  It is well known that the category of covering projections (that is, locally
constant objects) of a locally connected topos is equivalent to the classifying
topos of a strict progroupoid (or, equivalently, a localic prodiscrete
groupoid), the \emph{fundamental progroupoid}, and that this progroupoid
represents first degree cohomology. In this paper we generalize these results
to an arbitrary topos. The fundamental progroupoid is now a localic
progroupoid, and can not be replaced by a localic groupoid. The classifying
topos in not any more a Galois topos. Not all locally constant objects can be
considered as covering projections. The key contribution of this paper is a
novel definition of covering projection for a general topos, which coincides
with the usual definition when the topos is locally connected. The results in
this paper were presented in a talk at the Category Theory Conference,
Vancouver July 2004.
