  We study the state-sum models of quantum gravity based on a representation
2-category of the Poincare 2-group. We call them spin-cube models, since they
are categorical generalizations of spin-foam models. A spin-cube state sum can
be considered as a path integral for a constrained 2-BF theory, and depending
on how the constraints are imposed, a spin-cube state sum can be reduced to a
path integral for the area-Regge model with the edge-length constraints, or to
a path integral for the Regge model. We also show that the effective actions
for these spin-cube models have the correct classical limit.
