{
  "annotation_id": "b6800267-5279-40cd-99a9-8529d03114c8",
  "date_created": "2026-02-17T05:53:20.173000Z",
  "date_modified": "2026-02-17T05:53:20.173000Z",
  "file_hash": "31faa1849ad3df3da5d9fa1617eac322ab0d577f02fda6e0707f6dd384df6aa5",
  "private": false,
  "record": {
    "abstract": "One of the major advantages of $\\infty$-category theory over classical $1$-category theory is its robust and homotopically meaningful framework for taking (co)limits of diagrams of $\\infty$-categories. However, it is both subtle and crucial to specify which variant of the $\\infty$-category of $\\infty$-categories is being used when forming such (co)limits. In this article, we present a concrete case study illustrating how (co)limits of $\\infty$-categories behave in a specific setting. We demonstrate that the span category of a profinite group can be realised as the colimit of the span categories of its quotients by open normal subgroups and provide a number of applications to the world of equivariant (higher) algebra.",
    "arxiv_id": "2601.09544",
    "authors": [
      "David Barnes",
      "Niall Taggart"
    ],
    "categories": [
      "math.CT",
      "math.AT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Deconstructing span categories for profinite groups",
    "url": "https://arxiv.org/abs/2601.09544",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ea1d3ddc-31f5-4957-8264-389559031316",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}