{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "SRRMJFCKVT"
    }
  ],
  "body": "\n## Summary\n\nA string diagram is a picture of a morphism in a [[monoidal category|M3MSQ3NKAE]]: wires stand for objects and boxes stand for morphisms.\nComposition is drawn by stacking boxes and the monoidal product by placing them side by side.\nA theorem of Joyal and Street says that diagrams that deform into each other in the plane, with wires kept upward, denote the same morphism.\nSo many computations with coherence isomorphisms become moves of pictures.\n\n## Explanations\n\n### L1 human\n\nDraw each object as a vertical line and each morphism as a box with lines entering at the bottom and leaving at the top.\nDoing one process after another stacks the boxes; doing two processes in parallel puts them next to each other.\nThe equation $(g \\otimes \\id) \\circ (\\id \\otimes f) = (\\id \\otimes f) \\circ (g \\otimes \\id)$ becomes obvious: one may slide box $g$ above or below box $f$ on its own wire.\nString diagrams are used in quantum computing, in linear algebra with tensors, and in the study of knots.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "18M30",
      "18M05"
    ],
    "name": "String diagram",
    "same_as": {
      "wikidata": "Q7623974",
      "wikipedia": "String diagram"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/String_diagram"
      }
    ],
    "tag": "5YHK0VS62A"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/5YHK0VS62A/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/5YHK0VS62A.md",
  "msc": [
    "18M30",
    "18M05"
  ],
  "name": "String diagram",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/5YH/5YHK0VS62A.md",
  "status": null,
  "tag": "5YHK0VS62A",
  "uri": "m2://5YHK0VS62A",
  "url": "https://tamnd.github.io/math2/wiki/string-diagram/",
  "writing": {
    "tag": "5YHK0VS62A",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}