{
  "id": "2407.17147",
  "version": "v1",
  "published": "2024-07-24T10:39:48.000Z",
  "updated": "2024-07-24T10:39:48.000Z",
  "title": "An introduction to monomorphism categories",
  "authors": [
    "Sondre Kvamme"
  ],
  "comment": "36 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "This manuscript was written for the Proceedings of the ICRA 2022 in Buenos Aires. It can be divided into four parts: The first part is an introduction to the theory of monomorphism categories, including a short survey on some representation theoretic results. The second part is a summary of some recent results on monomorphism categories based on joint work with Nan Gao, Julian K\\\"ulshammer and Chrysostomos Psaroudakis. It also includes a new result, namely a classification of all monomorphism categories of finite type over cyclic abelian groups. The third part concerns the relationship between submodule categories and $p$-valuated abelian groups. The last part contains a proof of wildness of a certain monomorphism category, rectifying a statement in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-24T10:39:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G70",
      "16G20",
      "20K27",
      "16E65"
    ],
    "keywords": [
      "monomorphism category",
      "introduction",
      "cyclic abelian groups",
      "representation theoretic results",
      "third part concerns"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 36,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}