"decategorification" meaning in English

See decategorification in All languages combined, or Wiktionary

Noun

Forms: decategorifications [plural]
Etymology: de- + categorification Etymology templates: {{prefix|en|de|categorification}} de- + categorification Head templates: {{en-noun}} decategorification (plural decategorifications)
  1. (mathematics) The reverse process of categorification: The mapping of a category theoretic category to a set by using a systematic process in which isomorphic objects in a category are identified as equal. Categories (topical): Mathematics
    Sense id: en-decategorification-en-noun-rpyxG4IA Categories (other): English entries with incorrect language header, English terms prefixed with de- Topics: mathematics, sciences

Inflected forms

Download JSON data for decategorification meaning in English (1.9kB)

{
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "de",
        "3": "categorification"
      },
      "expansion": "de- + categorification",
      "name": "prefix"
    }
  ],
  "etymology_text": "de- + categorification",
  "forms": [
    {
      "form": "decategorifications",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "decategorification (plural decategorifications)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
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          "source": "w"
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          "kind": "other",
          "name": "English terms prefixed with de-",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Mathematics",
          "orig": "en:Mathematics",
          "parents": [
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "2013, Octavian Iordache, Polytope Projects, page 6",
          "text": "For the n-levels systems approach we may associate categorification with increasing the level and decategorification with decreasing the level of complexity.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The reverse process of categorification: The mapping of a category theoretic category to a set by using a systematic process in which isomorphic objects in a category are identified as equal."
      ],
      "id": "en-decategorification-en-noun-rpyxG4IA",
      "links": [
        [
          "mathematics",
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        ],
        [
          "categorification",
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        ],
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          "category theoretic",
          "category theory"
        ],
        [
          "category",
          "category"
        ],
        [
          "set",
          "set"
        ],
        [
          "isomorphic",
          "isomorphic"
        ]
      ],
      "raw_glosses": [
        "(mathematics) The reverse process of categorification: The mapping of a category theoretic category to a set by using a systematic process in which isomorphic objects in a category are identified as equal."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "decategorification"
}
{
  "etymology_templates": [
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      "args": {
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        "2": "de",
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  ],
  "etymology_text": "de- + categorification",
  "forms": [
    {
      "form": "decategorifications",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "decategorification (plural decategorifications)",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
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      "examples": [
        {
          "ref": "2013, Octavian Iordache, Polytope Projects, page 6",
          "text": "For the n-levels systems approach we may associate categorification with increasing the level and decategorification with decreasing the level of complexity.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "The reverse process of categorification: The mapping of a category theoretic category to a set by using a systematic process in which isomorphic objects in a category are identified as equal."
      ],
      "links": [
        [
          "mathematics",
          "mathematics"
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          "category theoretic",
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        ],
        [
          "category",
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        [
          "set",
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        ],
        [
          "isomorphic",
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        ]
      ],
      "raw_glosses": [
        "(mathematics) The reverse process of categorification: The mapping of a category theoretic category to a set by using a systematic process in which isomorphic objects in a category are identified as equal."
      ],
      "topics": [
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "decategorification"
}

This page is a part of the kaikki.org machine-readable English 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.