions almost effortless. This chapter discusses a number of techniques for performing sheaf encodings of systems, explains some of the relationships among these encodings, and describes some of the analytical techniques that can be used on sheaf-encoded models.

Mathematical constructions of sheaves
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Since topological spaces in their full generality tend to admit rather pathological properties that are not reflected in practical models, it is wise to apply constraints. There are several other possibilities for the topological space, and they vary in expressiveness. In the author’s experience, locally finite topological spaces, cell complexes, abstract simplicial complexes, and partial orders are the most useful for problems involving models of systems. Of these, locally finite topological spaces are 