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PreprintarXiv licencearXiv

Auslander-Reiten-Serre duality revisited

  • Ji-Wei He
  • Jixing Pan
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Abstract

Let (π’ž,𝔼,s) be an extriangulated category with a right Auslander-Reiten-Serre (ARS for short) duality $(Ο„, Ξ·)$ in the sense of Iyama, Nakaoka and Palu. We show $(Ο„, Ξ·)$ induces right ARS dualities on the relative theories of (π’ž,𝔼,s). Under relative structures, we show that the functor Ο„ is indeed an exact functor between extriangulated categories and preserves almost split exangles. Finally, we give some applications and examples on these results. For instance, we generalize a recent result by A. Hubery to a categorical framework.

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Cite

BibTeXRIS
BibTeX
@misc{he2026auslanderreitenserre,
  title = {{Auslander-Reiten-Serre duality revisited}},
  author = {Ji-Wei He and Jixing Pan},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29584},
  eprint = {2608.29584},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29584},
}
RIS
TY  - UNPB
TI  - Auslander-Reiten-Serre duality revisited
AU  - Ji-Wei He
AU  - Jixing Pan
PY  - 2026
DA  - 2026/08/30
PB  - arXiv
DO  - 10.48550/arxiv.2608.29584
UR  - https://arxiv.org/abs/2608.29584
AB  - Let (π’ž,𝔼,s) be an extriangulated category with a right Auslander-Reiten-Serre (ARS for short) duality $(Ο„, Ξ·)$ in the sense of Iyama, Nakaoka and Palu. We show $(Ο„, Ξ·)$ induces right ARS dualities on the relative theories of (π’ž,𝔼,s). Under relative structures, we show that the functor Ο„ is indeed an exact functor between extriangulated categories and preserves almost split exangles. Finally, we give some applications and examples on these results. For instance, we generalize a recent result by A. Hubery to a categorical framework.
ER  -