Braided equivariant crossed modules and cohomology of Gamma -modules

If $\Gamma $ is a group, then braided $\Gamma $-crossed modules are classified by braided strict $\Gamma $-graded categorial groups. The Schreier theory obtained for $\Gamma $-module extensions of the type of an abelian $\Gamma $-crossed module is a generalization of the theory of $\Gamma $-module extensions.