{
  "abstract": "Canonical ideal quotients of extriangulated categories admit natural one-sided triangulated or pretriangulated structures. A fundamental question is whether these quotient structures still retain enough information to recover higher orthogonality properties of the subcategory being factored out. We show that, for a strongly functorially finite $n$-rigid subcategory, such information is encoded by the nilpotency of the canonical suspension and, equivalently, of the canonical loop. More precisely, this nilpotency characterizes two-sided maximal $n$-orthogonality. We further establish an objectwise recognition criterion that combines one-sided higher orthogonality with the vanishing of the $n$th suspension or loop. In the triangulated setting, our results give a converse to the known truncation construction and show that the quotient is $n$-truncated if and only if the subcategory is $(n+1)$-cluster tilting. Moreover, in the nonsplit case, the nilpotency index is exactly $n$. These results turn truncation from a consequence of higher orthogonality into a sharp criterion for recognizing it.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34289",
  "author_total": 2,
  "authors": [
    {
      "name": "Yixia Zhang"
    },
    {
      "name": "Panyue Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6m45bpa3gyb2m.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34289",
  "fulltext_url": null,
  "id": "6m45bpa3gyb2m",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34289",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7214792535",
  "pdf_url": "https://arxiv.org/pdf/2609.34289",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6m45bpa3gyb2m.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.34289",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34289"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Higher orthogonality and truncation in canonical pretriangulated quotients",
  "title_text": "Higher orthogonality and truncation in canonical pretriangulated quotients",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/6m45bpa3gyb2m",
  "venue": "arXiv",
  "versions": []
}