{
  "id": "1007.4110",
  "version": "v1",
  "published": "2010-07-23T12:08:55.000Z",
  "updated": "2010-07-23T12:08:55.000Z",
  "title": "Cohomology of products and coproducts of augmented algebras",
  "authors": [
    "Matthew Towers"
  ],
  "comment": "14 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We show that the ordinary cohomology functor from the category of augmented $k$-algebras to itself exchanges coproducts and products, and that Hochschild cohomology is close to sending coproducts to products if the factors are self-injective. We identify the multiplicative structure of the Hochschild cohomology of a product modulo a certain ideal in terms of the cohomology of the factors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-07-23T12:08:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "16E40"
    ],
    "keywords": [
      "augmented algebras",
      "hochschild cohomology",
      "ordinary cohomology functor",
      "product modulo",
      "exchanges coproducts"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1007.4110T"
    }
  }
}