{
  "abstract": "In this paper, we formulate Land-Tamme's $\\boxtimes$-construction and $\\odot$-construction for continuous exact monads on dualizable stable $\\infty$-categories, and establish the behaviour of localizing invariants on pushouts of left modules over continuous exact monads on dualizable stable $\\infty$-categories. Combining the Land-Tamme theory of continuous exact monads with the theory of analytic functors in Goodwillie calculus, we show that the reduced K-theory on modules over free tensor algebras of dualizable t-categories is modified 1-coanalytic or modified 2-coanalytic, depending on the coconnectivity of the base algebras. In particular, this answers Efimov's question concerning coanalyticity in the affirmative.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41566",
  "author_total": 1,
  "authors": [
    {
      "name": "Li He"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5ttnmhd9zb5hy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41566",
  "fulltext_url": null,
  "id": "5ttnmhd9zb5hy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41566",
  "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.CT"
    ],
    [
      "arxiv",
      "math.KT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41566",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5ttnmhd9zb5hy.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41566",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41566"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The coanalyticity of the reduced K-theory on modules over free tensor algebras of dualizable t-categories",
  "title_text": "The coanalyticity of the reduced K-theory on modules over free tensor algebras of dualizable t-categories",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/5ttnmhd9zb5hy",
  "venue": "arXiv",
  "versions": []
}