Protoadditive functors, derived torsion theories and homology
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Tomas Everaert [1] ; Marino Gran [2]
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[1] Vrije Universiteit Brussel
Vrije Universiteit Brussel
Arrondissement Brussel-Hoofdstad, Bélgica
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[2] Université Catholique de Louvain
Université Catholique de Louvain
Arrondissement de Nivelles, Bélgica
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- Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 8 (August 2015), 2015, págs. 3629-3676
- Idioma: inglés
- DOI: 10.1016/j.jpaa.2014.12.015
- Enlaces
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Resumen
Protoadditive functors are designed to replace additive functors in a non-abelian setting. Their properties are studied, in particular in relation to torsion theories, Galois theory, homology and factorisation systems. It is shown how a protoadditive torsion-free reflector induces a chain of derived torsion theories in the categories of higher extensions, similar to the Galois structures of higher central extensions previously considered in semi-abelian homological algebra. Such higher central extensions are also studied, with respect to Birkhoff subcategories whose reflector is protoadditive or, more generally, factors through a protoadditive reflector. In this way we obtain simple descriptions of the non-abelian derived functors of the reflectors via higher Hopf formulae. Various examples are considered in the categories of groups, compact groups, internal groupoids in a semi-abelian category, and other ones.
