{
  "id": "2303.14925",
  "version": "v1",
  "published": "2023-03-27T05:48:34.000Z",
  "updated": "2023-03-27T05:48:34.000Z",
  "title": "Stratifications of abelian categories",
  "authors": [
    "Giulian Wiggins"
  ],
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "This paper studies abelian categories that can be decomposed into smaller abelian categories via iterated recollements - such a decomposition we call a stratification. Examples include the categories of (equivariant) perverse sheaves and epsilon-stratified categories (in particular highest weight categories) in the sense of Brundan-Stroppel (2018). We give necessary and sufficient conditions for an abelian category with a stratification to be equivalent to a category of finite dimensional modules of a finite dimensional algebra - this generalizes the main result of Cipriani-Woolf (2022). Furthermore, we give necessary and sufficient conditions for such a category to be epsilon-stratified - this generalizes the characterisation of highest weight categories given by Krause (2017).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-27T05:48:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16D90",
      "16P10"
    ],
    "keywords": [
      "abelian category",
      "highest weight categories",
      "stratification",
      "sufficient conditions",
      "paper studies abelian categories"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}