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

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

2007-08-09

arxiv.org/abs/0708.1348v2

Mathematics

Category Theory

12 pager, For reduction, the abstract and subsection 1.1 have been edited; section 2 and the beginning of section 5 have been

Scientific paper

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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