On Gr-Functors between Gr-Categories: Obstruction theory for Gr-Functors of the type $(φ,f)$
Abstract
Description
Each Gr-functor of the type $(φ,f)$ of a Gr-category of the type $(Π,\C)$ has the obstruction be an element $\overline{k}\in H^3(Π,\C).$ When this obstruction vanishes, there exists a bijection between congruence classes of Gr-functors of the type $(φ,f)$ and the cohomology group $H^2(Π,\C).$ 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.
12 pager, For reduction, the abstract and subsection 1.1 have been edited; section 2 and the beginning of section 5 have been omitted. The definition of the functors of the type $(φ,f)$ has been introduced in order to represent some theorems and their proofs in other words
12 pager, For reduction, the abstract and subsection 1.1 have been edited; section 2 and the beginning of section 5 have been omitted. The definition of the functors of the type $(φ,f)$ has been introduced in order to represent some theorems and their proofs in other words