Manifold calculus adapted for simplicial complexes

Abstract: We develop a generalization of manifold calculus in the sense of Goodwillie-Weiss where the manifold is replaced by a simplicial complex. We consider functors from the category of open subsets of a fixed simplical complex into the category of topological spaces and prove an analogue of the approximation theorem. Namely, under certain conditions such a functor can be approximated by a tower of (appropriately adapted) polynomial functors.