  We give a brief overview how to couple general relativity to the Standard
Model of elementary particles, within the higher gauge theory framework,
suitable for the spinfoam quantization procedure. We begin by providing a short
review of all relevant mathematical concepts, most notably the idea of a
categorical ladder, 3-groups and generalized parallel transport. Then, we give
an explicit construction of the algebraic structure which describes the full
Standard Model coupled to Einstein-Cartan gravity, along with the classical
action, written in the form suitable for the spinfoam quantization procedure.
We emphasize the usefulness of the 3-group concept as a superior tool to
describe gauge symmetry, compared to an ordinary Lie group, as well as the
possibility to employ this new structure to classify matter fields and study
their spectrum, including the origin of fermion families.
