"exponential object" meaning in All languages combined

{
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      "form": "exponential objects",
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      "expansion": "exponential object (plural exponential objects)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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          "name": "English entries with incorrect language header",
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      "examples": [
        {
          "text": "An exponential object generalizes its interpretation in category #x5C;mathbf#x7B;Set#x7D;; namely, that of as a function set or internal hom-set.",
          "type": "example"
        },
        {
          "text": "The pair Z^Y,#x5C;mbox#x7B;eval#x7D;#x3A;Z^Y#x5C;timesY#x5C;rightarrowZ is the terminal object of the comma category (-#x5C;timesY)#x5C;downarrowZ. Therefore the exponential object is a kind of universal morphism.",
          "type": "example"
        }
      ],
      "glosses": [
        "An object which indexes a family of arrows between two given objects in a universal way, meaning that any other indexed family of arrows between the same given pair of objects must factor uniquely through this universally-indexed family of arrows."
      ],
      "hypernyms": [
        {
          "word": "internal Hom"
        }
      ],
      "id": "en-exponential_object-en-noun-k7zB07oz",
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          "object",
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      ],
      "raw_glosses": [
        "(category theory) An object which indexes a family of arrows between two given objects in a universal way, meaning that any other indexed family of arrows between the same given pair of objects must factor uniquely through this universally-indexed family of arrows."
      ],
      "related": [
        {
          "roman": "an instance of which is the transpositioning λ in the figure",
          "word": "currying ∼ exportation_(logic)"
        },
        {
          "alt": "homologous to the universal evaluation morphism, eval",
          "word": "modus ponens"
        }
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        "exponential object"
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  "word": "exponential object"
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{
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      "word": "internal Hom"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "roman": "an instance of which is the transpositioning λ in the figure",
      "word": "currying ∼ exportation_(logic)"
    },
    {
      "alt": "homologous to the universal evaluation morphism, eval",
      "word": "modus ponens"
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          "text": "An exponential object generalizes its interpretation in category #x5C;mathbf#x7B;Set#x7D;; namely, that of as a function set or internal hom-set.",
          "type": "example"
        },
        {
          "text": "The pair Z^Y,#x5C;mbox#x7B;eval#x7D;#x3A;Z^Y#x5C;timesY#x5C;rightarrowZ is the terminal object of the comma category (-#x5C;timesY)#x5C;downarrowZ. Therefore the exponential object is a kind of universal morphism.",
          "type": "example"
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      ],
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        "An object which indexes a family of arrows between two given objects in a universal way, meaning that any other indexed family of arrows between the same given pair of objects must factor uniquely through this universally-indexed family of arrows."
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        "(category theory) An object which indexes a family of arrows between two given objects in a universal way, meaning that any other indexed family of arrows between the same given pair of objects must factor uniquely through this universally-indexed family of arrows."
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