{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "VE4SJTXFBV"
    }
  ],
  "body": "\n## Summary\n\nDay terms are a finite chain of quaternary terms of a [[variety|AJNZJD8442]] that satisfy certain identities.\nBy Day's theorem, a variety has Day terms if and only if it is a [[congruence-modular variety|QAQAS3JWXW]].\nThey give a Mal'cev condition for congruence modularity, in the same way that [[Jónsson terms|3M8Y76E4AG]] do for congruence distributivity.\n\n## Explanations\n\n### L1 human\n\nDay terms are a list of formulas with four inputs that step from the first input to the last one.\nEach formula returns $x$ when its inputs have the pattern $x, y, y, x$.\nNeighbouring formulas agree on inputs of certain patterns with repeated values.\nTheir existence is exactly what makes all congruence lattices in the variety modular.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "08B05",
      "08B10"
    ],
    "name": "Day terms",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Modular_lattice"
      }
    ],
    "tag": "B0YKA8401M"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/B0YKA8401M/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/B0YKA8401M.md",
  "msc": [
    "08B05",
    "08B10"
  ],
  "name": "Day terms",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/B0Y/B0YKA8401M.md",
  "status": null,
  "tag": "B0YKA8401M",
  "uri": "m2://B0YKA8401M",
  "url": "https://tamnd.github.io/math2/wiki/day-terms/",
  "writing": {
    "tag": "B0YKA8401M",
    "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
      }
    ]
  }
}