{
  "id": "1702.06333",
  "version": "v1",
  "published": "2017-02-21T11:25:32.000Z",
  "updated": "2017-02-21T11:25:32.000Z",
  "title": "Cohomology and extensions of ordered groupoids",
  "authors": [
    "B. O. Bainson",
    "N. D. Gilbert"
  ],
  "comment": "18 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "We adapt and generalise results of Loganathan on the cohomology of inverse semigroups to the cohomology of ordered groupoids. We then derive a five-term exact sequence in cohomology from an extension of ordered groupoids, and show that this sequence leads to a classification of extensions by a second cohomology group. Our methods use structural ideas in cohomology as far as possible, rather than computation with cocycles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-21T11:25:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20L05"
    ],
    "keywords": [
      "ordered groupoids",
      "second cohomology group",
      "five-term exact sequence",
      "structural ideas",
      "inverse semigroups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}