{
  "id": "2006.07715",
  "version": "v1",
  "published": "2020-06-13T20:36:04.000Z",
  "updated": "2020-06-13T20:36:04.000Z",
  "title": "Axiomatizing Subcategories of Abelian Categories",
  "authors": [
    "Sondre Kvamme"
  ],
  "comment": "27 pages",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "We investigate how to characterize subcategories of abelian categories in terms of intrinsic axioms. In particular, we find intrinsic axioms which characterize generating cogenerating functorially finite subcategories, precluster tilting subcategories, and cluster tilting subcategories of abelian categories. As a consequence of this we prove that any $d$-abelian category is equivalent to a $d$-cluster tilting subcategory of an abelian category, without any assumption on the categories being projectively generated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-13T20:36:04.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "abelian category",
      "axiomatizing subcategories",
      "cluster tilting subcategory",
      "intrinsic axioms",
      "generating cogenerating functorially finite subcategories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}