{
  "id": "2211.13197",
  "version": "v1",
  "published": "2022-11-23T18:38:12.000Z",
  "updated": "2022-11-23T18:38:12.000Z",
  "title": "Limits and colimits in the category of Banach $L^0$-modules",
  "authors": [
    "Enrico Pasqualetto"
  ],
  "comment": "24 pages",
  "categories": [
    "math.FA",
    "math.CT"
  ],
  "abstract": "We prove that the category of Banach $L^0$-modules over a given $\\sigma$-finite measure space is both complete and cocomplete, which means that it admits all small limits and colimits.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-23T18:38:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "53C23",
      "18F15",
      "16D90",
      "13C05"
    ],
    "keywords": [
      "finite measure space",
      "small limits",
      "cocomplete"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}