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PreprintCC BY 4.0arXiv

A right pretriangulated category which is not right triangulated

  • Jing He
  • Panyue Zhou
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Abstract

Chen, Liu, Lu, and Zhang recently constructed a pretriangulated category with invertible suspension in which Verdier's octahedral axiom fails. We introduce a general enlargement construction for right pretriangulated categories and show that it preserves axioms (RTR1)-(RTR3), while failure of (RTR4) is detected by the forgetful functor. Applied to their type A5 example, the construction yields a right pretriangulated category that is not right triangulated. In this example, the suspension is faithful but not essentially surjective.

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Cite

BibTeXRIS
BibTeX
@misc{he2026right,
  title = {{A right pretriangulated category which is not right triangulated}},
  author = {Jing He and Panyue Zhou},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.00602},
  eprint = {2609.00602},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.00602},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A right pretriangulated category which is not right triangulated
AU  - Jing He
AU  - Panyue Zhou
PY  - 2026
DA  - 2026/09/01
PB  - arXiv
DO  - 10.48550/arxiv.2609.00602
UR  - https://arxiv.org/abs/2609.00602
AB  - Chen, Liu, Lu, and Zhang recently constructed a pretriangulated category with invertible suspension in which Verdier's octahedral axiom fails. We introduce a general enlargement construction for right pretriangulated categories and show that it preserves axioms (RTR1)-(RTR3), while failure of (RTR4) is detected by the forgetful functor. Applied to their type A_5 example, the construction yields a right pretriangulated category that is not right triangulated. In this example, the suspension is faithful but not essentially surjective.
ER  -