the way that larry harper describes his generalized directed graph morphisms involves the idea that "vertexes can get mapped either to vertexes or to edges". i'll have to think about that. one thought is that maybe they're all getting mapped to edges, with the ones that look like they're going to vertexes actually going to degenerate edges. that might not be on the right track though; it might actually be a case of v -> v+e, just as harper says.