UNIVERSALITY OF NONABELIAN COHOMOLOGY

Abstract

Let be the Grothendieck topology and a sheaf of nonabelian groups on it. We can define the one-dimensional cohomology of either as the Cech cohomology [Dedecker, C. R. Acad. Sci. Paris 247 (1958), 1160-1163] or as the set of -sheaves locally isomorphic to [Giraud, Cohomologie non abelienne]. In this note we put forward a construction which gives rise to a sequence of cohomological functors on the category of sheaves of nonabelian groups, which in favorable cases are shown to be universal [Grothendieck, Tohoku Math. J. (2) 9 (1957), 119-221] and at the same time to coincide.Bibliography: 13 items.