{
  "id": "1905.07927",
  "version": "v1",
  "published": "2019-05-20T07:47:31.000Z",
  "updated": "2019-05-20T07:47:31.000Z",
  "title": "Cotorsion pairs and adjoint functors in the homotopy category of $N$-complexes",
  "authors": [
    "Payam Bahiraei"
  ],
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "In this paper, we first construct some complete cotorson pairs on the category $\\mathbb{C}_N(\\mathcal{G})$ of unbounded $N$-complexes of Grothendieck category $\\mathcal{G}$, from two given cotorsion pairs in $\\mathcal{G}$. Next as an application, we focus on particular homotopy categories and the existence of adjoint functors between them. These are an $N$-complex version of the results were shown by Neeman in the category of ordinary complexes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-20T07:47:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "18E15",
      "55U35",
      "18G55"
    ],
    "keywords": [
      "adjoint functors",
      "homotopy category",
      "cotorsion pairs",
      "complete cotorson pairs",
      "first construct"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}