"adjunction" meaning in All languages combined

See adjunction on Wiktionary

Noun [English]

Audio: LL-Q1860 (eng)-Flame, not lame-adjunction.wav Forms: adjunctions [plural]
Etymology: From Latin adjunctio, from adjungere: compare French adjonction, and see adjunct. Etymology templates: {{root|en|ine-pro|*yewg-}}, {{uder|en|la|adjunctio}} Latin adjunctio, {{uder|en|fr|adjonction}} French adjonction Head templates: {{en-noun|~}} adjunction (countable and uncountable, plural adjunctions)
  1. The act of joining; the thing joined or added. Tags: countable, uncountable Translations (the act of joining): adiunkcja [feminine] (Polish), adjunção [feminine] (Portuguese)
    Sense id: en-adjunction-en-noun-en:joining Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 11 1 6 17 31 33 Disambiguation of Entries with translation boxes: 15 3 4 19 28 31 Disambiguation of Pages with 1 entry: 13 2 9 14 28 33 Disambiguation of Pages with entries: 17 1 2 17 28 34 Disambiguation of 'the act of joining': 84 10 2 1 2 2
  2. (law) The joining of personal property owned by one to that owned by another. Tags: countable, uncountable Categories (topical): Law
    Sense id: en-adjunction-en-noun-en:legal Topics: law
  3. (mathematics, chiefly algebra and number theory) The process of adjoining elements to an algebraic structure (usually a ring or field); the result of such a process. Tags: countable, uncountable Categories (topical): Algebra, Mathematics, Number theory
    Sense id: en-adjunction-en-noun-dqGNkwoE Topics: algebra, mathematics, number-theory, sciences
  4. (category theory, loosely) A relationship between a pair of categories that makes the pair, in a weak sense, equivalent. Tags: broadly, countable, uncountable Categories (topical): Category theory Hyponyms: equivalence of categories, isomorphism of categories, Galois connection Translations (a form of similarity between a pair of categories mapped to each other by dual morphisms): adiunkcja [feminine] (Polish)
    Sense id: en-adjunction-en-noun-mjWL-6Om Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 11 1 6 17 31 33 Disambiguation of Entries with translation boxes: 15 3 4 19 28 31 Disambiguation of Pages with 1 entry: 13 2 9 14 28 33 Disambiguation of Pages with entries: 17 1 2 17 28 34 Topics: category-theory, computing, engineering, mathematics, natural-sciences, physical-sciences, sciences Disambiguation of 'a form of similarity between a pair of categories mapped to each other by dual morphisms': 3 1 5 38 27 27
  5. (category theory, strictly) A natural isomorphism between a pair of functors satisfying certain conditions, whose existence implies a close relationship between the functors and between their (co)domains; the natural isomorphism, functors, and their (co)domains thought of as a single object. Tags: countable, uncountable Categories (topical): Category theory
    Sense id: en-adjunction-en-noun-en:category Categories (other): English entries with incorrect language header, Entries with translation boxes, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 11 1 6 17 31 33 Disambiguation of Entries with translation boxes: 15 3 4 19 28 31 Disambiguation of Pages with 1 entry: 13 2 9 14 28 33 Disambiguation of Pages with entries: 17 1 2 17 28 34 Topics: category-theory, computing, engineering, mathematics, natural-sciences, physical-sciences, sciences
  6. (category theory, strictly) A natural isomorphism between a pair of functors satisfying certain conditions, whose existence implies a close relationship between the functors and between their (co)domains; the natural isomorphism, functors, and their (co)domains thought of as a single object.
    (formally, given two categories 𝒞 and 𝒟 and (covariant) functors F:𝒞→𝒟 and G:𝒟→𝒞) A natural isomorphism Φ: operatorname Hom_( mathcal )C(G·,·)→ operatorname Hom_( mathcal )D(·,F·) (where the hom-functors are understood as bifunctors from 𝒟^( operatorname )op×𝒞 to mathbf Set). See Adjoint functors on Wikipedia.Wikipedia.
    Tags: countable, formal, uncountable Categories (topical): Category theory
    Sense id: en-adjunction-en-noun-en:category1 Categories (other): English entries with incorrect language header, English undefined derivations, Entries with translation boxes, Pages with 1 entry, Pages with entries, Terms with Bulgarian translations, Terms with Polish translations, Terms with Portuguese translations Disambiguation of English entries with incorrect language header: 11 1 6 17 31 33 Disambiguation of English undefined derivations: 14 3 9 17 25 32 Disambiguation of Entries with translation boxes: 15 3 4 19 28 31 Disambiguation of Pages with 1 entry: 13 2 9 14 28 33 Disambiguation of Pages with entries: 17 1 2 17 28 34 Disambiguation of Terms with Bulgarian translations: 17 3 7 19 23 31 Disambiguation of Terms with Polish translations: 17 4 7 18 22 31 Disambiguation of Terms with Portuguese translations: 16 4 8 19 23 30 Topics: category-theory, computing, engineering, mathematics, natural-sciences, physical-sciences, sciences
The following are not (yet) sense-disambiguated
Derived forms: biadjunction

Inflected forms

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          "mathematics"
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        [
          "algebra",
          "algebra"
        ],
        [
          "number theory",
          "number theory"
        ],
        [
          "adjoin",
          "adjoin"
        ],
        [
          "algebraic structure",
          "algebraic structure"
        ],
        [
          "ring",
          "ring"
        ],
        [
          "field",
          "field"
        ]
      ],
      "raw_glosses": [
        "(mathematics, chiefly algebra and number theory) The process of adjoining elements to an algebraic structure (usually a ring or field); the result of such a process."
      ],
      "tags": [
        "countable",
        "uncountable"
      ],
      "topics": [
        "algebra",
        "mathematics",
        "number-theory",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Category theory"
      ],
      "glosses": [
        "A relationship between a pair of categories that makes the pair, in a weak sense, equivalent."
      ],
      "hyponyms": [
        {
          "word": "equivalence of categories"
        },
        {
          "word": "isomorphism of categories"
        },
        {
          "word": "Galois connection"
        }
      ],
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "categories",
          "category"
        ]
      ],
      "raw_glosses": [
        "(category theory, loosely) A relationship between a pair of categories that makes the pair, in a weak sense, equivalent."
      ],
      "tags": [
        "broadly",
        "countable",
        "uncountable"
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Category theory"
      ],
      "glosses": [
        "A natural isomorphism between a pair of functors satisfying certain conditions, whose existence implies a close relationship between the functors and between their (co)domains; the natural isomorphism, functors, and their (co)domains thought of as a single object."
      ],
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "natural isomorphism",
          "natural isomorphism"
        ],
        [
          "functor",
          "functor"
        ],
        [
          "co",
          "codomain"
        ],
        [
          "domain",
          "domain"
        ],
        [
          "object",
          "object"
        ]
      ],
      "qualifier": "strictly",
      "raw_glosses": [
        "(category theory, strictly) A natural isomorphism between a pair of functors satisfying certain conditions, whose existence implies a close relationship between the functors and between their (co)domains; the natural isomorphism, functors, and their (co)domains thought of as a single object."
      ],
      "senseid": [
        "en:category"
      ],
      "tags": [
        "countable",
        "uncountable"
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Category theory"
      ],
      "examples": [
        {
          "text": "Meronyms: adjoint, left adjoint, right adjoint"
        }
      ],
      "glosses": [
        "A natural isomorphism between a pair of functors satisfying certain conditions, whose existence implies a close relationship between the functors and between their (co)domains; the natural isomorphism, functors, and their (co)domains thought of as a single object.",
        "A natural isomorphism Φ: operatorname Hom_( mathcal )C(G·,·)→ operatorname Hom_( mathcal )D(·,F·) (where the hom-functors are understood as bifunctors from 𝒟^( operatorname )op×𝒞 to mathbf Set). See Adjoint functors on Wikipedia.Wikipedia."
      ],
      "links": [
        [
          "category theory",
          "category theory"
        ],
        [
          "natural isomorphism",
          "natural isomorphism"
        ],
        [
          "functor",
          "functor"
        ],
        [
          "co",
          "codomain"
        ],
        [
          "domain",
          "domain"
        ],
        [
          "object",
          "object"
        ],
        [
          "covariant",
          "covariant"
        ],
        [
          "bifunctor",
          "bifunctor"
        ],
        [
          "Adjoint functors",
          "w:Adjoint functors"
        ]
      ],
      "qualifier": "strictly",
      "raw_glosses": [
        "(category theory, strictly) A natural isomorphism between a pair of functors satisfying certain conditions, whose existence implies a close relationship between the functors and between their (co)domains; the natural isomorphism, functors, and their (co)domains thought of as a single object.",
        "(formally, given two categories 𝒞 and 𝒟 and (covariant) functors F:𝒞→𝒟 and G:𝒟→𝒞) A natural isomorphism Φ: operatorname Hom_( mathcal )C(G·,·)→ operatorname Hom_( mathcal )D(·,F·) (where the hom-functors are understood as bifunctors from 𝒟^( operatorname )op×𝒞 to mathbf Set). See Adjoint functors on Wikipedia.Wikipedia."
      ],
      "senseid": [
        "en:category"
      ],
      "tags": [
        "countable",
        "formal",
        "uncountable"
      ],
      "topics": [
        "category-theory",
        "computing",
        "engineering",
        "mathematics",
        "natural-sciences",
        "physical-sciences",
        "sciences"
      ]
    }
  ],
  "sounds": [
    {
      "audio": "LL-Q1860 (eng)-Flame, not lame-adjunction.wav",
      "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/95/LL-Q1860_%28eng%29-Flame%2C_not_lame-adjunction.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-adjunction.wav.mp3",
      "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/9/95/LL-Q1860_%28eng%29-Flame%2C_not_lame-adjunction.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-adjunction.wav.ogg"
    }
  ],
  "translations": [
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "the act of joining",
      "tags": [
        "feminine"
      ],
      "word": "adiunkcja"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "the act of joining",
      "tags": [
        "feminine"
      ],
      "word": "adjunção"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "a form of similarity between a pair of categories mapped to each other by dual morphisms",
      "tags": [
        "feminine"
      ],
      "word": "adiunkcja"
    }
  ],
  "wikipedia": [
    "adjunction"
  ],
  "word": "adjunction"
}

Download raw JSONL data for adjunction meaning in All languages combined (7.2kB)

{
  "called_from": "form_descriptions/1831",
  "msg": "unrecognized sense qualifier: formally, given two categories 𝒞 and 𝒟 and (covariant) functors F:𝒞→𝒟 and G:𝒟→𝒞",
  "path": [
    "adjunction"
  ],
  "section": "English",
  "subsection": "noun",
  "title": "adjunction",
  "trace": ""
}

{
  "called_from": "form_descriptions/1831",
  "msg": "unrecognized sense qualifier: formally, given two categories 𝒞 and 𝒟 and (covariant) functors F:𝒞→𝒟 and G:𝒟→𝒞",
  "path": [
    "adjunction"
  ],
  "section": "English",
  "subsection": "noun",
  "title": "adjunction",
  "trace": ""
}

This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-01-13 from the enwiktionary dump dated 2025-01-01 using wiktextract (4ba5975 and 4ed51a5). 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.