The Yoneda isomorphism commutes with homology

• George Peschke ^[1] ; Tim Van der Linden ^[2]
  1. [1] University of Alberta

     University of Alberta

     Canadá

     
  2. [2] Université Catholique de Louvain

     Université Catholique de Louvain

     Arrondissement de Nivelles, Bélgica

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 220, Nº 2 (February 2016), 2016, págs. 495-517
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2015.05.005
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• Resumen

  • We show that, for a right exact functor from an abelian category to abelian groups, Yoneda's isomorphism commutes with homology and, hence, with functor derivation. Then we extend this result to semiabelian domains. An interpretation in terms of satellites and higher central extensions follows. As an application, we develop semiabelian (higher) torsion theories and the associated theory of (higher) universal (central) extensions.