  There are few known computable examples of non-abelian surface holonomy. In
this paper, we give several examples whose structure 2-groups are covering
2-groups and show that the surface holonomies can be computed via a simple
formula in terms of paths of 1-dimensional holonomies inspired by earlier work
of Chan Hong-Mo and Tsou Sheung Tsun on magnetic monopoles. As a consequence of
our work and that of Schreiber and Waldorf, this formula gives a rigorous
meaning to non-abelian magnetic flux for magnetic monopoles. In the process, we
discuss gauge covariance of surface holonomies for spheres for any 2-group,
therefore generalizing the notion of the reduced group introduced by Schreiber
and Waldorf. Using these ideas, we also prove that magnetic monopoles have an
abelian group structure.
