{
  "abstract": "In this work, we develop a fibrational approach to freely adjoining adjoints in an $(\\infty,2)$-category. We construct the universal bifibration obtained from a cocartesian fibration of $(\\infty,2)$-categories by adjoining cartesian lifts over a chosen class of $1$-morphisms in the base. We then use this construction to provide an explicit model for freely adjoining adjoints, together with a zig-zag formula for the resulting mapping $(\\infty,1)$-categories. As applications, we give a model-independent proof of the universal property of the walking adjunction, providing an alternative proof of a theorem of Riehl--Verity, and establish the universal characterization of the simplex $2$-category conjectured by Dyckerhoff--Kapranov--Schechtman--Soibelman.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17282",
  "author_total": 1,
  "authors": [
    {
      "name": "Fernando Abellán"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8hep6kxhkedzn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17282",
  "fulltext_url": null,
  "id": "8hep6kxhkedzn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17282",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.CT"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
    ]
  ],
  "openalex": "W7213438791",
  "pdf_url": "https://arxiv.org/pdf/2609.17282",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8hep6kxhkedzn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:45Z",
      "native_id": "2609.17282",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17282"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Free bifibrations of $(\\infty,2)$-categories, 2-simplicial objects and the walking adjunction",
  "title_text": "Free bifibrations of (∞,2)-categories, 2-simplicial objects and the walking adjunction",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:45Z",
  "url": "https://research.draconitic.com/paper/8hep6kxhkedzn",
  "venue": "arXiv",
  "versions": []
}