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On the second cohomology group in semi-abelian categories

Marino Gran·Tim Van der Linden
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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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Marino Gran, Tim Van der Linden. 2007-05-07. On the second cohomology group in semi-abelian categories. https://doi.org/10.1016/j.jpaa.2007.06.009

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