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Register a new userOn Gr-Functors between Gr-Categories: Obstruction theory for Gr-Functors of the type $(varphi,f)$
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Nguyen Tien Quang
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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 congruence classes 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 extension problem can be established and used to prove that each Gr-category is Gr-equivalent to a strict one.
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