Nakayama functors on proper abelian subcategories
Representation Theory
2025-08-06 v2
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 -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.
Cite
@article{arxiv.2312.07323,
title = {Nakayama functors on proper abelian subcategories},
author = {David Nkansah},
journal= {arXiv preprint arXiv:2312.07323},
year = {2025}
}
Comments
32 pages. Title change, added '0.2. Some useful results', included Lemma 1.2 and fixed some minor corrections. Accepted for publication in Publicacions Matem\'atiques