{
  "id": "2206.01672",
  "version": "v1",
  "published": "2022-06-03T16:33:00.000Z",
  "updated": "2022-06-03T16:33:00.000Z",
  "title": "Correspondence between factorability and normalisation in monoids",
  "authors": [
    "Alen Đurić"
  ],
  "comment": "24 pages",
  "categories": [
    "math.GR"
  ],
  "abstract": "The purpose of this note is to investigate the relation between two notions concerning monoids: factorability structure, introduced to simplify the bar complex; and quadratic normalisation, introduced to generalise quadratic rewriting systems and normalisations arising from Garside families. We characterise factorable monoids in the axiomatic setting of quadratic normalisation as monoids admitting quadratic normalisation satisfying a condition stronger than the class (5,4) yet weaker than the class (4,4). We also prove an equivalence between the two assumptions known to ensure the convergence of the rewriting system associated to factorability.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-03T16:33:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M05",
      "68Q42"
    ],
    "keywords": [
      "correspondence",
      "generalise quadratic rewriting systems",
      "bar complex",
      "notions concerning monoids",
      "monoids admitting quadratic normalisation satisfying"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}