Cohomological and homotopical classification of singular extensions of categorical groups

If G is a categorical group, a G-module is defined to be a braided categori cal group (A, c) together with an action of G on (A; c). We associate to an y G-module (A, c) a Kan simplicial set Ner(G, (A; c)) and a Kan fibration N er(G, (A, c)) phi<($)under right arrow> Ner(G). In addition, we define the set of equivalence classes of singular extensions of G by (A, c), and also a 1-cohomology set of G with coefficients in (A; c). We construct bijection s between these sets, and also with the set of fibre homotopy classes of cr oss-sections of the fibration phi. (C) Academie des Sciences/Elsevier, Pari s.