{
  "id": "2010.04393",
  "version": "v1",
  "published": "2020-10-09T07:00:07.000Z",
  "updated": "2020-10-09T07:00:07.000Z",
  "title": "Semibricks in extriangulated categories",
  "authors": [
    "Li Wang",
    "Jiaqun Wei",
    "Haicheng Zhang"
  ],
  "comment": "19 pages",
  "categories": [
    "math.RT",
    "math.CT",
    "math.RA"
  ],
  "abstract": "Let $\\mathcal{X}$ be a semibrick in an extriangulated category $\\mathscr{C}$. Let $\\mathcal{T}$ be the filtration subcategory generated by $\\mathcal{X}$. We give a one-to-one correspondence between simple semibricks and length wide subcategories in $\\mathscr{C}$. This generalizes a bijection given by Ringel in module categories, which has been generalized by Enomoto to exact categories. Moreover, we also give a one-to-one correspondence between cotorsion pairs in $\\mathcal{T}$ and certain subsets of $\\mathcal{X}$. Applying to the simple minded systems of an triangulated category, we recover a result given by Dugas.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-09T07:00:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "extriangulated category",
      "one-to-one correspondence",
      "length wide subcategories",
      "simple minded systems",
      "filtration subcategory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}