Abstract
Abelian track categories can be classified via the third Baues–Wirsching cohomology of small categories. This approach is used in this paper to derive the different generalizations of the obstruction theory of non-abelian group extensions, due to Cegarra, Garzón and Grandjean, Cegarra, Garzón and Ortega, and Chen, Du and Wang as particular cases of a general theory of abelian track categories and to give unified proofs of the main properties of these obstruction classes.
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