{
  "abstract": "We introduce a new secondary cohomology operation, the naturality defect product, associated with a graded natural transformation between the cohomology functors of two differential graded functors, and study its main properties. We then prove that a pretriangulated category satisfies the octahedral axiom if and only if the naturality defect product associated with the natural isomorphism given by a theorem of Heller vanishes on the homotopy category of acyclic complexes over it. This characterization extends immediately to n-angulated categories. As an application, we exhibit non-vanishing instances for the recently found examples of pretriangulated categories which are not triangulated. Finally, we show that horizontal composition of these natural isomorphisms preserves n-angulated structures, and we use it to obtain, from each of these examples and for every r >= 1, a pre-3r-angulated category which is not 3r-angulated.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35232",
  "author_total": 2,
  "authors": [
    {
      "name": "Javier Díaz Cabrera"
    },
    {
      "name": "Fernando Muro"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9da5vwzaw507t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35232",
  "fulltext_url": null,
  "id": "9da5vwzaw507t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35232",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.KT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223979083",
  "pdf_url": "https://arxiv.org/pdf/2610.35232",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9da5vwzaw507t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35232",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35232"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A cohomology operation encoding the octahedral axiom",
  "title_text": "A cohomology operation encoding the octahedral axiom",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/9da5vwzaw507t",
  "venue": "arXiv",
  "versions": []
}