Nakayama functors on proper abelian subcategories

David Nkansah

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arXiv · 2312.07323

Nakayama functors on proper abelian subcategories

David Nkansah

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Abstract

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 modules over a finite dimensional algebra.

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BibTeX RIS

David Nkansah. 2023-12-12. Nakayama functors on proper abelian subcategories. https://arxiv.org/abs/2312.07323

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