{
  "abstract": "We study the truncation $(-)^{\\leq0}$ of dg categories. We first show that given a dg category $\\mathscr{C}$ with shifts, for example a pretriangulated dg category, the canonical functor $\\mathscr{C}^{\\leq0}\\to\\mathscr{C}$ is a localization whose kernel is compactly generated by the $0$-th cohomology. Next we demonstrate that the derived category of the truncation serves as a triangulated analogue of the Auslander's category of coherent functors over abelian categories. We give a description of the Auslander-Reiten-Serre duality in terms of the inverse dualizing bimodule of the truncation. Building on truncations, we introduce the notion of connective resolutions of dg categories, defined as a localization functor from a connective dg category. This notion encompasses non-commutative resolutions of algebras in module categories, cluster tilting objects in triangulated categories, and also the truncation as the universal connective resolution. We give a sufficient condition for an object in a triangulated category to give a connective resolution of its enhancement in terms of finiteness of resolution dimension. Furthermore, we show that every proper dg module over a connective dg algebra is a direct summand of a dg module giving a connective resolution. Consequently, for every proper connective dg algebra, its bounded dg derived category has a connective resolution. Finally, we give some explicit description of the truncation for some categories including the derived and cluster categories of a Dynkin quiver, and the Yoneda category of a finite dimensional algebra.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.08218",
  "author_total": 1,
  "authors": [
    {
      "name": "Norihiro Hanihara"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0dd5aty134s0e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.08218",
  "fulltext_url": null,
  "id": "0dd5aty134s0e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.08218",
  "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.AC"
    ],
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7221009059",
  "pdf_url": "https://arxiv.org/pdf/2610.08218",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0dd5aty134s0e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2610.08218",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.08218"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AC",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Truncation of dg categories and connective resolutions",
  "title_text": "Truncation of dg categories and connective resolutions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/0dd5aty134s0e",
  "venue": "arXiv",
  "versions": []
}