{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "JFJYSSWSSR"
    }
  ],
  "body": "\n## Summary\n\nA minimal clone on a set $A$ is a clone that lies just above the clone of [[projections|769B35T6WG]] in the [[lattice of clones|EX9NCDFYC7]].\nIt is generated by any one of its non-projection operations.\nOn a finite set, every clone other than the projection clone contains a minimal clone, and there are only finitely many minimal clones.\nMinimal clones are the atoms of the clone lattice, dual to the maximal clones.\n\n## Explanations\n\n### L1 human\n\nThe smallest clone can only copy inputs.\nA minimal clone adds the least possible amount of power to it.\nFor example, on $\\set{0, 1}$ the clone generated by negation $\\neg$ is minimal.\nEvery operation in it is a projection or a negated projection, and each negated projection generates $\\neg$ back.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "08A40"
    ],
    "name": "Minimal clone",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Clone_(algebra)"
      }
    ],
    "specializes": [
      "PTKR703G6A"
    ],
    "tag": "1V9GKBY29Y"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/1V9GKBY29Y/",
  "links": [
    {
      "field": "specializes",
      "target": "PTKR703G6A"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/1V9GKBY29Y.md",
  "msc": [
    "08A40"
  ],
  "name": "Minimal clone",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/1V9/1V9GKBY29Y.md",
  "status": null,
  "tag": "1V9GKBY29Y",
  "uri": "m2://1V9GKBY29Y",
  "url": "https://tamnd.github.io/math2/wiki/minimal-clone/",
  "writing": {
    "tag": "1V9GKBY29Y",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}
