{
  "id": "1404.2528",
  "version": "v4",
  "published": "2014-04-09T15:59:22.000Z",
  "updated": "2014-11-24T09:57:29.000Z",
  "title": "Classification theory for accessible categories",
  "authors": [
    "Michael Lieberman",
    "Jirí Rosický"
  ],
  "comment": "17 pages",
  "categories": [
    "math.LO",
    "math.CT"
  ],
  "abstract": "We show that a number of results on abstract elementary classes (AECs) hold in accessible categories with concrete directed colimits. In particular, we prove a generalization of a recent result of Boney on tameness under a large cardinal assumption. We also show that such categories support a robust version of the Ehrenfeucht-Mostowski construction. This analysis has the added benefit of producing a purely language-free characterization of AECs, and highlights the precise role played by the coherence axiom.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-07-27T20:10:30.000Z",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2014-11-24T09:57:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03C45",
      "03C95",
      "03G30"
    ],
    "keywords": [
      "accessible categories",
      "classification theory",
      "abstract elementary classes",
      "large cardinal assumption",
      "concrete directed colimits"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.2528L"
    }
  }
}