Baer invariants in semi-abelian categories I: General theory

Everaert, Tomas;Van der Linden, Tim
(2004) Theory and Applications of Categories — Vol. 12, n° 1, p. 1-33 (2004)

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Extending the work of Frohlich, 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 semiabelian category.
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Everaert, T., & Van der Linden, T. (2004). Baer invariants in semi-abelian categories I: General theory. Theory and Applications of Categories, 12(1), 1-33. https://hdl.handle.net/2078.5/59234 (Original work published 2004)