  In this mostly expository article, elements of higher category theory
essential to the construction of a class of four dimensional quantum geometric
models are reviewed. These models improve current state sum models for Quantum
Gravity, such as the Barrett-Crane model, in that they appear, for instance, to
remove degeneracies which swamp the partition function. Much work remains to be
done before a complete construction is reached, but the crucial categorical
notion of internalisation already illuminates the idea that a full unified
model may result from few, albeit as yet poorly understood, additional
principles. In particular, a spacetime and matter duality principle is employed
through an understanding of the role of pseudomonoidal objects in categorified
cohomology.
