{
  "abstract": "In this paper, we investigate monoidal derived equivalences between tensor categories with infinitely many isomorphism classes of simple objects. We introduce the notion of a simple-shifted monoidal derived equivalence and prove that a simple-shifted monoidal derived equivalence gives rise to a tensor equivalence. In addition, we investigate which tensor categories have the property that every monoidal derived equivalence between them is necessarily simple-shifted, and we establish some sufficient conditions for this property. As a corollary, we prove that if a tensor category is monoidally derived equivalent to the finite-dimensional representation category of either the quantized enveloping algebra $U_q(\\mathfrak{g})$, the quantized Borel subalgebra $U_q^{\\geq 0}(\\mathfrak{g})$, or the quantized coordinate ring $\\mathcal{O}_{q}(G)$ (for a suitable $q$), it is tensor equivalent to the corresponding category.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.26196",
  "author_total": 1,
  "authors": [
    {
      "name": "Jing Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8h4wx988bd8f6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.26196",
  "fulltext_url": null,
  "id": "8h4wx988bd8f6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.26196",
  "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"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7223017668",
  "pdf_url": "https://arxiv.org/pdf/2610.26196",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8h4wx988bd8f6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:38Z",
      "native_id": "2610.26196",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.26196"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Simple-shifted monoidal derived equivalences for tensor categories",
  "title_text": "Simple-shifted monoidal derived equivalences for tensor categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:38Z",
  "url": "https://research.draconitic.com/paper/8h4wx988bd8f6",
  "venue": "arXiv",
  "versions": []
}