A relative theory of universal central extensions

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.

21 pages

References in corpus (4)

• Higher Hopf formulae for homology via Galois Theory
• On the second cohomology group in semi-abelian categories
• Higher central extensions and Hopf formulae
• Internal object actions in homological categories

Cited by in corpus (1)

• On Lie-central extensions of Leibniz algebras