{
  "abstract": "This paper studies orthogonal model structures, i.e., model structures such that a lifting in the Lifting axiom is unique. Cofibrant (fibrant) objects are defined without initial (terminal) objects. For an orthogonal model structure on a category with enough cofibrant objects and fibrant objects, it is proved that the homotopy category is equivalent to the full subcategory of cofibrant-fibrant objects. TTF model structures, bi-reflective model structures, and torsion model structures, are introduced. They are all orthogonal. One to one correspondences between TTF model structures and TTF triples in an abelian category, bi-reflective model structures and bi-reflective pairs in any category, and torsion model structures and twin torsion pairs in an abelian category, are established in a constructive way. Torsion model structures on a poset, on the category of $G$-sets, and on the category of topological groups, are also constructed. The homotopy categories of all these model structures are computed. In particular, the homotopy category of a TTF model structure is an abelian category.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39317",
  "author_total": 3,
  "authors": [
    {
      "name": "Yang Gao"
    },
    {
      "name": "Yu-xiao Yang"
    },
    {
      "name": "Pu Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5sxppzy5668w3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39317",
  "fulltext_url": null,
  "id": "5sxppzy5668w3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39317",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7215090049",
  "pdf_url": "https://arxiv.org/pdf/2609.39317",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5sxppzy5668w3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39317",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39317"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Orthogonal Model Structures",
  "title_text": "Orthogonal Model Structures",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/5sxppzy5668w3",
  "venue": "arXiv",
  "versions": []
}