  We generalize toposic Galois theory to higher topoi. We show that locally
constant sheaves in a locally (n-1)-connected n-topos are equivalent to
representations of its fundamental pro-n-groupoid, and that the latter can be
described in terms of Galois torsors. We also show that finite locally constant
sheaves in an arbitrary infinity-topos are equivalent to finite representations
of its fundamental pro-infinity-groupoid. Finally, we relate the fundamental
pro-infinity-groupoid of 1-topoi to the construction of Artin and Mazur and, in
the case of the \'etale topos of a scheme, to its refinement by Friedlander.
