Cohomology of cofibred categorical groups Original Research Article

In this paper we study and interpret a certain non-abelian cohomology image, 0≤i≤2, of a small category image with coefficients in a image-cofibred categorical group image. The work is developed in a purely abstract setting, but several examples that indicate a very close connection with algebraic and topological problems are discussed explicitly. For instance, we obtain two new interpretations for the Brauer group of a Galois extension of commutative rings: an algebraic one in terms of equivalence classes of torsors over the Galois group and a topological one in terms of homotopy classes of cross-sections for a fibration over an Eilenberg–MacLane space of type K(G,1).