  For each graph on two vertices, and each divisor on the graph in the sense of
Baker-Norine, we describe a sheaf of vector spaces on a finite category whose
zeroth Betti number is the Baker-Norine "Graph Riemann-Roch" rank of the
divisor plus one. We prove duality theorems that generalize the Baker-Norine
"Graph Riemann-Roch" Theorem.
