{
  "abstract": "Let $(\\V, \\otimes, I,[-,-])$ be a closed symmetric monoidal category with finite (co)limits. Assume that $\\V$ is weakly idempotent complete and additive. For a given small $\\V$-category $\\A$, we investigate sufficient conditions on $\\A$ under which the ordinary category $[\\A, \\V]_0$ of $\\V$-functors from $\\A$ to $\\V$, equipped with the exact structure $\\mathcal{E}_{\\textrm{lowt}}$, is a Frobenius exact category,and hence, induces a triangulated stable category. The exact structure $\\mathcal{E}_{\\textrm{lowt}}$ encompasses the degre-wise trivial exact structure on categories of $N$-chain complexes and $m$-periodic chain complexes, with terms in a variety of settings, including left $R$-modules, quasi-coherent sheaves on a scheme, and Banach spaces. We subsequently address the question of describing abstract left and right homotopy relations in $([\\A, \\V]_0;\\mathcal{E}_{\\textrm{lowt}})$ in terms of families of morphisms defined objectwise, as in the cases of chain-homotopy and relative homotopy relations. To this end, we introduce the notion of left/right-weak Serre $\\V$-functors on $\\A$, and investigate their relationships with the classical Serre functor relative to a commutative ring $k$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40746",
  "author_total": 1,
  "authors": [
    {
      "name": "Sinem Odabasi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fjr7h7c7j04m8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40746",
  "fulltext_url": null,
  "id": "fjr7h7c7j04m8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40746",
  "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"
    ],
    [
      "arxiv",
      "math.KT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40746",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fjr7h7c7j04m8.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.40746",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40746"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Homotopy in enriched functor categories: Frobenius exact structures and weak Serre functors",
  "title_text": "Homotopy in enriched functor categories: Frobenius exact structures and weak Serre functors",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/fjr7h7c7j04m8",
  "venue": "arXiv",
  "versions": []
}