{
  "id": "2001.01254",
  "version": "v1",
  "published": "2020-01-05T15:16:24.000Z",
  "updated": "2020-01-05T15:16:24.000Z",
  "title": "Representation of n-abelian categories in abelian categories",
  "authors": [
    "Ramin Ebrahimi",
    "Alireza Nasr-Isfahani"
  ],
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "Let $\\mathcal{M}$ be a small $n$-abelian category. We show that the category of absolutely pure group valued functors over $\\mathcal{M}$, denote by $\\mathcal{L}_2(\\mathcal{M},\\mathcal{G})$, is an abelian category and $\\mathcal{M}$ is equivalent to a full subcategory of $\\mathcal{L}_2(\\mathcal{M},\\mathcal{G})$ in such a way that $n$-kernels and $n$-cokernels are precisely exact sequences of $\\mathcal{L}_2(\\mathcal{M},\\mathcal{G})$ with terms in $\\mathcal{M}$. This gives a higher-dimensional version of the Freyd-Mitchell embedding theorem for $n$-abelian categories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-05T15:16:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E10",
      "18E20",
      "18E99"
    ],
    "keywords": [
      "abelian category",
      "n-abelian categories",
      "representation",
      "absolutely pure group valued functors",
      "freyd-mitchell embedding theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}