2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67936This is intended as a self-contained introduction to the representation theory developed in order to create a Poincare 2-category state sum model for Quantum Gravity in 4 dimensions. We review the structure of a new representation 2-category appropriate to Lie 2-group symmetries and discuss its application to the problem of finding a state sum model for Quantum Gravity. There is a remarkable richness in its details, reflecting some desirable characteristics of physical 4-dimensionality. We begin with a review of the method of orbits in Geometric Quantization, as an aid to the intuition that the geometric picture unfolded here may be seen as a categorification of this process.16 pages, 1 figure, LaTeXQuantum AlgebraGeneral Relativity and Quantum CosmologyCategory Theorytext