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Each Gr-functor of the type $(\varphi,f)$ of a Gr-category of the type$(\Pi,\C)$ has the obstruction be an element $\overline{k}\in H^3(\Pi,\C).$When this obstruction vanishes, there exists a bijection between congruenceclasses of Gr-functors of the type $(\varphi,f)$ and the cohomology group$H^2(\Pi,\C).$ Then the relation of Gr-category theory and the group extensionproblem can be established and used to prove that each Gr-category isGr-equivalent to a strict one.

On Gr-Functors between Gr-Categories: Obstruction theory for Gr-Functors of the type $(\varphi,f)$