{
  "id": "1901.03606",
  "version": "v1",
  "published": "2019-01-11T15:02:21.000Z",
  "updated": "2019-01-11T15:02:21.000Z",
  "title": "Comparison of Waldhausen constructions",
  "authors": [
    "Julia E. Bergner",
    "Angélica M. Osorno",
    "Viktoriya Ozornova",
    "Martina Rovelli",
    "Claudia I. Scheimbauer"
  ],
  "categories": [
    "math.AT",
    "math.CT",
    "math.KT"
  ],
  "abstract": "In previous work, we develop a generalized Waldhausen $S_{\\bullet}$-construction whose input is an augmented stable double Segal space and whose output is a unital 2-Segal space. Here, we prove that this construction recovers the previously known $S_{\\bullet}$-constructions for exact categories and for stable and exact $(\\infty,1)$-categories, as well as the relative $S_{\\bullet}$-construction for exact functors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-11T15:02:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55U10",
      "55U35",
      "55U40",
      "18D05",
      "18G55",
      "18G30",
      "19D10"
    ],
    "keywords": [
      "waldhausen constructions",
      "comparison",
      "augmented stable double segal space",
      "exact categories",
      "exact functors"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}