  We give a geometric interpretation of sheaf cohomology for higher degrees n
in terms of torsors on the member of degree d=n-1 in hypercoverings of type
r=n-2, endowed with an additional data, the so-called rigidification. This
generalizes the fact that cohomology in degree one is the group of isomorphism
classes of torsors, where the rigidification becomes vacuous, and that
cohomology in degree two can be expressed in terms of bundle gerbes, where the
rigidification becomes an associativity constraint.
