  We study a generalization of Kitaev's abelian toric code model defined on CW
complexes. In this model qudits are attached to $n$ dimensional cells and the
interaction is given by generalized star and plaquette operators. These are
defined in terms of coboundary and boundary maps in the locally finite cellular
cochain complex and the cellular chain complex. We find that the set of
frustration free ground states and the types of charges carried by certain
localized excitations depend only on the proper homotopy type of the CW
complex. As an application we show that the homological product of a CSS code
with the infinite toric code has excitations with abelian anyonic statistics.
