{
  "id": "2104.12258",
  "version": "v1",
  "published": "2021-04-25T21:05:18.000Z",
  "updated": "2021-04-25T21:05:18.000Z",
  "title": "Triangulation and persistence: Algebra 101",
  "authors": [
    "Paul Biran",
    "Octav Cornea",
    "Jun Zhang"
  ],
  "categories": [
    "math.AT",
    "math.AG",
    "math.SG"
  ],
  "abstract": "This paper lays the foundations of triangulated persistence categories (TPC), which brings together persistence modules with the theory of triangulated categories. As a result we introduce several measurements and metrics on the set of objects of some triangulated categories. We also provide examples of TPCs coming from algebra, algebraic topology, microlocal sheaf theory and symplectic topology.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-25T21:05:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N31",
      "53D12",
      "35A27"
    ],
    "keywords": [
      "triangulation",
      "microlocal sheaf theory",
      "triangulated categories",
      "symplectic topology",
      "persistence modules"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}