{
  "abstract": "We propose a definition of a finite linear 2-category, as a 2-categorical analogue of the notion of a finite abelian category of Etingof-Ostrik. We go on to prove that finite linear 2-categories with adjunctible projectives are precisely the Morita 2-categories of (all) algebras in a finite multitensor category. Thus, finite linear 2-categories with adjunctible projectives can be viewed as `non-semisimple' generalizations of the finite semisimple 2-categories of Douglas-Reutter. Secondly, we study finite multitensor 2-categories, that is, finite linear 2-categories equipped with a monoidal structure for which every objects has duals. We extend several results about fusion 2-categories to our present setting. In particular, we investigate the properties of the 2-category of bimodules over a rigid algebra $\\mathcal{A}$ in a finite tensor 2-category $\\mathfrak{C}$. We show that, if $\\mathfrak{C}$ has adjunctible projectives, then the 2-category of $\\mathcal{A}$-$\\mathcal{A}$-bimodules in $\\mathfrak{C}$ is a finite multitensor 2-category. This construction provides many examples of finite tensor 2-categories. For instance, the Drinfeld center of a finite tensor 2-category with adjunctible projectives is a finite tensor 2-category.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37016",
  "author_total": 3,
  "authors": [
    {
      "name": "Thibault D. Décoppet"
    },
    {
      "name": "Mateusz Stroiński"
    },
    {
      "name": "Tony Zorman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9m86dxz05981t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37016",
  "fulltext_url": null,
  "id": "9m86dxz05981t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37016",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CT"
    ],
    [
      "arxiv",
      "math.QA"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7224136383",
  "pdf_url": "https://arxiv.org/pdf/2610.37016",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9m86dxz05981t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37016",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37016"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Finite Tensor 2-Categories",
  "title_text": "Finite Tensor 2-Categories",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/9m86dxz05981t",
  "venue": "arXiv",
  "versions": []
}