{
  "id": "1407.5964",
  "version": "v2",
  "published": "2014-07-22T18:08:54.000Z",
  "updated": "2015-06-12T09:27:01.000Z",
  "title": "Homogeneous strict polynomial functors as unstable modules",
  "authors": [
    "Nguyen The Cuong"
  ],
  "comment": "In this version, the result is generalized to all prime number. The paper is shortened and restructured. More examples are given",
  "categories": [
    "math.AT"
  ],
  "abstract": "A relation between Schur algebras and Steenrod algebra is shown in [Hai10] where to each strict polynomial functor the author associates an unstable module. We show that the restriction of Hai's functor to the subcategory of strict polynomial functors of a given degree is fully faithfull.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-07-22T18:08:54.000Z",
      "title": "On Hai's functor $\\bar{m}_{d}:\\mathcal{P}_{d}\\to\\mathcal{U}$",
      "abstract": "The forgetful functor $\\mathcal{O}:\\mathcal{P}_{d}\\to\\mathcal{F}$ has a factorization through the category $\\mathcal{U}$ of unstable modules via Hai's functor $\\bar{m}_{d}:\\mathcal{P}_d\\to \\mathcal{U}$ [Hai10]. The exactness and the commutativity with tensor products are the first two items of the list of properties of the functor $\\bar{m}_{d}$. In this article, we make this list longer by proving that Hai's functor $\\bar{m}_{d}$ is fully faithful. The category $\\mathcal{P}_{d}$ therefore can be considered as a full subcategory of $\\mathcal{U}$.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-06-12T09:27:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hais functor",
      "full subcategory",
      "list longer",
      "tensor products",
      "unstable modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1407.5964C"
    }
  }
}