  We introduce a formalism based on a combinatorial notion of cell complex
subject to an inclusion-reversing duality operation. Our main goal is to open
the way for a functorial definition of field theories in a context where no
manifold or topological structure is assumed. This is achieved via a discrete
notion of cobordism for which a composition operation is defined. Our main
theorem enables the composition of cobordisms by showing that certain sequences
of maps between cell complexes are in bijective correspondence with a cell
complex of dimension one higher. As a result we obtain a category whose
morphisms are cobordisms having a causal structure generalizing that of Causal
Dynamical Triangulations as well as dualities inherited from the duality map
defined on cell complexes.
