"representable functor" meaning in English

{
  "etymology_text": "If a representable functor is naturally isomorphic to a hom functor mbox Hom(C,-) or mbox Hom(-,C), then the object C is said to represent that representable functor.",
  "forms": [
    {
      "form": "representable functors",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "representable functor (plural representable functors)",
      "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"
        }
      ],
      "glosses": [
        "A functor from some category to the category of sets (Set) which is naturally isomorphic to a hom functor."
      ],
      "id": "en-representable_functor-en-noun-IEX86-b1",
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "functor",
          "functor"
        ],
        [
          "category",
          "category"
        ],
        [
          "hom functor",
          "hom functor"
        ]
      ],
      "raw_glosses": [
        "(category theory) A functor from some category to the category of sets (Set) which is naturally isomorphic to a hom functor."
      ],
      "synonyms": [
        {
          "word": "representable presheaf"
        }
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    }
  ],
  "word": "representable functor"
}

{
  "etymology_text": "If a representable functor is naturally isomorphic to a hom functor mbox Hom(C,-) or mbox Hom(-,C), then the object C is said to represent that representable functor.",
  "forms": [
    {
      "form": "representable functors",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "representable functor (plural representable functors)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Category theory"
      ],
      "glosses": [
        "A functor from some category to the category of sets (Set) which is naturally isomorphic to a hom functor."
      ],
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "functor",
          "functor"
        ],
        [
          "category",
          "category"
        ],
        [
          "hom functor",
          "hom functor"
        ]
      ],
      "raw_glosses": [
        "(category theory) A functor from some category to the category of sets (Set) which is naturally isomorphic to a hom functor."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    }
  ],
  "synonyms": [
    {
      "word": "representable presheaf"
    }
  ],
  "word": "representable functor"
}