{
  "id": "1101.3872",
  "version": "v1",
  "published": "2011-01-20T11:40:51.000Z",
  "updated": "2011-01-20T11:40:51.000Z",
  "title": "Monomorphism categories, cotilting theory, and Gorenstein-projective modules",
  "authors": [
    "Pu Zhang"
  ],
  "comment": "20 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "The monomorphism category $\\mathcal S_n(\\mathcal X)$ is introduced, where $\\mathcal X$ is a full subcategory of the module category $A$-mod of Artin algebra $A$. The key result is a reciprocity of the monomorphism operator $\\mathcal S_n$ and the left perpendicular operator $^\\perp$: for a cotilting $A$-module $T$, there is a canonical construction of a cotilting $T_n(A)$-module ${\\rm \\bf m}(T)$, such that $\\mathcal S_n(^\\perp T) = \\ ^\\perp {\\rm \\bf m}(T)$. As applications, $\\mathcal S_n(\\mathcal X)$ is a resolving contravariantly finite subcategory in $T_n(A)$-mod with $\\hat{\\mathcal S_n(\\mathcal X)} = T_n(A)$-mod if and only if $\\mathcal X$ is a resolving contravariantly finite subcategory in $A$-mod with $\\hat{\\mathcal X} = A$-mod. For a Gorenstein algebra $A$, the category $T_n(A)\\mbox{-}\\mathcal Gproj$ of Gorenstein-projective $T_n(A)$-modules can be explicitly determined as $\\mathcal S_n(^\\perp A)$. Also, self-injective algebras $A$ can be characterized by the property $T_n(A)\\mbox{-}\\mathcal Gproj = \\mathcal S_n(A)$. Using $\\mathcal S_n(A)= \\ ^\\perp {\\rm \\bf m}(D(A_A))$, a characterization of $\\mathcal S_n(A)$ of finite type is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-01-20T11:40:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G10",
      "16E65",
      "16G50"
    ],
    "keywords": [
      "monomorphism category",
      "gorenstein-projective modules",
      "cotilting theory",
      "resolving contravariantly finite subcategory",
      "left perpendicular operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}