{
  "id": "2005.06690",
  "version": "v1",
  "published": "2020-05-14T02:13:52.000Z",
  "updated": "2020-05-14T02:13:52.000Z",
  "title": "Almost Split Triangles and Morphisms Determined by Objects in Extriangulated Categories",
  "authors": [
    "Tiwei Zhao",
    "Lingling Tan",
    "Zhaoyong Huang"
  ],
  "journal": "Journal of Algebra 559 (2020) 346-378",
  "doi": "10.1016/j.jalgebra.2020.04.021",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Let $(\\mathfrak{C},\\mathbb{E},\\mathfrak{s})$ be an Ext-finite, Krull-Schmidt and $k$-linear extriangulated category with $k$ a commutative artinian ring. We define an additive subcategory $\\mathfrak{C}_r$ (respectively, $\\mathfrak{C}_l$) of $\\mathfrak{C}$ in terms of the representable functors from the stable category of $\\mathfrak{C}$ modulo $\\mathfrak{s}$-injectives (respectively, $\\mathfrak{s}$-projectives) to $k$-modules, which consists of all $\\mathfrak{s}$-projective (respectively, $\\mathfrak{s}$-injective) objects and objects isomorphic to direct summands of finite direct sums of all third (respectively, first) terms of almost split $\\mathfrak{s}$-triangles. We investigate the subcategories $\\mathfrak{C}_r$ and $\\mathfrak{C}_l$ in terms of morphisms determined by objects, and then give equivalent characterizations on the existence of almost split $\\mathfrak{s}$-triangles.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-05-14T02:13:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30",
      "18E10",
      "16G70"
    ],
    "keywords": [
      "split triangles",
      "finite direct sums",
      "subcategory",
      "objects isomorphic",
      "direct summands"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Elsevier"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}