On state sums, internalisation and unification

Abstract

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.