"exponential object" meaning in English

{
  "forms": [
    {
      "form": "exponential objects",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "exponential object (plural exponential objects)",
      "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": "topical",
          "langcode": "en",
          "name": "Category theory",
          "orig": "en:Category theory",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "text": "An exponential object generalizes its interpretation in category mathbf Set; namely, that of as a function set or internal hom-set."
        },
        {
          "text": "The pair Z^Y, mbox eval:Z^Y×Y→Z is the terminal object of the comma category (-×Y)↓Z. Therefore the exponential object is a kind of universal morphism."
        }
      ],
      "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",
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "object",
          "object"
        ],
        [
          "universal",
          "universal morphism"
        ]
      ],
      "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"
        }
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ],
      "wikipedia": [
        "exponential object"
      ]
    }
  ],
  "word": "exponential object"
}

{
  "forms": [
    {
      "form": "exponential objects",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "exponential object (plural exponential objects)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "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"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Category theory"
      ],
      "examples": [
        {
          "text": "An exponential object generalizes its interpretation in category mathbf Set; namely, that of as a function set or internal hom-set."
        },
        {
          "text": "The pair Z^Y, mbox eval:Z^Y×Y→Z is the terminal object of the comma category (-×Y)↓Z. Therefore the exponential object is a kind of universal morphism."
        }
      ],
      "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."
      ],
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "object",
          "object"
        ],
        [
          "universal",
          "universal morphism"
        ]
      ],
      "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."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ],
      "wikipedia": [
        "exponential object"
      ]
    }
  ],
  "word": "exponential object"
}