{
  "abstract": "We develop a method for constructing abelian model structures on the category Q,AMod of Q-shaped modules from cotorsion pairs in AMod, where Q is a small preadditive category satisfying certain conditions and AMod denotes the category of left A-modules for any ring A. More precisely, we construct two cotorsion pairs in Q,AMod from a given cotorsion pair in AMod. This leads to a construction of projective model structures on Q,AMod under the condition that Q has no cycles. We further apply this method to the category Dif(A) of differential left A-modules, viewed as a category of Q-shaped modules for a suitable choice of Q. In this case, the induced cotorsion pairs are shown to be compatible, thereby giving rise to abelian model structures on Dif(A).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.29267",
  "author_total": 2,
  "authors": [
    {
      "name": "Yajun Ma"
    },
    {
      "name": "Peiru Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a51dvxjyhw05d.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.29267",
  "fulltext_url": null,
  "id": "a51dvxjyhw05d",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.29267",
  "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.RA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7204913541",
  "pdf_url": "https://arxiv.org/pdf/2608.29267",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a51dvxjyhw05d.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.29267",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.29267"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Model structures on the category of Q-shaped modules",
  "title_text": "Model structures on the category of Q-shaped modules",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/a51dvxjyhw05d",
  "venue": "arXiv",
  "versions": []
}