Geodesic
Baer invariants in semi-abelian categories I: General theory
Theory and applications of categories, Tome 12 (2004), pp. 1-33

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Classification : Primary 20J05, Secondary 18E10 18G50.
Keywords: Baer invariant, exact, protomodular, semi-abelian category, centrality, nilpotency 
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     author = {T. Everaert and T. Van der Linden},
     title = {Baer invariants in semi-abelian categories {I:} {General} theory},
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     volume = {12},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2004_12_a0/}
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T. Everaert; T. Van der Linden. Baer invariants in semi-abelian categories I: General theory. Theory and applications of categories, Tome 12 (2004), pp. 1-33. http://geodesic.mathdoc.fr/item/TAC_2004_12_a0/