{
  "abstract": "We study bounded derived categories of semisimple tensor categories and their semisimple module categories. These categories may have infinitely many simple isomorphism classes. We classify bounded monoidal $t$-structures by integer-valued characters of the universal grading group and an integer deviation. We also classify compatible module $t$-structures using stabilizer subgroups of the module components. The corresponding hearts are tensor and module equivalent to the original categories. It follows that a monoidal derived equivalence and a coherent derived module equivalence recover both the tensor category and its module category.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06753",
  "author_total": 1,
  "authors": [
    {
      "name": "Sheng Tan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8pbymegzxzq4w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06753",
  "fulltext_url": null,
  "id": "8pbymegzxzq4w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.06753",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7212077732",
  "pdf_url": "https://arxiv.org/pdf/2609.06753",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8pbymegzxzq4w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.06753",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06753"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Derived Reconstruction of Semisimple Tensor and Module Categories",
  "title_text": "Derived Reconstruction of Semisimple Tensor and Module Categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/8pbymegzxzq4w",
  "venue": "arXiv",
  "versions": []
}