{
  "id": "2108.12824",
  "version": "v1",
  "published": "2021-08-29T11:19:32.000Z",
  "updated": "2021-08-29T11:19:32.000Z",
  "title": "A General Theory of Pointlike Sets",
  "authors": [
    "Karsten Henckell",
    "Samuel Herman"
  ],
  "comment": "54 pages",
  "categories": [
    "math.GR",
    "math.LO",
    "math.RA"
  ],
  "abstract": "We introduce a general unifying framework for the investigation of pointlike sets. The pointlike functors are considered as distinguished elements of a certain lattice of subfunctors of the power semigroup functor; in particular, we exhibit the pointlike functors as the fixed points of a closure operator induced by an antitone Galois connection between this lattice of functors and the lattice of pseudovarieties. Notably, this provides a characterization of pointlikes which does not mention relational morphisms. Along the way, we formalize various common heuristics and themes in the study of pointlike sets. As an application, we provide a general method for transferring lower bounds for pointlikes along a large class of continuous operators on the lattice of pseudovarieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-29T11:19:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20M07",
      "20M50"
    ],
    "keywords": [
      "pointlike sets",
      "general theory",
      "pointlike functors",
      "antitone galois connection",
      "mention relational morphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 54,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}