  To any moment graph G we assign a subcategory V of the category of sheaves on
G together with an exact structure. We show that in the case that the graph is
associated to a non-critical block of the equivariant category O over a
symmetrizable Kac-Moody algebra, V is equivalent (as an exact category) to the
subcategory of modules that admit a Verma flag. The projective modules
correspond under this equivalence to the intersection cohomology sheaves on the
graph.
