{
  "abstract": "Originating in ergodic structure theory, nilspace theory is concerned with the study of cubical spaces. A first key result in this theory, the weak structure theorem, is the representation of a concrete fibrant compact cubespace as a tower of its canonical truncations, exhibiting each step over the previous one as a principal bundle by a compact abelian group. We present a categorical proof of the weak structure theorem by systematically interpreting the relevant concepts in an appropriate context.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10415",
  "author_total": 2,
  "authors": [
    {
      "name": "Noa Bihlmaier"
    },
    {
      "name": "Nick Ruoff"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/79t4efkpe1vqk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10415",
  "fulltext_url": null,
  "id": "79t4efkpe1vqk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10415",
  "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.CO"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.DS"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.10415",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/79t4efkpe1vqk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:16Z",
      "native_id": "2609.10415",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10415"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.DS",
      "subfield": "dynamical-systems"
    }
  ],
  "title": "A Categorical Approach to Nilspace Theory",
  "title_text": "A Categorical Approach to Nilspace Theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:16Z",
  "url": "https://research.draconitic.com/paper/79t4efkpe1vqk",
  "venue": "arXiv",
  "versions": []
}