{
  "abstract": "Group representations very comfortably admit a higher categorical generalization. This includes induction and restriction for 2-representations that very directly parallel classical definitions. An appropriate character theory for 2-representations has been more opaque. In this paper we draw from a range of motivations to provide an intuitive character theory for 2-representations. It is built from the bicategorical trace developed to describe topological fixed point theory. We use the secondary traces of Ben-Zvi and Nadler which connect to Riemann-Roch and Lefschetz-type theorems in the context of differential graded categories and Fourier-Mukai transforms. Additional sources of motivation include Lipmans' work on Grothendieck duality and, crucially, the Bartlett and Ganter--Kapranov approaches to characters. (The second of these was in turn motivated by Hopkins, Kuhn and Ravenel's work on equivariant Morava $E$-theories.) Our characters are compatible with restriction and induction and, in cases that are sufficiently finite, admit a secondary character.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21052",
  "author_total": 2,
  "authors": [
    {
      "name": "Kate Ponto"
    },
    {
      "name": "Travis Wheeler"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/42x7swwyx3gw7.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21052",
  "fulltext_url": null,
  "id": "42x7swwyx3gw7",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21052",
  "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.AT"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "openalex",
      "2608|Algebraic structures and combinatorial models"
    ]
  ],
  "openalex": "W7213870686",
  "pdf_url": "https://arxiv.org/pdf/2609.21052",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/42x7swwyx3gw7.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21052",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21052"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Character theory for 2-representations",
  "title_text": "Character theory for 2-representations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/42x7swwyx3gw7",
  "venue": "arXiv",
  "versions": []
}