APPLICATIONS OF THE NOTION OF NERVE OF A (BRAIDED) CATEGORICAL GROUP

This goes accompanied with another Note [2]. The higher Poincare group oids rho(n), (X, ) have a structure of categorical group for n = 2 an d a structure of braided categorical group for n = 3. A categorical gr oup and a braided categorical group have, respectively, associated cer tain simplicial sets, which should be called their nerves. By using th ese constructions, rho(n) and Ner, and the cohomology of categorical g roups with coefficients in braided categorical groups,,ve give a cohom ological classification of homotopy classes of maps between spaces wit h only two homotopy groups pi(1) and pi(2) or pi(2) and pi(3).