{
  "id": "math/0008236",
  "version": "v1",
  "published": "2000-08-31T14:05:32.000Z",
  "updated": "2000-08-31T14:05:32.000Z",
  "title": "Exactness and stability in homotopical algebra",
  "authors": [
    "Marco Grandis"
  ],
  "comment": "24 pages",
  "categories": [
    "math.AT",
    "math.CT"
  ],
  "abstract": "Exact sequences are a well known notion in homological algebra. We investigate here the more vague properties of 'homotopical exactness', appearing for instance in the fibre or cofibre sequence of a map. Such notions of exactness can be given for very general 'categories with homotopies' having homotopy kernels and cokernels, but become more interesting under suitable stability hypotheses, satisfied - in particular - by chain complexes. It is then possible to measure the default of homotopical exactness of a sequence by the homotopy type of a certain object, a sort of 'homotopical homology'.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2000-08-31T14:05:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55U35",
      "18G55",
      "55U15"
    ],
    "keywords": [
      "homotopical algebra",
      "homotopical exactness",
      "chain complexes",
      "vague properties",
      "suitable stability hypotheses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2000math......8236G"
    }
  }
}