  Using the theory of measurable categories developped by Yetter in work in
preparation, we provide a notion of representations of 2-groups more
well-suited to physically and geometrically interesting examples than that
proposed in unpublished work of Barrett and Mackaay using 2-VECT of Kapranov
and Voevodsky. Using this theory we sketch a 2-categorical approach to the
state-sum model for Lorentzian quantum gravity proposed in by the authors in
previous work and suggest state-integral constructions for 4-manifold
invariants.
