{
  "abstract": "We consider noncommutative analogues of associated fibre bundles where the total space, base space and even the fiber may be nonaffine, that is, not represented by a single algebra, and where the structure group is replaced by a Hopf algebra $H$. We choose to describe gluing of affine pieces by corings. In the role of a principal bundle we take an internal $E$-coring $M$ in the monoidal category of right $H$-comodules where $E$ is a faithfully flat right Hopf-Galois extension. In a role of a fibre we either take a left $H$-comodule algebra $F$, or more generally an internal $F$-coring $N$ in the monoidal category of left $H$-comodules. Cotensor products combining these data is used to obtain an ordinary coring representing the total space of an associated bundle. If the fiber coring $N$ is equipped with a choice of an $H$-coinvariant grouplike element, then we exhibit a canonical morphisms of corings from the $H$-coinvariant coring of $M$ to the associated bundle coring which is viewed as a dual to the projection of an associated bundle.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41774",
  "author_total": 1,
  "authors": [
    {
      "name": "Zoran Škoda"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/djyq7yekd5y5p.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41774",
  "fulltext_url": null,
  "id": "djyq7yekd5y5p",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41774",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.QA"
    ],
    [
      "arxiv",
      "math.RA"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41774",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/djyq7yekd5y5p.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41774",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41774"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Coring morphisms presenting nonaffine noncommutative fibre bundles",
  "title_text": "Coring morphisms presenting nonaffine noncommutative fibre bundles",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:53Z",
  "url": "https://research.draconitic.com/paper/djyq7yekd5y5p",
  "venue": "arXiv",
  "versions": []
}