{
  "id": "2307.03044",
  "version": "v1",
  "published": "2023-07-06T15:09:44.000Z",
  "updated": "2023-07-06T15:09:44.000Z",
  "title": "Asymptotics in finite monoidal categories",
  "authors": [
    "Abel Lacabanne",
    "Daniel Tubbenhauer",
    "Pedro Vaz"
  ],
  "comment": "9 pages, many figures, comments welcome",
  "categories": [
    "math.RT",
    "math.CT",
    "math.RA"
  ],
  "abstract": "We give explicit formulas for the asymptotic growth rate of the number of summands in tensor powers in certain monoidal categories with finitely many indecomposable objects, and related structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-07-06T15:09:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N45",
      "18M05",
      "16T05",
      "18M20",
      "26A12"
    ],
    "keywords": [
      "finite monoidal categories",
      "asymptotic growth rate",
      "explicit formulas",
      "tensor powers",
      "indecomposable objects"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}