{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "0R47MAD57S"
    },
    {
      "field": "uses",
      "target": "27ZPTJP9PP"
    },
    {
      "field": "uses",
      "target": "59GFP54D78"
    },
    {
      "field": "uses",
      "target": "6Q96TKGZX2"
    },
    {
      "field": "uses",
      "target": "6YJ77MYM0Q"
    },
    {
      "field": "uses",
      "target": "B1TVEMYMC0"
    },
    {
      "field": "uses",
      "target": "CZW4BPZPZC"
    },
    {
      "field": "uses",
      "target": "CZWDNA1HA7"
    },
    {
      "field": "uses",
      "target": "DN2MNQGN4S"
    },
    {
      "field": "uses",
      "target": "H4JSMZK622"
    },
    {
      "field": "uses",
      "target": "H5765CJ7VB"
    },
    {
      "field": "uses",
      "target": "HEKDP2TDNZ"
    },
    {
      "field": "uses",
      "target": "JEWP2J397B"
    },
    {
      "field": "uses",
      "target": "K1SQAAN8D3"
    },
    {
      "field": "uses",
      "target": "Q07RA7AMDE"
    },
    {
      "field": "uses",
      "target": "QVWHWDJ5X1"
    },
    {
      "field": "uses",
      "target": "RDSY11X6N2"
    },
    {
      "field": "uses",
      "target": "RFKHKD4KXY"
    },
    {
      "field": "specializes",
      "target": "CV013KHVJG"
    },
    {
      "field": "specializes",
      "target": "G5S1M9"
    },
    {
      "field": "specializes",
      "target": "RA56GHB9JZ"
    },
    {
      "field": "about",
      "target": "HEKDP2TDNZ"
    }
  ],
  "body": "\n## Summary\n\nA monoid is a semigroup that has an identity element.\nExamples are the natural numbers with addition and the maps from a set to itself with composition.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "20M10"
    ],
    "name": "Monoid",
    "same_as": {
      "wikidata": "Q208237",
      "wikipedia": "Monoid"
    },
    "sources": [
      {
        "locator": "Definition",
        "url": "https://en.wikipedia.org/wiki/Monoid"
      }
    ],
    "specializes": [
      "0XMEM406JM"
    ],
    "tag": "0N6R902FG1"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/0N6R902FG1/",
  "links": [
    {
      "field": "specializes",
      "target": "0XMEM406JM"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/0N6R902FG1.md",
  "msc": [
    "20M10"
  ],
  "name": "Monoid",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0N6/0N6R902FG1.md",
  "status": null,
  "tag": "0N6R902FG1",
  "uri": "m2://0N6R902FG1",
  "url": "https://tamnd.github.io/math2/wiki/monoid/",
  "writing": {
    "tag": "0N6R902FG1",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      }
    ]
  }
}