Exceptional model structures and the induced extriangulated categories

@misc{zhang2026exceptional,
  title = {{Exceptional model structures and the induced extriangulated categories}},
  author = {Chencheng Zhang and Pu Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.03524},
  eprint = {2609.03524},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.03524},
  note = {CC0},
}

TY  - UNPB
TI  - Exceptional model structures and the induced extriangulated categories
AU  - Chencheng Zhang
AU  - Pu Zhang
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.03524
UR  - https://arxiv.org/abs/2609.03524
AB  - A Hovey triple (𝒞, ℱ, 𝒲) is {\it exceptional}, if (𝒞 ∩ ℱ, 𝒞 ∩ ℱ ∩ 𝒲) is not a Frobenius pair. One has a disjoint union {Hovey triple} = {Hereditary Hovey triple} ⋃̇ {Exceptional Hovey triple} \ ⋃̇ {non−hereditary and non−exceptional Hovey triple}. Exceptional Hovey triples appear widely. For a selfinjective Nakayama algebra A= kC_n/J^t, A−mod admits exceptional Hovey triples if and only if gcd (n, t) ≥ 2 and t ≥ 3. Their homotopy categories reveal new phenomena. Nakaoka-Palu's Theorem implies that there is a triangulation on 𝒞∩ℱ/𝒞∩ℱ∩𝒲. It is proved that a Hovey triple in a weakly idempotent complete extriangulated category (𝒜, 𝔼, s) is exceptional if and only if the induced extriangulated structure (𝒞∩ℱ/𝒞∩ℱ∩𝒲, 𝔼̅, s̅) is not {\it canonically triangulated}. Between this extriangulated structure and the one arising from the triangulation, the intermediate extriangulated structures are in one-to-one correspondence with Serre subcategories of fp((𝒫(𝒞∩ℱ)/𝒞∩ℱ∩𝒲)^op, Ab).
ER  -