On the second cohomology group in semi-abelian categories

By Marino Gran, Tim Van der Linden. 2005

50 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0f545c0803fe47b18f99f83a0df16f48cf89c403

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In Algebra and Number Theory

1. Sandra Mantovani
2. Giuseppe Metere

In Geometry and Topology

1. Sandra Mantovani
2. Giuseppe Metere

In Mathematical Physics

1. Sandra Mantovani
2. Giuseppe Metere

Citations in the corpus

• Normalities and commutators (2010, methodology): “two subobjects is the whole A. In this case we can freely refer to the commutator [A,K] (notice that when Kis normal, the last coincides also with the normalization of Smith’s commutator, as shown in [GVdL08]). The case H = Ais special even because in this circumstance thecommutatorbehaves well w.r.”