A relative theory of universal central extensions

Details A relative theory of universal central extensions A relative theory of universal central extensions

2009-08-26

arxiv.org/abs/0908.3762v4

Mathematics

Algebraic Topology

Under revision: withdrawn after persistent problems with Lemma 2.20

Scientific paper

Basing ourselves on Janelidze and Kelly's general notion of central extension, we study universal central extensions in the context of semi-abelian categories. Thus we unify classical, recent and new results in one conceptual framework. The theory we develop is relative to a chosen Birkhoff subcategory of the category considered: for instance, we consider groups vs. abelian groups, Lie algebras vs. vector spaces, precrossed modules vs. crossed modules and Leibniz algebras vs. Lie algebras.

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