{
  "abstract": "Let $\\mathcal{B}$ be a braided finite tensor category and let $A$ be a simple commutative algebra in $\\mathcal{B}$. We construct an order-reversing Galois connection between subalgebras of $A$ and tensor subcategories of $\\mathcal{B}_A$. Let $\\mathcal{B}'$ denote the Müger center and set $A':=A\\cap\\mathcal{B}'$. The closure operators are $B\\mapsto\\langle B,A'\\rangle_{\\mathrm{alg}}$ and $\\mathcal{E}\\mapsto\\langle\\mathcal{E},\\mathcal{B}_A^{\\mathrm{loc}}\\rangle_{\\otimes}$. Thus the closed subalgebras are those containing $A'$, while the closed tensor subcategories are those containing $\\mathcal{B}_A^{\\mathrm{loc}}$; equivalently, the fixed-point intervals $[A',A]_{\\mathrm{alg}}$ and $[\\mathcal{B}_A^{\\mathrm{loc}},\\mathcal{B}_A]_{\\otimes}$ are anti-isomorphic as lattices. For a finite tensor category $\\mathcal{C}$, the canonical algebra in $\\mathcal{Z}(\\mathcal{C})$ yields an anti-isomorphism between its subalgebras and tensor subcategories of $\\mathcal{C}$. When $\\mathcal{B}$ is nondegenerate, Frobenius extensions correspond to unimodular tensor subcategories. For a Hopf algebra in $\\mathcal{B}$, the correspondence specializes to an order-preserving bijection between Hopf ideals and normal left coideal subalgebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04073",
  "author_total": 2,
  "authors": [
    {
      "name": "Kenichi Shimizu"
    },
    {
      "name": "Harshit Yadav"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/af0va4ajfsb0s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04073",
  "fulltext_url": null,
  "id": "af0va4ajfsb0s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04073",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7208714104",
  "pdf_url": "https://arxiv.org/pdf/2609.04073",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/af0va4ajfsb0s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04073",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04073"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Galois connection between subalgebras and tensor subcategories",
  "title_text": "A Galois connection between subalgebras and tensor subcategories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/af0va4ajfsb0s",
  "venue": "arXiv",
  "versions": []
}