{
  "id": "1902.05447",
  "version": "v1",
  "published": "2019-02-13T13:37:50.000Z",
  "updated": "2019-02-13T13:37:50.000Z",
  "title": "Correspondence functors and finiteness conditions",
  "authors": [
    "Serge Bouc",
    "Jacques Thévenaz"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1510.03034",
  "categories": [
    "math.RT",
    "math.CO",
    "math.CT",
    "math.GR"
  ],
  "abstract": "We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various specific properties which do not hold for other types of func-tors. In particular, if k is a field and if F is a correspondence functor, then F is finitely generated if and only if the dimension of F (X) grows exponentially in terms of the cardinality of the finite set X. Moreover, in such a case, F has actually finite length. Also, if k is noetherian, then any subfunctor of a finitely generated functor is finitely generated.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-13T13:37:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "correspondence functor",
      "finiteness conditions",
      "finite set",
      "representation theory",
      "finite length"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}