On the second cohomology group in semi-abelian categories

Gran, Marino;Van der Linden, Tim
(2008) Journal of Pure and Applied Algebra — Vol. 212, n° 3, p. 636-651 (2008)

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Abstract
We develop some new aspects of cohomology in the context of semi-abelian categories: we establish a Hochschild-Serre 5-term exact sequence extending the classical one for groups and Lie algebras; we prove that an object is perfect if and only if it admits a universal central extension; we show how the second Barr-Beck cohomology group classifies isomorphism classes of central extensions; we prove a universal coefficient theorem to explain the relationship with homology.
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Gran, M., & Van der Linden, T. (2008). On the second cohomology group in semi-abelian categories. Journal of Pure and Applied Algebra, 212(3), 636-651. https://doi.org/10.1016/j.jpaa.2007.06.009 (Original work published 2008)