"cocompletion" meaning in All languages combined

See cocompletion on Wiktionary

Noun [English]

Forms: cocompletions [plural]
Etymology: co- + completion Etymology templates: {{prefix|en|co|completion}} co- + completion Head templates: {{en-noun}} cocompletion (plural cocompletions)
  1. (mathematics) A full embedding whose image is a cocomplete category and for which every functor with a cocomplete image has an extension to a cocontinuous functor that is unique up to natural isomorphism. Categories (topical): Mathematics
    Sense id: en-cocompletion-en-noun-Gb3uSoQ- Categories (other): English entries with incorrect language header, English terms prefixed with co- Topics: mathematics, sciences

Inflected forms

Download JSON data for cocompletion meaning in All languages combined (2.0kB)

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "co",
        "3": "completion"
      },
      "expansion": "co- + completion",
      "name": "prefix"
    }
  ],
  "etymology_text": "co- + completion",
  "forms": [
    {
      "form": "cocompletions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "cocompletion (plural cocompletions)",
      "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",
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          "source": "w"
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        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2015, Rory B. B. Lucyshyn-Wright, “Enriched algebraic theories and monads for a system of arities”, in arXiv",
          "text": "We show that j satisfies this condition if and only if j presents #x5C;mathcal#x7B;V#x7D; as a free cocompletion of #x5C;mathcal#x7B;J#x7D; with respect to the weights for left Kan extensions along j, and so we call such systems of arities eleutheric.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A full embedding whose image is a cocomplete category and for which every functor with a cocomplete image has an extension to a cocontinuous functor that is unique up to natural isomorphism."
      ],
      "id": "en-cocompletion-en-noun-Gb3uSoQ-",
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        [
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        [
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        ],
        [
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        ],
        [
          "unique",
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        ],
        [
          "isomorphism",
          "isomorphism"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A full embedding whose image is a cocomplete category and for which every functor with a cocomplete image has an extension to a cocontinuous functor that is unique up to natural isomorphism."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "cocompletion"
}
{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "co",
        "3": "completion"
      },
      "expansion": "co- + completion",
      "name": "prefix"
    }
  ],
  "etymology_text": "co- + completion",
  "forms": [
    {
      "form": "cocompletions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "cocompletion (plural cocompletions)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
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        {
          "ref": "2015, Rory B. B. Lucyshyn-Wright, “Enriched algebraic theories and monads for a system of arities”, in arXiv",
          "text": "We show that j satisfies this condition if and only if j presents #x5C;mathcal#x7B;V#x7D; as a free cocompletion of #x5C;mathcal#x7B;J#x7D; with respect to the weights for left Kan extensions along j, and so we call such systems of arities eleutheric.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A full embedding whose image is a cocomplete category and for which every functor with a cocomplete image has an extension to a cocontinuous functor that is unique up to natural isomorphism."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
        ],
        [
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        ],
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        ],
        [
          "unique",
          "unique"
        ],
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          "isomorphism",
          "isomorphism"
        ]
      ],
      "raw_glosses": [
        "(mathematics) A full embedding whose image is a cocomplete category and for which every functor with a cocomplete image has an extension to a cocontinuous functor that is unique up to natural isomorphism."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "cocompletion"
}

This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-06-04 from the enwiktionary dump dated 2024-05-02 using wiktextract (e9e0a99 and db5a844). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.

If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.