Higher category theory can be employed to generalize the notion of symmetry, by passing from a gauge group to the notion of a gauge n-group. The n-groups are designed to generalize notions of connection and parallel transport, from curves to manifolds of dimension higher than one. They also give rise to a class of topological actions called nBF actions. One can then employ a 3-group as a gauge symmetry and the corresponding 3BF action, to describe the full Einstein-Cartan theory of gravity coupled to Standard Model fields. Such an action is naturally adapted to the spinfoam quantization technique, with the aim to construct a full model of quantum gravity with matter.

Once constructed, the properties of the model open up the possibility of a nontrivial unification of all fields. A 3-group naturally contains additional novel gauge groups which specify the spectrum of fermions and scalars present in the theory, just like the ordinary gauge group specifies the spectrum of gauge bosons in the Yang-Mills theory. The presence and the properties of new gauge groups have the potential to explain fermion families, and other structure in the matter spectrum of the Standard Model.