{
  "id": "math/0504081",
  "version": "v1",
  "published": "2005-04-05T19:27:43.000Z",
  "updated": "2005-04-05T19:27:43.000Z",
  "title": "Local theory of almost split sequences for comodules",
  "authors": [
    "William Chin",
    "Mark Kleiner",
    "Declan Quinn"
  ],
  "categories": [
    "math.RT",
    "math.RA"
  ],
  "abstract": "We show that almost split sequences in the category of comodules over a coalgebra with finite-dimensional right-hand term are direct limits of almost split sequences over finite dimensional subcoalgebras. In previous work we showed that such almost split sequences exist if the right hand term has a quasifinitely copresented linear dual. Conversely, taking limits of almost split sequences over finte-dimensional comodule categories, we then show that, for countable-dimensional coalgebras, certain exact sequences exist which satisfy a condition weaker than being almost split, which we call ``finitely almost split''. Under additional assumptions, these sequences are shown to be almost split in the appropriate category.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-04-05T19:27:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16G70",
      "16W30"
    ],
    "keywords": [
      "split sequences",
      "local theory",
      "finite dimensional subcoalgebras",
      "finte-dimensional comodule categories",
      "right hand term"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......4081C"
    }
  }
}