"natural transformation" meaning in All languages combined

{
  "forms": [
    {
      "form": "natural transformations",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "natural transformation (plural natural transformations)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "German terms in nonstandard scripts",
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          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Category theory",
          "orig": "en:Category theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "Cartesian natural transformation"
        }
      ],
      "glosses": [
        "A morphism between a pair of parallel functors such that if each object of the shared domain category subtends a correlated arrow — called a component — in the shared codomain (which arrow represents the difference between applying the second functor and the first functor to the correlated object) then each arrow of the shared domain subtends a commuting square — called a naturality square — between two components (correlated to the domain and codomain of the arrow)."
      ],
      "id": "en-natural_transformation-en-noun-v9zhstyy",
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "functor",
          "functor"
        ]
      ],
      "raw_glosses": [
        "(category theory) A morphism between a pair of parallel functors such that if each object of the shared domain category subtends a correlated arrow — called a component — in the shared codomain (which arrow represents the difference between applying the second functor and the first functor to the correlated object) then each arrow of the shared domain subtends a commuting square — called a naturality square — between two components (correlated to the domain and codomain of the arrow)."
      ],
      "related": [
        {
          "word": "natural isomorphism"
        }
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ],
      "translations": [
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "natürliche Transformation"
        },
        {
          "code": "de",
          "lang": "Russian",
          "sense": "Translations",
          "tags": [
            "neuter"
          ],
          "word": "естественное преобразование"
        }
      ],
      "wikipedia": [
        "natural transformation"
      ]
    }
  ],
  "word": "natural transformation"
}

{
  "derived": [
    {
      "word": "Cartesian natural transformation"
    }
  ],
  "forms": [
    {
      "form": "natural transformations",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
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      "expansion": "natural transformation (plural natural transformations)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "natural isomorphism"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "German terms in nonstandard scripts",
        "Translation table header lacks gloss",
        "en:Category theory"
      ],
      "glosses": [
        "A morphism between a pair of parallel functors such that if each object of the shared domain category subtends a correlated arrow — called a component — in the shared codomain (which arrow represents the difference between applying the second functor and the first functor to the correlated object) then each arrow of the shared domain subtends a commuting square — called a naturality square — between two components (correlated to the domain and codomain of the arrow)."
      ],
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "functor",
          "functor"
        ]
      ],
      "raw_glosses": [
        "(category theory) A morphism between a pair of parallel functors such that if each object of the shared domain category subtends a correlated arrow — called a component — in the shared codomain (which arrow represents the difference between applying the second functor and the first functor to the correlated object) then each arrow of the shared domain subtends a commuting square — called a naturality square — between two components (correlated to the domain and codomain of the arrow)."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ],
      "wikipedia": [
        "natural transformation"
      ]
    }
  ],
  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "natürliche Transformation"
    },
    {
      "code": "de",
      "lang": "Russian",
      "sense": "Translations",
      "tags": [
        "neuter"
      ],
      "word": "естественное преобразование"
    }
  ],
  "word": "natural transformation"
}