{
  "abstract": "By equipping the category $\\mathcal{M}$ of modules over a finite dimensional algebra with the action of a finite tensor category $\\mathcal{C}$, we introduce a subcategory $\\mathcal{PM}$ satisfying numerous remarkable properties: it is generating and cogenerating, functorially finite, closed under Auslander--Reiten translations (i.e. precluster tilting), and it computes the finitistic dimension. Through a functor category perspective, $\\mathcal{PM}$ is identified with the $\\mathcal{C}$-module functors that are projective, and we also prove a $\\mathcal{C}$-equivariant version of the Auslander(--Solberg) correspondence. As examples, we show that $\\mathcal{PM}$ contains only finitely many indecomposable modules for some tensor product algebras. For some family of 1-Iwanaga--Gorenstein algebras introduced by Geiss--Leclerc--Schröer, we show that $\\mathcal{PM}$ is exactly the subcategory of $τ$-locally free modules.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.17646",
  "author_total": 2,
  "authors": [
    {
      "name": "Kevin Coulembier"
    },
    {
      "name": "Edmund Heng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2b2e5fj4g5zaa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.17646",
  "fulltext_url": null,
  "id": "2b2e5fj4g5zaa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.17646",
  "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.QA"
    ],
    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
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  "openalex": "W7221751040",
  "pdf_url": "https://arxiv.org/pdf/2610.17646",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2b2e5fj4g5zaa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:19Z",
      "native_id": "2610.17646",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.17646"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A subcategory with remarkable homological properties via actions of tensor categories",
  "title_text": "A subcategory with remarkable homological properties via actions of tensor categories",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:14Z",
  "url": "https://research.draconitic.com/paper/2b2e5fj4g5zaa",
  "venue": "arXiv",
  "versions": []
}