{
  "id": "1211.4968",
  "version": "v2",
  "published": "2012-11-21T09:06:12.000Z",
  "updated": "2015-06-04T17:07:47.000Z",
  "title": "Self-Similarity in Geometry, Algebra and Arithmetic",
  "authors": [
    "Arash Rastegar"
  ],
  "comment": "15 pages. arXiv admin note: substantial text overlap with arXiv:math/0404498",
  "categories": [
    "math.NT",
    "math.AC",
    "math.AG"
  ],
  "abstract": "We define the concept of self-similarity of an object by considering endomorphisms of the object as `similarity' maps. A variety of interesting examples of self-similar objects in geometry, algebra and arithmetic are introduced. Self-similar objects provide a framework in which, one can unite some results and conjectures in different mathematical frameworks. In some general situations, one can define a well-behaved notion of dimension for self-similar objects. Morphisms between self-similar objects are also defined and a categorical treatment of this concept is provided. We conclude by some philosophical remarks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-11-21T09:06:12.000Z",
      "comment": "14 pages. arXiv admin note: substantial text overlap with arXiv:math/0404498",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-06-04T17:07:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "self-similar objects",
      "self-similarity",
      "arithmetic",
      "general situations",
      "considering endomorphisms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1211.4968R"
    }
  }
}