"contravariant functor" meaning in English

{
  "forms": [
    {
      "form": "contravariant functors",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "contravariant functor (plural contravariant 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": "Entries with translation boxes",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Icelandic translations",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Terms with Portuguese translations",
          "parents": [],
          "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": "A contravariant functor F#x3A;#x5C;mathcal#x7B;C#x7D;#x5C;rightarrow#x5C;mathcal#x7B;D#x7D; is the same as a covariant functor F#x3A;#x5C;mathcal#x7B;C#x7D;#x7B;op#x7D;#x5C;rightarrow#x5C;mathcal#x7B;D#x7D;.",
          "type": "example"
        }
      ],
      "glosses": [
        "A functor which maps a morphism f:X → Y to a morphism F(f):F(Y) → F(X), such that if h=g∘f, then F(h)=F(f)∘F(g)."
      ],
      "id": "en-contravariant_functor-en-noun-~4Tho6ST",
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "functor",
          "functor"
        ],
        [
          "morphism",
          "morphism"
        ]
      ],
      "raw_glosses": [
        "(category theory) A functor which maps a morphism f:X → Y to a morphism F(f):F(Y) → F(X), such that if h=g∘f, then F(h)=F(f)∘F(g)."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ],
      "translations": [
        {
          "code": "is",
          "lang": "Icelandic",
          "sense": "category theory: functor",
          "tags": [
            "masculine"
          ],
          "word": "hjávarpi"
        },
        {
          "code": "is",
          "lang": "Icelandic",
          "sense": "category theory: functor",
          "tags": [
            "masculine"
          ],
          "word": "andbrigður varpi"
        },
        {
          "code": "is",
          "lang": "Icelandic",
          "sense": "category theory: functor",
          "tags": [
            "masculine"
          ],
          "word": "mótbrigður varpi"
        },
        {
          "code": "pt",
          "lang": "Portuguese",
          "sense": "category theory: functor",
          "tags": [
            "masculine"
          ],
          "word": "functor/funtor contravariante"
        }
      ]
    }
  ],
  "word": "contravariant functor"
}

{
  "forms": [
    {
      "form": "contravariant functors",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "contravariant functor (plural contravariant 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",
        "English terms with usage examples",
        "Entries with translation boxes",
        "Pages with 1 entry",
        "Pages with entries",
        "Terms with Icelandic translations",
        "Terms with Portuguese translations",
        "en:Category theory"
      ],
      "examples": [
        {
          "text": "A contravariant functor F#x3A;#x5C;mathcal#x7B;C#x7D;#x5C;rightarrow#x5C;mathcal#x7B;D#x7D; is the same as a covariant functor F#x3A;#x5C;mathcal#x7B;C#x7D;#x7B;op#x7D;#x5C;rightarrow#x5C;mathcal#x7B;D#x7D;.",
          "type": "example"
        }
      ],
      "glosses": [
        "A functor which maps a morphism f:X → Y to a morphism F(f):F(Y) → F(X), such that if h=g∘f, then F(h)=F(f)∘F(g)."
      ],
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "functor",
          "functor"
        ],
        [
          "morphism",
          "morphism"
        ]
      ],
      "raw_glosses": [
        "(category theory) A functor which maps a morphism f:X → Y to a morphism F(f):F(Y) → F(X), such that if h=g∘f, then F(h)=F(f)∘F(g)."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    }
  ],
  "translations": [
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "category theory: functor",
      "tags": [
        "masculine"
      ],
      "word": "hjávarpi"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "category theory: functor",
      "tags": [
        "masculine"
      ],
      "word": "andbrigður varpi"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "category theory: functor",
      "tags": [
        "masculine"
      ],
      "word": "mótbrigður varpi"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "category theory: functor",
      "tags": [
        "masculine"
      ],
      "word": "functor/funtor contravariante"
    }
  ],
  "word": "contravariant functor"
}