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

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 Added by Tien Quang Nguyen
 Publication date 2009
  fields
and research's language is English




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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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