{
  "abstract": "We extend a six-functor formalism $D\\colon\\mathrm{Span}(C,E)\\to\\mathrm{Cat}$ to a lax symmetric monoidal functor of $(\\infty,2)$-categories $\\mathbf{Span}^2(C,E)^P_I\\to\\mathbf{Cat}$, where $P$ and $I$ are the classes of $D$-proper and $D$-étale morphisms, respectively. This proves a conjecture of Mann and generalizes a special case of a theorem of Cnossen, Lenz, and Linskens. To prove this result, we develop a theory of internal $\\mathsf{E}$-monoidal categories and $\\mathsf{E}$-operads, where $\\mathsf{E}$ is a local class of morphisms in an $\\infty$-topos. These notions generalize the internal symmetric monoidal categories and operads developed by Martini and Wolf.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.37520",
  "author_total": 3,
  "authors": [
    {
      "name": "Shachar Carmeli"
    },
    {
      "name": "Guy Kapon"
    },
    {
      "name": "Noam Nissan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bycqjy8rs1sp9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.37520",
  "fulltext_url": null,
  "id": "bycqjy8rs1sp9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.37520",
  "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.AG"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7214895378",
  "pdf_url": "https://arxiv.org/pdf/2609.37520",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bycqjy8rs1sp9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:35Z",
      "native_id": "2609.37520",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.37520"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Six functor formalisms via internal higher algebra",
  "title_text": "Six functor formalisms via internal higher algebra",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/bycqjy8rs1sp9",
  "venue": "arXiv",
  "versions": []
}