{
  "abstract": "Assume that $n$ is a non-negative integer and $\\C$ an $n$-Frobenius category. This paper is concerned with the natural transformations between extension functors on $\\C$. The main result of the paper indicates that for any pair of objects $M, N\\in \\C$, the group of all natural transformations from $\\Ext^{n+1}_{\\C}(N, -)$ to $\\Ext^{n+1}_{\\C}(M, -)$ is isomorphic to the quotient group $\\Ext^n_{\\C}(M, \\syz^nN)/{\\p}$, where $\\p$ is the subgroup consisting of those Yoneda extensions of length $n$ arising as a push-out along a morphism $P\\rt\\syz^nN$, with $P$ $n$-projective. This result is fruitful from the point of view that, $n$-Frobenius categories may not have projective objects.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.23495",
  "author_total": 2,
  "authors": [
    {
      "name": "Abdolnaser Bahlekeh"
    },
    {
      "name": "Shokrollah Salarian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7fr7mv386hz09.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.23495",
  "fulltext_url": null,
  "id": "7fr7mv386hz09",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.23495",
  "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.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7171550617",
  "pdf_url": "https://arxiv.org/pdf/2607.23495",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7fr7mv386hz09.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2607.23495",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.23495"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the natural transformations of extension functors",
  "title_text": "On the natural transformations of extension functors",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/7fr7mv386hz09",
  "venue": "arXiv",
  "versions": []
}