{
  "abstract": "A Hovey triple $(\\mathcal{C}, \\mathcal{F}, \\mathcal{W})$ is {\\it exceptional}, if $(\\mathcal{C} \\cap \\mathcal{F}, \\ \\mathcal{C} \\cap \\mathcal{F} \\cap \\mathcal{W})$ is not a Frobenius pair. One has a disjoint union $\\{\\text{Hovey triple}\\} = \\{\\text{Hereditary Hovey triple}\\} \\ \\dot\\bigcup \\ \\{\\text{Exceptional Hovey triple}\\}$ \\ $\\dot\\bigcup \\ \\{\\text{non-hereditary and non-exceptional Hovey triple}\\}.$ Exceptional Hovey triples appear widely. For a selfinjective Nakayama algebra $A= kC_n/J^t$, $A\\mbox{-}{\\rm mod}$ admits exceptional Hovey triples if and only if $\\gcd (n, t) \\ge 2$ and $t \\geq 3$. Their homotopy categories reveal new phenomena. Nakaoka-Palu's Theorem implies that there is a triangulation on $\\frac{\\mathcal C\\cap\\mathcal F}{\\mathcal C\\cap\\mathcal F\\cap\\mathcal W}.$ It is proved that a Hovey triple in a weakly idempotent complete extriangulated category $(\\mathcal A, \\mathbb E, \\mathfrak s)$ is exceptional if and only if the induced extriangulated structure $\\bigl(\\frac{\\mathcal C\\cap\\mathcal F}{\\mathcal C\\cap\\mathcal F\\cap\\mathcal W}, \\ \\overline{\\mathbb E}, \\ \\overline{\\mathfrak s}\\bigr)$ 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 $\\mathrm{fp}((\\frac{\\mathcal P(\\mathcal C\\cap\\mathcal F)}{\\mathcal C\\cap\\mathcal F\\cap\\mathcal W})^{\\mathrm{op}}, \\mathrm{Ab})$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.03524",
  "author_total": 2,
  "authors": [
    {
      "name": "Chencheng Zhang"
    },
    {
      "name": "Pu Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ef60696ww8nzn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03524",
  "fulltext_url": null,
  "id": "ef60696ww8nzn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03524",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7208773159",
  "pdf_url": "https://arxiv.org/pdf/2609.03524",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ef60696ww8nzn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:36Z",
      "native_id": "2609.03524",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03524"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Exceptional model structures and the induced extriangulated categories",
  "title_text": "Exceptional model structures and the induced extriangulated categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:36Z",
  "url": "https://research.draconitic.com/paper/ef60696ww8nzn",
  "venue": "arXiv",
  "versions": []
}