{
  "abstract": "We construct an endofunctor on (small) simplicial sets which freely adjoins a zero object to a (small) infinity-category, as the co-cone construction freely adjoins a terminal object. We then prove that this endofunctor induces a left adjoint to the inclusion of the infinity-category of (small) pointed infinity-categories and morphisms that preserve zero objects into the infinity-category of (small) infinity-categories. This adjunction, in turn, leads to the definition of a coherent choice of nullhomotopies on a pointed infinity-category. A coherent choice of nullhomotopies is a non-canonical, coherent choice of \"higher zeroes\" on a pointed infinity-category, mirroring the obvious definition of higher zeroes on the differential graded nerve of a differential graded category of chain complexes over an additive category. We then show that coherent choices of nullhomotopies give an alternate characterization of fiber sequences in pointed infinity-categories, generalizing the 1-categorical definition of kernels in terms of morphisms that compose to zero.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.04167",
  "author_total": 1,
  "authors": [
    {
      "name": "Thomas Rush Brown"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/84spm9jevv373.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.04167",
  "fulltext_url": null,
  "id": "84spm9jevv373",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.04167",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.04167",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/84spm9jevv373.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:29Z",
      "native_id": "2611.04167",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.04167"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Higher zeroes in pointed infinity-categories",
  "title_text": "Higher zeroes in pointed infinity-categories",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/84spm9jevv373",
  "venue": "arXiv",
  "versions": []
}