{
  "id": "1804.06354",
  "version": "v1",
  "published": "2018-04-17T16:27:10.000Z",
  "updated": "2018-04-17T16:27:10.000Z",
  "title": "Minimality in diagrams of simplicial sets",
  "authors": [
    "Carles Broto",
    "Ramón Flores",
    "Carlos Giraldo"
  ],
  "comment": "29 pages",
  "categories": [
    "math.AT"
  ],
  "abstract": "If $\\mathcal{C}$ is a small category, we use the simplicial cofibrantly generated model structure over the category $\\mathbf{S}^\\mathcal{C}$ of $\\mathcal{C}$-diagrams of simplicial sets to formulate a definition of minimality for $\\mathcal{C}$-diagrams which are free. When $\\mathcal{C}$ is an artinian $EI$-category, we are able to show that every free diagram $X$ has a well-behaved minimal model. By generalizing the concepts of twisted cartesian product and fiber bundle to the category $\\mathbf{S}^\\mathcal{C}$ of $\\mathcal{C}$-diagrams of simplicial sets, we also establish a classification result for fibrations in $\\mathbf{S}^\\mathcal{C}$ over a constant diagram, as it is done in the classical way for Kan fibrations in $\\mathbf{S}$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-17T16:27:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "55P15"
    ],
    "keywords": [
      "simplicial sets",
      "minimality",
      "simplicial cofibrantly generated model structure",
      "small category",
      "kan fibrations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}