"generalized element" meaning in English

{
  "forms": [
    {
      "form": "generalized elements",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "generalized element (plural generalized elements)",
      "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": [
        {
          "ref": "1995, Colin McLarty, Elementary Categories, Elementary Toposes, Oxford University Press, page 17",
          "text": "Thinking of x∈_AB as a generalized element, for any f:B→C, we may write f(x) for the composite f∘x. In this notation the first domain–codomain axiom reads as follows: for any x∈_AB and f:B→C there is a well-defined f(x)∈_AC; that is, at each stage A, f takes A-elements of B to A-elements of C.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A morphism whose codomain is some specified object."
      ],
      "hyponyms": [
        {
          "word": "generic element"
        }
      ],
      "id": "en-generalized_element-en-noun-h~bULnGv",
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "morphism",
          "morphism"
        ],
        [
          "codomain",
          "codomain"
        ],
        [
          "object",
          "object"
        ]
      ],
      "raw_glosses": [
        "(category theory) A morphism whose codomain is some specified object."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    }
  ],
  "word": "generalized element"
}

{
  "forms": [
    {
      "form": "generalized elements",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "generalized element (plural generalized elements)",
      "name": "en-noun"
    }
  ],
  "hyponyms": [
    {
      "word": "generic element"
    }
  ],
  "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"
      ],
      "examples": [
        {
          "ref": "1995, Colin McLarty, Elementary Categories, Elementary Toposes, Oxford University Press, page 17",
          "text": "Thinking of x∈_AB as a generalized element, for any f:B→C, we may write f(x) for the composite f∘x. In this notation the first domain–codomain axiom reads as follows: for any x∈_AB and f:B→C there is a well-defined f(x)∈_AC; that is, at each stage A, f takes A-elements of B to A-elements of C.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A morphism whose codomain is some specified object."
      ],
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "morphism",
          "morphism"
        ],
        [
          "codomain",
          "codomain"
        ],
        [
          "object",
          "object"
        ]
      ],
      "raw_glosses": [
        "(category theory) A morphism whose codomain is some specified object."
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    }
  ],
  "word": "generalized element"
}