{
  "abstract": "We show that, under some mild assumptions, every quasi-pointed category C carries a canonical near-torsion theory (T,F), where T consists of the 0-supported objects, that is, those admitting a morphism to the initial object 0, and F consists of the subterminal objects. The coreflection and the reflection of an object A are then given by the projection $A \\times 0 \\to A$ and by the strong-epimorphic part of $A \\to 1$, respectively. Using the general construction of the \"largest\" non-pointed torsion theory associated with a near-torsion theory, we prove that (T,F) is a (non-pointed) torsion theory in the full subcategory of those objects A for which the canonical sequence $t(A) \\to A \\to f(A)$ is short exact, in the sense that it is both a kernel and a cokernel diagram. This subcategory is the whole of C whenever C is sequentiable, that is, a regular protomodular and quasi-pointed category. We describe the resulting torsion theories in the category of Lie-Rinehart algebras and in the categories of crossed modules over a fixed group. We also show that (T,F) is a torsion theory in the (non-protomodular) category of monoids over a group G all of whose elements have finite order.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.05309",
  "author_total": 2,
  "authors": [
    {
      "name": "Marino Gran"
    },
    {
      "name": "George Janelidze"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f2mz24b5k3vq2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.05309",
  "fulltext_url": null,
  "id": "f2mz24b5k3vq2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.05309",
  "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.CT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7220691657",
  "pdf_url": "https://arxiv.org/pdf/2610.05309",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f2mz24b5k3vq2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.05309",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.05309"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Quasi-pointed exactness and torsion",
  "title_text": "Quasi-pointed exactness and torsion",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/f2mz24b5k3vq2",
  "venue": "arXiv",
  "versions": []
}