On the second cohomology group in semi-abelian categories

• Autores: Marino Gran, Tim Van der Linden
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 212, Nº 3, 2008, págs. 636-651
• Idioma: inglés
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• Resumen

  • 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.