  In the setting of generalized class field theory, one has a field K with a
hyper-class formation C, a complex of G_K-modules that plays the role of a
class formation. Letting C(L) denote H^0(G_L, C), there is a distinguished
cohomology class in H^2(Gal(L/K), C(L)), the hyper-fundamental class. In this
paper, we prove that a group extension of Gal(L/K) by C(L) whose corresponding
cohomology class is the hyper-fundamental class satisfies the classical axioms
of a Weil group.
