Abstract
For any group G , a certain cohomology theory of G -modules is developed. This cohomology arises from the homotopy theory of G -spaces and it is called the “abelian cohomology of G -modules”. Then, as the main results of this paper, natural one-to-one correspondences between elements of the 3 rd cohomology groups of G -modules, G -equivariant pointed simply-connected homotopy 3-types and equivalence classes of braided G -graded categorical groups are established. The relationship among all these objects with equivariant quadratic functions between G -modules is also discussed.
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