  In this note we consider a few interesting properties of discrete connections
on principal bundles when the structure group of the bundle is an abelian Lie
group. In particular, we show that the discrete connection form and its
curvature can be interpreted as singular $1$ and $2$ cochains respectively,
with the curvature being the coboundary of the connection form. Using this
formalism we prove a discrete analogue of a formula for the holonomy around a
loop given by Marsden, Montgomery and Ratiu for (continuous) connections in a
similar setting.
