On the second cohomology group in semi-abelian categories

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dc.creatorGran, Marino
dc.creatorVan der Linden, Tim
dc.date2005-11-14
dc.date2007-05-07
dc.date.accessioned2026-07-07T08:42:44Z
dc.date.available2026-07-07T08:42:44Z
dc.descriptionWe 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.
dc.description23 pages, major changes in sections 4 and 6, minor changes elsewhere
dc.identifierhttps://arxiv.org/abs/math/0511357
dc.identifierhttp://arxiv.org/abs/math/0511357
dc.identifierJournal of Pure and Applied Algebra 212 (2008) 636-651
dc.identifierdoi:10.1016/j.jpaa.2007.06.009
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142067
dc.subjectK-Theory and Homology
dc.subjectCategory Theory
dc.subject18G99; 20J06
dc.titleOn the second cohomology group in semi-abelian categories
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