{
  "id": "1205.3669",
  "version": "v3",
  "published": "2012-05-16T13:22:28.000Z",
  "updated": "2014-01-08T20:28:42.000Z",
  "title": "Categorification of persistent homology",
  "authors": [
    "Peter Bubenik",
    "Jonathan A. Scott"
  ],
  "comment": "27 pages, v3: minor changes, to appear in Discrete & Computational Geometry",
  "journal": "Discrete Comput. Geom. 51 (2014) 600-627",
  "doi": "10.1007/s00454-014-9573-x",
  "categories": [
    "math.AT",
    "cs.CG",
    "math.CT"
  ],
  "abstract": "We redevelop persistent homology (topological persistence) from a categorical point of view. The main objects of study are diagrams, indexed by the poset of real numbers, in some target category. The set of such diagrams has an interleaving distance, which we show generalizes the previously-studied bottleneck distance. To illustrate the utility of this approach, we greatly generalize previous stability results for persistence, extended persistence, and kernel, image and cokernel persistence. We give a natural construction of a category of interleavings of these diagrams, and show that if the target category is abelian, so is this category of interleavings.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2014-01-08T20:28:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55N99",
      "68W30",
      "18A25",
      "18E10",
      "54E35"
    ],
    "keywords": [
      "categorification",
      "target category",
      "redevelop persistent homology",
      "real numbers",
      "main objects"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1205.3669B"
    }
  }
}