{
  "id": "1603.09379",
  "version": "v1",
  "published": "2016-03-30T20:55:20.000Z",
  "updated": "2016-03-30T20:55:20.000Z",
  "title": "Co-t-structures: The First Decade",
  "authors": [
    "Peter Jorgensen"
  ],
  "comment": "12 pages",
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "Co-t-structures were introduced about ten years ago as a type of mirror image of t-structures. Like t-structures, they permit to divide an object in a triangulated category T into a \"left part\" and a \"right part\", but there are crucial differences. For instance, a bounded t-structure gives rise to an abelian subcategory of T, while a bounded co-t-structure gives rise to a so-called silting subcategory. This brief survey will emphasise three philosophical points. First, bounded t-structures are akin to the canonical example of \"soft\" truncation of complexes in the derived category. Secondly, bounded co-t-structures are akin to the canonical example of \"hard\" truncation of complexes in the homotopy category. Thirdly, a triangulated category T may be skewed towards t-structures or co-t-structures, in the sense that one type of structure is more useful than the other for studying T. In particular, we think of derived categories as skewed towards t-structures, and of homotopy categories as skewed towards co-t-structures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-30T20:55:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "18E30"
    ],
    "keywords": [
      "first decade",
      "homotopy category",
      "bounded co-t-structure",
      "derived category",
      "canonical example"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160309379J"
    }
  }
}