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arXiv · 0908.3762

A relative theory of universal central extensions

Jose Manuel Casas·Tim Van der Linden
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Abstract

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. We consider a fundamental condition on composition of central extensions and give examples of categories which do, or do not, satisfy this condition.

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Jose Manuel Casas, Tim Van der Linden. 2009-08-26. A relative theory of universal central extensions. https://arxiv.org/abs/0908.3762

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