  Minimal cellular resolutions of the edge ideals of cointerval hypergraphs are
constructed. This class of d-uniform hypergraphs coincides with the complements
of interval graphs (for the case d=2), and strictly contains the class of
`strongly stable' hypergraphs corresponding to pure shifted simplicial
complexes. The polyhedral complexes supporting the resolutions are described as
certain spaces of directed graph homomorphisms, and are realized as
subcomplexes of mixed subdivisions of the Minkowski sums of simplices.
Resolutions of more general hypergraphs are obtained by considering
decompositions into cointerval hypergraphs.
