Dynamical generalization of Yetter’s model based on a crossed module of discrete groups

We construct a dynamical lattice model based on crossed module of possibly non-abelian finite groups. Its degrees freedom are defined links and plaquettes, while gauge transformations vertices the underlying lattice. specify Hilbert space, define basic observables (including Hamiltonian) initiate a~discussion model's phase diagram. The constructed generalizes, in appropriate limits reduces to, topological theories with symmetries described by groups modules, Yang-Mills theory $2$-form electrodynamics. conclude reviewing classifying spaces an emphasis direct relation between their geometry properties under consideration.