2005/11/30 by Marino Gran, Tim Van der Linden · 42 citations
Mathematics · #Abelian category #Abelian group #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Cohomology #Discrete mathematics #Equivariant cohomology #Exact sequence #Group cohomology #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Isomorphism (crystallography) #Mathematics #Pure mathematics #math.CT #math.KT #msc:18G99 #msc:20J06
paper · pdf · doi:10.1016/j.jpaa.2007.06.009
published in Journal of Pure and Applied Algebra 212(3), 636-651 (Elsevier BV) · 23 pages, major changes in sections 4 and 6, minor changes elsewhere
arxiv created 2007/05/07 · openalex publication_date 2007/09/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.