{
  "id": "2109.01354",
  "version": "v1",
  "published": "2021-09-03T07:43:02.000Z",
  "updated": "2021-09-03T07:43:02.000Z",
  "title": "Balanced pairs and recollements in extriangulated categories with negative first extensions",
  "authors": [
    "Jian He",
    "Panyue Zhou"
  ],
  "comment": "18 pages. arXiv admin note: text overlap with arXiv:2109.00932. text overlap with arXiv:2104.04924",
  "categories": [
    "math.RT",
    "math.CT"
  ],
  "abstract": "A notion of balanced pairs in an extriangulated category with a negative first extension is defined in this article. We prove that there exists a bijective correspondence between balanced pairs and proper classes $\\xi$ with enough $\\xi$-projectives and enough $\\xi$-injectives. It can be regarded as a simultaneous generalization of Fu-Hu-Zhang-Zhu and Wang-Li-Huang. Besides, we show that if $(\\mathcal A ,\\mathcal B,\\mathcal C)$ is a recollement of extriangulated categories, then balanced pairs in $\\mathcal B$ can induce balanced pairs in $\\mathcal A$ and $\\mathcal C$ under natural assumptions. As a application, this result gengralizes a result by Fu-Hu-Yao in abelian categories. Moreover, it highlights a new phenomena when it applied to triangulated categories.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-09-03T07:43:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "negative first extension",
      "extriangulated category",
      "recollement",
      "proper classes",
      "induce balanced pairs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}