{
  "abstract": "For every integer $s$ and every $n \\geq 1$, we construct a symmetric monoidal $(\\infty,n)$-category $\\mathrm{Leg}_n^s$ whose objects are $s$-shifted contact derived Artin stacks and whose $i$-morphisms are $i$-fold Legendrian correspondences. The construction is based on the fact that an $s$-shifted contact structure on a derived Artin stack $X$ is an $s$-shifted symplectic structure on $X$ relative to $B\\mathbb{G}_m$, twisted by the weight-one line bundle, and that Legendrian structures are the corresponding relative Lagrangian structures. This lets us obtain the $(\\infty,n)$-categories $\\mathrm{Leg}_n^s$ as twisted forms over $B\\mathbb{G}_m$ of the $(\\infty,n)$-categories of iterated Lagrangian correspondences of Calaque, Haugseng and Scheimbauer, with the fiber product over $B\\mathbb{G}_m$ as tensor product. For an $s$-shifted contact stack $X$, we then obtain the derived Legendrian category $\\mathcal{F}_{c}(X)$. Its objects are Legendrian morphisms into $X$, and its mapping categories are categories of Legendrians in derived Legendrian intersections, which carry $(s-1)$-shifted contact structures. The AKSZ construction gives oriented extended topological field theories with values in $\\mathrm{Leg}_n^s$, as well as shifted contact structures on the quotient mapping stacks $[\\mathrm{Map}(Y,\\widetilde X)/\\mathbb{G}_m]$. Our definitions of contact and Legendrian structures agree with those of Berktav where both are defined, for every shift.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.13792",
  "author_total": 2,
  "authors": [
    {
      "name": "Efe İzbudak"
    },
    {
      "name": "Kadri İlker Berktav"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4tnnmy0re4qj6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.13792",
  "fulltext_url": null,
  "id": "4tnnmy0re4qj6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.13792",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "arxiv",
      "math.SG"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7162446768",
  "pdf_url": "https://arxiv.org/pdf/2605.13792",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4tnnmy0re4qj6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:26Z",
      "native_id": "2605.13792",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.13792"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.SG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A Derived Legendrian Category for Shifted Contact Stacks",
  "title_text": "A Derived Legendrian Category for Shifted Contact Stacks",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:26Z",
  "url": "https://research.draconitic.com/paper/4tnnmy0re4qj6",
  "venue": "arXiv",
  "versions": []
}