{
  "abstract": "We study exact sequences of representation categories of weak Hopf algebras over an arbitrary field. Given a sequence $A\\overset{k}{\\to} B\\oversetπ{\\to} H$, where $A$ and $B$ are weak Hopf algebras and $H$ is a Hopf algebra, we develop verifiable algebraic conditions on $k$ and $π$ under which there is an exact sequence $\\mathrm{Rep}(H)\\to\\mathrm{Rep}(B)\\to\\mathrm{Rep}(A)$ of tensor categories in the sense of Bruguières and Natale (2011). Along the way, we develop a generalization of the restriction of scalars functor for maps $π:B\\to H$ between associative algebras satisfying a weakened multiplicativity constraint depending on a relatively separable subalgebra $B_r\\subseteq B$, as well as a theory of kernels and cokernels for weak Hopf algebras. We, in particular, find that the cokernel of a weak Hopf algebra homomorphism $k:A\\to B$ always exists, is a Hopf algebra, and the cokernel map is surjective when $A$ is connected. We conclude by studying examples of such exact sequences built from groupoids, formal ribbon extensions of quasitriangular weak Hopf algebras, and cocycled crossed products of a Hopf algebra acting weakly on a weak Hopf algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.40298",
  "author_total": 1,
  "authors": [
    {
      "name": "Quinn T. Kolt"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/axpfw9je46tx3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.40298",
  "fulltext_url": null,
  "id": "axpfw9je46tx3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.40298",
  "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.QA"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
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  "openalex": "W7215097994",
  "pdf_url": "https://arxiv.org/pdf/2609.40298",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/axpfw9je46tx3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:35Z",
      "native_id": "2609.40298",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.40298"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.QA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Exact sequences of representation categories of weak Hopf algebras",
  "title_text": "Exact sequences of representation categories of weak Hopf algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:35Z",
  "url": "https://research.draconitic.com/paper/axpfw9je46tx3",
  "venue": "arXiv",
  "versions": []
}