Each Gr-functor of the type (φ, f) of a Gr-category of the type (Π, C) has the obstruction be an element k ∈ H(Π, C). When this obstruction vanishes, there exists a bijection between congruence classes of Gr-functors of the type (φ, f) and the cohomology group H(Π,C). Then the relation of Gr-category theory and the group extension problem can be established and used to prove that each Gr-catego...
