{
  "id": "1902.07162",
  "version": "v1",
  "published": "2019-02-19T17:44:45.000Z",
  "updated": "2019-02-19T17:44:45.000Z",
  "title": "The dual of compact partially ordered spaces is a variety",
  "authors": [
    "Marco Abbadini"
  ],
  "categories": [
    "math.LO"
  ],
  "abstract": "In a recent paper (2018), D. Hofmann, R. Neves and P. Nora proved that the dual of the category of compact partially ordered spaces and monotone continuous maps is a quasi-variety - not finitary, but bounded by $\\aleph_1$. An open question was: is it also a variety? We show that the answer is affirmative. We describe the variety by means of a finite set of finitary operations, together with a single operation of countably infinite arity, and equational axioms. The dual equivalence is induced by the dualizing object [0,1].",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-19T17:44:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C05",
      "08A65",
      "18B30",
      "18C10",
      "54A05",
      "54F05"
    ],
    "keywords": [
      "compact partially ordered spaces",
      "single operation",
      "monotone continuous maps",
      "finite set",
      "finitary operations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}