"homomorphism" meaning in All languages combined

See homomorphism on Wiktionary

Noun [English]

Forms: homomorphisms [plural]
Etymology: homo- + morphism. Etymology templates: {{prefix|en|homo|morphism}} homo- + morphism Head templates: {{en-noun}} homomorphism (plural homomorphisms)
  1. (algebra) A structure-preserving map between two algebraic structures of the same type, such as groups, rings, or vector spaces. Categories (topical): Algebra, Functions Hyponyms (structure-preserving map between algebraic structures): automorphism, endomorphism, epimorphism, isomorphism, linear map, monomorphism Translations (notion in mathematics): تَشَاكُل (tašākul) [masculine] (Arabic), հոմոմորֆիզմը (homomorfizmə) (Armenian), homomorfismus [masculine] (Czech), homomorfi [common-gender] (Danish), homomorfisme [neuter] (Dutch), homomorfismi (Finnish), homomorphisme [masculine] (French), ჰომომორფიზმი (homomorpizmi) (Georgian), Homomorphismus [masculine] (German), ομομορφισμός (omomorfismós) [masculine] (Greek), homomorfizmus (Hungarian), mótun [feminine] (Icelandic), sammótun [feminine] (Icelandic), homamorfacht [feminine] (Irish), omomorfismo [masculine] (Italian), homomorfizmas (Lithuanian), همریختی (Persian), homomorfizm [masculine] (Polish), homomorfismo [masculine] (Portuguese), ਹੋਮੋਮੌਰਫਿਜ਼ਮ (homomaurphizam) (Punjabi), гомоморфи́зм (gomomorfízm) [masculine] (Russian), homomorfizam [masculine] (Serbo-Croatian), homomorfizem [masculine] (Slovene), homomorfismo [masculine] (Spanish), homomorfi [common-gender] (Swedish), homomorfism [common-gender] (Swedish), гомоморфізм (homomorfizm) [masculine] (Ukrainian), phép đồng cấu (Vietnamese)
    Sense id: en-homomorphism-en-noun-en:mathematics Categories (other): English entries with incorrect language header Disambiguation of English entries with incorrect language header: 49 51 Topics: algebra, mathematics, sciences Disambiguation of 'structure-preserving map between algebraic structures': 79 21 Disambiguation of 'notion in mathematics': 67 33
  2. (biology) A similar appearance of two unrelated organisms or structures, as for example with fish and whales. Categories (topical): Biology, Logic
    Sense id: en-homomorphism-en-noun-en:biology Disambiguation of Logic: 44 56 Categories (other): English entries with incorrect language header, English entries with topic categories using raw markup, English terms prefixed with homo- Disambiguation of English entries with incorrect language header: 49 51 Disambiguation of English entries with topic categories using raw markup: 40 60 Disambiguation of English terms prefixed with homo-: 38 62 Topics: biology, natural-sciences
The following are not (yet) sense-disambiguated
Derived forms: connecting homomorphism, ring homomorphism, semigroup homomorphism, boundary homomorphism, homomorphous Related terms: morphism, convergent evolution [biology, natural-sciences]

Inflected forms

Download JSON data for homomorphism meaning in All languages combined (9.0kB)

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  "derived": [
    {
      "_dis1": "0 0",
      "word": "connecting homomorphism"
    },
    {
      "_dis1": "0 0",
      "word": "ring homomorphism"
    },
    {
      "_dis1": "0 0",
      "word": "semigroup homomorphism"
    },
    {
      "_dis1": "0 0",
      "word": "boundary homomorphism"
    },
    {
      "_dis1": "0 0",
      "word": "homomorphous"
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        {
          "text": "Coordinate term: homology"
        },
        {
          "text": "A field homomorphism is a map from one field to another one which is additive, multiplicative, zero-preserving, and unit-preserving."
        },
        {
          "text": "1954, Kuo-Tsai Chen, Iterated Integrals and Exponential Homomorphisms, Proceedings of the London Mathematical Society, Reprinted in 2001, Philippe Tondeur (editor), Collected Papers of K.-T. Chen, Birkhäuser, page 54,\nThis motivates a generalization, and exponential homomorphisms are now defined, in an algebraic fashion, from certain free products to formal power series rings with non-commutative indeterminates."
        },
        {
          "ref": "1997, Glen E. Bredon, Sheaf Theory, 2nd edition, Springer, page 8",
          "text": "A homomorphism of presheaves h#x3A;A#x5C;rightarrowB is a collection of homomorphisms h#x5F;U#x3A;A(U)#x5C;rightarrowB(U) commuting with restrictions.",
          "type": "quotation"
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          "ref": "2003, Brian C. Hall, Lie Groups, Lie Algebras, and Representations: An Elementary Introduction, Springer, page 17",
          "text": "Definition 1.15. Let G and H be matrix Lie groups. A map #x5C;Phi from G to H is called a Lie group homomorphism if (1) #x5C;Phi is a group homomorphism and (2) #x5C;Phi is continuous.",
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          "_dis1": "79 21",
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          "_dis1": "79 21",
          "sense": "structure-preserving map between algebraic structures",
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          "_dis1": "79 21",
          "sense": "structure-preserving map between algebraic structures",
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          "_dis1": "79 21",
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          "word": "isomorphism"
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          "_dis1": "79 21",
          "sense": "structure-preserving map between algebraic structures",
          "word": "linear map"
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          "_dis1": "79 21",
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          "word": "monomorphism"
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      "id": "en-homomorphism-en-noun-en:mathematics",
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        {
          "_dis1": "67 33",
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          "roman": "tašākul",
          "sense": "notion in mathematics",
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          "_dis1": "67 33",
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          "sense": "notion in mathematics",
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          "sense": "notion in mathematics",
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          "code": "de",
          "lang": "German",
          "sense": "notion in mathematics",
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            "masculine"
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          "word": "Homomorphismus"
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          "code": "el",
          "lang": "Greek",
          "roman": "omomorfismós",
          "sense": "notion in mathematics",
          "tags": [
            "masculine"
          ],
          "word": "ομομορφισμός"
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          "_dis1": "67 33",
          "code": "hu",
          "lang": "Hungarian",
          "sense": "notion in mathematics",
          "word": "homomorfizmus"
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          "code": "is",
          "lang": "Icelandic",
          "sense": "notion in mathematics",
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          "_dis1": "67 33",
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          "lang": "Icelandic",
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          "_dis1": "67 33",
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          "lang": "Irish",
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        {
          "_dis1": "67 33",
          "code": "it",
          "lang": "Italian",
          "sense": "notion in mathematics",
          "tags": [
            "masculine"
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          "word": "omomorfismo"
        },
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          "_dis1": "67 33",
          "code": "lt",
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          "sense": "notion in mathematics",
          "word": "homomorfizmas"
        },
        {
          "_dis1": "67 33",
          "code": "fa",
          "lang": "Persian",
          "sense": "notion in mathematics",
          "word": "همریختی"
        },
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          "_dis1": "67 33",
          "code": "pl",
          "lang": "Polish",
          "sense": "notion in mathematics",
          "tags": [
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          "word": "homomorfizm"
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          "_dis1": "67 33",
          "code": "pt",
          "lang": "Portuguese",
          "sense": "notion in mathematics",
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          "word": "homomorfismo"
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        {
          "_dis1": "67 33",
          "code": "pa",
          "lang": "Punjabi",
          "roman": "homomaurphizam",
          "sense": "notion in mathematics",
          "word": "ਹੋਮੋਮੌਰਫਿਜ਼ਮ"
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          "code": "ru",
          "lang": "Russian",
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          "lang": "Spanish",
          "sense": "notion in mathematics",
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          "word": "homomorfismo"
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          "code": "sv",
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          "sense": "notion in mathematics",
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          "_dis1": "67 33",
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          "_dis1": "67 33",
          "code": "uk",
          "lang": "Ukrainian",
          "roman": "homomorfizm",
          "sense": "notion in mathematics",
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          "_dis1": "67 33",
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          "lang": "Vietnamese",
          "sense": "notion in mathematics",
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          "text": "Coordinate term: homology"
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  "wikipedia": [
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  "word": "homomorphism"
}
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      "word": "connecting homomorphism"
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      "word": "ring homomorphism"
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          "text": "Coordinate term: homology"
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        {
          "text": "A field homomorphism is a map from one field to another one which is additive, multiplicative, zero-preserving, and unit-preserving."
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        {
          "text": "1954, Kuo-Tsai Chen, Iterated Integrals and Exponential Homomorphisms, Proceedings of the London Mathematical Society, Reprinted in 2001, Philippe Tondeur (editor), Collected Papers of K.-T. Chen, Birkhäuser, page 54,\nThis motivates a generalization, and exponential homomorphisms are now defined, in an algebraic fashion, from certain free products to formal power series rings with non-commutative indeterminates."
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          "ref": "1997, Glen E. Bredon, Sheaf Theory, 2nd edition, Springer, page 8",
          "text": "A homomorphism of presheaves h#x3A;A#x5C;rightarrowB is a collection of homomorphisms h#x5F;U#x3A;A(U)#x5C;rightarrowB(U) commuting with restrictions.",
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  "translations": [
    {
      "code": "ar",
      "lang": "Arabic",
      "roman": "tašākul",
      "sense": "notion in mathematics",
      "tags": [
        "masculine"
      ],
      "word": "تَشَاكُل"
    },
    {
      "code": "hy",
      "lang": "Armenian",
      "roman": "homomorfizmə",
      "sense": "notion in mathematics",
      "word": "հոմոմորֆիզմը"
    },
    {
      "code": "cs",
      "lang": "Czech",
      "sense": "notion in mathematics",
      "tags": [
        "masculine"
      ],
      "word": "homomorfismus"
    },
    {
      "code": "da",
      "lang": "Danish",
      "sense": "notion in mathematics",
      "tags": [
        "common-gender"
      ],
      "word": "homomorfi"
    },
    {
      "code": "nl",
      "lang": "Dutch",
      "sense": "notion in mathematics",
      "tags": [
        "neuter"
      ],
      "word": "homomorfisme"
    },
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "notion in mathematics",
      "word": "homomorfismi"
    },
    {
      "code": "fr",
      "lang": "French",
      "sense": "notion in mathematics",
      "tags": [
        "masculine"
      ],
      "word": "homomorphisme"
    },
    {
      "code": "ka",
      "lang": "Georgian",
      "roman": "homomorpizmi",
      "sense": "notion in mathematics",
      "word": "ჰომომორფიზმი"
    },
    {
      "code": "de",
      "lang": "German",
      "sense": "notion in mathematics",
      "tags": [
        "masculine"
      ],
      "word": "Homomorphismus"
    },
    {
      "code": "el",
      "lang": "Greek",
      "roman": "omomorfismós",
      "sense": "notion in mathematics",
      "tags": [
        "masculine"
      ],
      "word": "ομομορφισμός"
    },
    {
      "code": "hu",
      "lang": "Hungarian",
      "sense": "notion in mathematics",
      "word": "homomorfizmus"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "notion in mathematics",
      "tags": [
        "feminine"
      ],
      "word": "mótun"
    },
    {
      "code": "is",
      "lang": "Icelandic",
      "sense": "notion in mathematics",
      "tags": [
        "feminine"
      ],
      "word": "sammótun"
    },
    {
      "code": "ga",
      "lang": "Irish",
      "sense": "notion in mathematics",
      "tags": [
        "feminine"
      ],
      "word": "homamorfacht"
    },
    {
      "code": "it",
      "lang": "Italian",
      "sense": "notion in mathematics",
      "tags": [
        "masculine"
      ],
      "word": "omomorfismo"
    },
    {
      "code": "lt",
      "lang": "Lithuanian",
      "sense": "notion in mathematics",
      "word": "homomorfizmas"
    },
    {
      "code": "fa",
      "lang": "Persian",
      "sense": "notion in mathematics",
      "word": "همریختی"
    },
    {
      "code": "pl",
      "lang": "Polish",
      "sense": "notion in mathematics",
      "tags": [
        "masculine"
      ],
      "word": "homomorfizm"
    },
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "notion in mathematics",
      "tags": [
        "masculine"
      ],
      "word": "homomorfismo"
    },
    {
      "code": "pa",
      "lang": "Punjabi",
      "roman": "homomaurphizam",
      "sense": "notion in mathematics",
      "word": "ਹੋਮੋਮੌਰਫਿਜ਼ਮ"
    },
    {
      "code": "ru",
      "lang": "Russian",
      "roman": "gomomorfízm",
      "sense": "notion in mathematics",
      "tags": [
        "masculine"
      ],
      "word": "гомоморфи́зм"
    },
    {
      "code": "sh",
      "lang": "Serbo-Croatian",
      "sense": "notion in mathematics",
      "tags": [
        "masculine"
      ],
      "word": "homomorfizam"
    },
    {
      "code": "sl",
      "lang": "Slovene",
      "sense": "notion in mathematics",
      "tags": [
        "masculine"
      ],
      "word": "homomorfizem"
    },
    {
      "code": "es",
      "lang": "Spanish",
      "sense": "notion in mathematics",
      "tags": [
        "masculine"
      ],
      "word": "homomorfismo"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "notion in mathematics",
      "tags": [
        "common-gender"
      ],
      "word": "homomorfi"
    },
    {
      "code": "sv",
      "lang": "Swedish",
      "sense": "notion in mathematics",
      "tags": [
        "common-gender"
      ],
      "word": "homomorfism"
    },
    {
      "code": "uk",
      "lang": "Ukrainian",
      "roman": "homomorfizm",
      "sense": "notion in mathematics",
      "tags": [
        "masculine"
      ],
      "word": "гомоморфізм"
    },
    {
      "code": "vi",
      "lang": "Vietnamese",
      "sense": "notion in mathematics",
      "word": "phép đồng cấu"
    }
  ],
  "wikipedia": [
    "homomorphism"
  ],
  "word": "homomorphism"
}

This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-05-03 from the enwiktionary dump dated 2024-05-02 using wiktextract (f4fd8c9 and c9440ce). 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.