{
  "id": "1609.00566",
  "version": "v1",
  "published": "2016-09-02T12:04:02.000Z",
  "updated": "2016-09-02T12:04:02.000Z",
  "title": "A comparison between pretriangulated $\\mbox{A}_{\\infty}$-categories and $\\infty$-Stable categories",
  "authors": [
    "Mattia Ornaghi"
  ],
  "comment": "22 pages. Preliminary version. Comments are welcome",
  "categories": [
    "math.AG",
    "math.CT"
  ],
  "abstract": "In this paper we will prove that the $\\mbox{A}_{\\infty}$-nerve of two quasi-equivalent $\\mbox{A}_{\\infty}$-categories are weak-equivalent in the Joyal model structure, a consequence of this fact is that the $\\mbox{A}_{\\infty}$-nerve of a pretriangulated $\\mbox{A}_{\\infty}$-category is $\\infty$-stable. Moreover we give a comparison between the notions of pretriangulated $\\mbox{A}_{\\infty}$-categories, pretriangulated dg-categories and $\\infty$-stable categories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-09-02T12:04:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stable categories",
      "comparison",
      "joyal model structure",
      "quasi-equivalent"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}