{
  "id": "2407.17369",
  "version": "v1",
  "published": "2024-07-24T15:49:19.000Z",
  "updated": "2024-07-24T15:49:19.000Z",
  "title": "Metric completions of discrete cluster categories",
  "authors": [
    "Charley Cummings",
    "Sira Gratz"
  ],
  "comment": "30 pages, 7 figures",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "Neeman shows that the completion of a triangulated category with respect to a good metric yields a triangulated category. We compute completions of discrete cluster categories with respect to metrics induced by internal t-structures. In particular, for a coaisle metric this yields a new triangulated category which can be interpreted as a topological completion of the associated combinatorial model. Moreover, we show that the completion of any triangulated category with respect to an internal aisle metric is a thick subcategory of the triangulated category itself.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-24T15:49:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18G80"
    ],
    "keywords": [
      "discrete cluster categories",
      "triangulated category",
      "metric completions",
      "internal aisle metric",
      "internal t-structures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}