"categorical dual" meaning in English

{
  "forms": [
    {
      "form": "categorical duals",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "categorical dual (plural categorical duals)",
      "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": [
        "For a given category C, its dual category Cᵒᵖ is obtained by reversing the direction of each one of the arrows of C."
      ],
      "id": "en-categorical_dual-en-noun-T3opArzo",
      "links": [
        [
          "category theory",
          "category theory"
        ]
      ],
      "raw_glosses": [
        "(category theory) For a given category C, its dual category Cᵒᵖ is obtained by reversing the direction of each one of the arrows of C."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ],
      "wikipedia": [
        "dual (category theory)"
      ]
    }
  ],
  "word": "categorical dual"
}

{
  "forms": [
    {
      "form": "categorical duals",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "categorical dual (plural categorical duals)",
      "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": [
        "For a given category C, its dual category Cᵒᵖ is obtained by reversing the direction of each one of the arrows of C."
      ],
      "links": [
        [
          "category theory",
          "category theory"
        ]
      ],
      "raw_glosses": [
        "(category theory) For a given category C, its dual category Cᵒᵖ is obtained by reversing the direction of each one of the arrows of C."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ],
      "wikipedia": [
        "dual (category theory)"
      ]
    }
  ],
  "word": "categorical dual"
}