  In this series of papers, we study a Hamiltonian model for 3+1d topological
phases, based on a generalisation of lattice gauge theory known as "higher
lattice gauge theory". Higher lattice gauge theory has so called "2-gauge
fields" describing the parallel transport of lines, just as ordinary gauge
fields describe the parallel transport of points. In the Hamiltonian model this
is represented by having labels on the plaquettes of the lattice, as well as
the edges. In this paper we summarize our findings in an accessible manner,
with more detailed results and proofs to be presented in the other papers in
the series. The Hamiltonian model supports both point-like and loop-like
excitations, with non-trivial braiding between these excitations. We explicitly
construct operators to produce and move these excitations, and use these to
find the loop-loop and point-loop braiding relations. These creation operators
also reveal that some of the excitations are confined, costing energy to
separate. This is discussed in the context of condensation/confinement
transitions between different cases of this model. We also discuss the
topological charges of the model and use explicit measurement operators to
re-derive a relationship between the number of charges measured by a 2-torus
and the ground-state degeneracy of the model on the 3-torus. From these
measurement operators, we can see that the ground state degeneracy on the
3-torus is related to the number of types of linked loop-like excitations.
