An outline of obstruction theories of extensions via track categories

Abelian track categories can be classified via the third Baues-Wirsching cohomology of small categories. This approach is used in this paper to compare and classify different generalisations of the obstruction theory of non-abelian group extensions, due to Cegarra, Garz'on and Grandjean, Cegarra, Garz'on and Ortega, and Chen, Du and Wang.