Nakayama functors on proper abelian subcategories

• Autores: David Nkansah
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 70, Nº 1, 2026, págs. 27-53
• Idioma: inglés
• DOI: 10.5565/publmat7012602
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• Resumen

  • We construct Nakayama functors on proper abelian subcategories of triangulated categories with a Serre functor using approximation theory. This, in turn, allows for the construction of Auslander–Reiten translates. As a result, we prove that suitable proper abelian subcategories are dualising k-varieties and have enough projectives if and only if they have enough injectives. As an application, we provide a new proof of the existence of Auslander–Reiten sequences in the category of finite-dimensional m odules over a fi nite-dimensional algebra.