Baer Invariants in Semi-abelian Categories Ii: Homology
نویسندگان
چکیده
This article treats the problem of deriving the reflector of a semi-abelian category A onto a Birkhoff subcategory B of A. Basing ourselves on Carrasco, Cegarra and Grandjeán’s homology theory for crossed modules, we establish a connection between our theory of Baer invariants with a generalization—to semi-abelian categories— of Barr and Beck’s cotriple homology theory. This results in a semi-abelian version of Hopf’s formula and the Stallings-Stammbach sequence from group homology.
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Baer Invariants in Semi-abelian Categories I: General Theory T. Everaert and T. Van Der Linden
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 the...
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