"Yoneda functor" meaning in All languages combined

{
  "etymology_text": "Named after the Japanese mathematician Nobuo Yoneda (1930–1996).",
  "forms": [
    {
      "form": "Yoneda functors",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Yoneda functor (plural Yoneda 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": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "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 a given category to the category of functors from that given category to Set (the category of sets) which maps any object of the given category to a hom functor represented by that object and any morphism to a natural isomorphism induced uniquely by that morphism according to the Yoneda lemma."
      ],
      "id": "en-Yoneda_functor-en-noun-5bDUjRwF",
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "hom functor",
          "hom functor"
        ],
        [
          "represented",
          "representable functor"
        ],
        [
          "natural isomorphism",
          "natural isomorphism"
        ],
        [
          "Yoneda lemma",
          "Yoneda lemma"
        ]
      ],
      "raw_glosses": [
        "(category theory) A functor from a given category to the category of functors from that given category to Set (the category of sets) which maps any object of the given category to a hom functor represented by that object and any morphism to a natural isomorphism induced uniquely by that morphism according to the Yoneda lemma."
      ],
      "related": [
        {
          "word": "Yoneda embedding"
        },
        {
          "word": "Yoneda lemma"
        }
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    }
  ],
  "word": "Yoneda functor"
}

{
  "etymology_text": "Named after the Japanese mathematician Nobuo Yoneda (1930–1996).",
  "forms": [
    {
      "form": "Yoneda functors",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "Yoneda functor (plural Yoneda functors)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "Yoneda embedding"
    },
    {
      "word": "Yoneda lemma"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "Pages with 1 entry",
        "Pages with entries",
        "en:Category theory"
      ],
      "glosses": [
        "A functor from a given category to the category of functors from that given category to Set (the category of sets) which maps any object of the given category to a hom functor represented by that object and any morphism to a natural isomorphism induced uniquely by that morphism according to the Yoneda lemma."
      ],
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "hom functor",
          "hom functor"
        ],
        [
          "represented",
          "representable functor"
        ],
        [
          "natural isomorphism",
          "natural isomorphism"
        ],
        [
          "Yoneda lemma",
          "Yoneda lemma"
        ]
      ],
      "raw_glosses": [
        "(category theory) A functor from a given category to the category of functors from that given category to Set (the category of sets) which maps any object of the given category to a hom functor represented by that object and any morphism to a natural isomorphism induced uniquely by that morphism according to the Yoneda lemma."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    }
  ],
  "word": "Yoneda functor"
}