"natural transformation" meaning in All languages combined

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  "lang_code": "en",
  "pos": "noun",
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      "derived": [
        {
          "word": "Cartesian natural transformation"
        }
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      "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)."
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      "id": "en-natural_transformation-en-noun-v9zhstyy",
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      "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)."
      ],
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        {
          "word": "natural isomorphism"
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      "translations": [
        {
          "code": "de",
          "lang": "German",
          "sense": "Translations",
          "tags": [
            "feminine"
          ],
          "word": "natürliche Transformation"
        },
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          "code": "ru",
          "lang": "Russian",
          "roman": "jestestvennoje preobrazovanije",
          "sense": "Translations",
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          "word": "естественное преобразование"
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      "wikipedia": [
        "natural transformation"
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  "word": "natural transformation"
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        "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)."
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        "(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)."
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  "translations": [
    {
      "code": "de",
      "lang": "German",
      "sense": "Translations",
      "tags": [
        "feminine"
      ],
      "word": "natürliche Transformation"
    },
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      "code": "ru",
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    }
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  "word": "natural transformation"
}