{
  "abstract": "The aim of this article is to leverage Enomoto's classification of exact structures to the dg level. Let $\\mathscr{A}$ be a connective additive idempotent complete dg category. We establish an intrinsic Enomoto-type classification of exact dg structures on $\\mathscr{A}$ in terms of bi-Serre subcategories in $\\mathsf{tr}(\\mathscr{A})$. Our proof is a direct dg argument based on dg totalizations of $3$-term complexes and dg duality, rather than a reduction to the greatest exact dg structure and the classification of its substructures. As a consequence, we establish a bijection between exact dg structures on $\\mathscr{A}$ and bi-Serre subcategories in $\\mathsf{tr}(\\mathscr{A})$. Moreover, this bijection is an isomorphism of posets and yields a complete lattice structure on the class of exact dg structures on $\\mathscr{A}$. In particular, we provide another construction of Rump--Chen's greatest exact dg structure on $\\mathscr{A}$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25583",
  "author_total": 1,
  "authors": [
    {
      "name": "Yasuaki Ogawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/c69008hf4h0ef.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25583",
  "fulltext_url": null,
  "id": "c69008hf4h0ef",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25583",
  "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.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7214087348",
  "pdf_url": "https://arxiv.org/pdf/2609.25583",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/c69008hf4h0ef.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25583",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25583"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Exact dg structures are classified intrinsically by bi-Serre subcategories",
  "title_text": "Exact dg structures are classified intrinsically by bi-Serre subcategories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/c69008hf4h0ef",
  "venue": "arXiv",
  "versions": []
}