Extending the work of Fröhlich, Lue and Furtado-Coelho, we consider the theory of Baer invariants in the context of semi-abelian categories. Several exact sequences, relative to a subfunctor of the identity functor, are obtained. We consider a notion of commutator which, in the case of abelianization, corresponds to Smith's. The resulting notion of centrality fits into Janelidze and Kelly's theory of central extensions. Finally we propose a notion of nilpotency, relative to a Birkhoff subcategory of a semi-abelian category.
Keywords: Baer invariant; exact, protomodular, semi-abelian category; centrality; nilpotency
2000 MSC: Primary 20J05; Secondary 18E10 18G50.
Theory and Applications of Categories,
Vol. 12, 2004,
No. 1, pp 1-33.
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