{
  "id": "2410.23935",
  "version": "v1",
  "published": "2024-10-31T13:49:21.000Z",
  "updated": "2024-10-31T13:49:21.000Z",
  "title": "The stable uniqueness theorem for unitary tensor category equivariant KK-theory",
  "authors": [
    "Sergio Girón Pacheco",
    "Kan Kitamura",
    "Robert Neagu"
  ],
  "categories": [
    "math.OA",
    "math.KT",
    "math.QA"
  ],
  "abstract": "We introduce the Cuntz-Thomsen picture of $\\mathcal{C}$-equivariant Kasparov theory, denoted $\\mathrm{KK}^\\mathcal{C}$, for a unitary tensor category $\\mathcal{C}$ with countably many isomorphism classes of simple objects. We use this description of $\\mathrm{KK}^\\mathcal{C}$ to prove the stable uniqueness theorem in this setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-31T13:49:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "19K35",
      "46L35",
      "46L37",
      "46L55"
    ],
    "keywords": [
      "unitary tensor category equivariant kk-theory",
      "stable uniqueness theorem",
      "equivariant kasparov theory",
      "cuntz-thomsen picture"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}