We develop some new aspects of cohomology in the context of semi-abeliancategories: we establish a Hochschild-Serre 5-term exact sequence extending theclassical one for groups and Lie algebras; we prove that an object is perfectif and only if it admits a universal central extension; we show how the secondBarr-Beck cohomology group classifies isomorphism classes of centralextensions; we prove a universal coefficient theorem to explain therelationship with homology.
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