  In this paper we consider simplicial families, that is, simplicial objects
indexed by a simplicial set. We develop a method to construct family hypercover
refinements of a cover family based on the notion of \emph{n-spans} that we
introduce here. In [The fundamental progroupoid of a general topos, Journal of
Pure and Applied Algebra 212 (2008)] we had introduced the notion of
\emph{covering projection} in a topos. They are locally constant objects
satisfying an additional condition which is valid in all locally constant
objects when the topos is locally connected, and developed the theory of the
fundamental groupoid of a general topos. Here we show that covering projections
can be obtained as objects constructed from a descent datum of a simplicial set
on a family of sets. We construct a groupoid $\nn{G}_\cc{H}$ such that the
category $\cc{G}_\cc{H}$ of covering projections trivialized by $\cc{H}$ is its
classifying topos. This determines a protopos $\{\cc{G} \cc{H}\}_\cc{H}$ and a
progroupoid $\{\nn{G}_\cc{H}\}_\cc{H}$, suitable indexed by a filtered poset of
hypercovers. Then we show that this progroupoid classifies torsors. This
construction is novel also in the case of locally connected topoi, showing that
locally constant object in a locally connected topos are constructed by descent
from a descent datum on a family of sets. The salient feature that
distinguishes locally connected topoi is that the progroupoid is \emph{strict},
that is, the transition morphisms are surjective on triangles, or,
equivalently, the transition inverse image functors in the underlying
indcategory are full and faithful.
