"homomorphism" meaning in English

See homomorphism in All languages combined, or Wiktionary

Noun

Audio: LL-Q1860 (eng)-Flame, not lame-homomorphism.wav Forms: homomorphisms [plural]
Etymology: From 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), समाकारिता (samākāritā) (Hindi), 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, English terms prefixed with homo-, Entries with translation boxes, Pages with 1 entry, Pages with entries Disambiguation of English entries with incorrect language header: 50 50 Disambiguation of English terms prefixed with homo-: 46 54 Disambiguation of Entries with translation boxes: 51 49 Disambiguation of Pages with 1 entry: 58 42 Disambiguation of Pages with entries: 48 52 Topics: algebra, mathematics, sciences Disambiguation of 'structure-preserving map between algebraic structures': 77 23 Disambiguation of 'notion in mathematics': 88 12
  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: 43 57 Categories (other): English entries with incorrect language header, English terms prefixed with homo-, Entries with translation boxes, Pages with entries, Terms with Arabic translations, Terms with Armenian translations, Terms with Czech translations, Terms with Danish translations, Terms with Dutch translations, Terms with Finnish translations, Terms with French translations, Terms with Georgian translations, Terms with German translations, Terms with Greek translations, Terms with Hindi translations, Terms with Hungarian translations, Terms with Icelandic translations, Terms with Irish translations, Terms with Italian translations, Terms with Lithuanian translations, Terms with Persian translations, Terms with Polish translations, Terms with Portuguese translations, Terms with Punjabi translations, Terms with Russian translations, Terms with Serbo-Croatian translations, Terms with Slovene translations, Terms with Spanish translations, Terms with Swedish translations, Terms with Ukrainian translations, Terms with Vietnamese translations Disambiguation of English entries with incorrect language header: 50 50 Disambiguation of English terms prefixed with homo-: 46 54 Disambiguation of Entries with translation boxes: 51 49 Disambiguation of Pages with entries: 48 52 Disambiguation of Terms with Arabic translations: 38 62 Disambiguation of Terms with Armenian translations: 37 63 Disambiguation of Terms with Czech translations: 37 63 Disambiguation of Terms with Danish translations: 40 60 Disambiguation of Terms with Dutch translations: 38 62 Disambiguation of Terms with Finnish translations: 38 62 Disambiguation of Terms with French translations: 38 62 Disambiguation of Terms with Georgian translations: 37 63 Disambiguation of Terms with German translations: 39 61 Disambiguation of Terms with Greek translations: 38 62 Disambiguation of Terms with Hindi translations: 39 61 Disambiguation of Terms with Hungarian translations: 37 63 Disambiguation of Terms with Icelandic translations: 39 61 Disambiguation of Terms with Irish translations: 38 62 Disambiguation of Terms with Italian translations: 38 62 Disambiguation of Terms with Lithuanian translations: 37 63 Disambiguation of Terms with Persian translations: 37 63 Disambiguation of Terms with Polish translations: 38 62 Disambiguation of Terms with Portuguese translations: 40 60 Disambiguation of Terms with Punjabi translations: 38 62 Disambiguation of Terms with Russian translations: 39 61 Disambiguation of Terms with Serbo-Croatian translations: 37 63 Disambiguation of Terms with Slovene translations: 37 63 Disambiguation of Terms with Spanish translations: 41 59 Disambiguation of Terms with Swedish translations: 38 62 Disambiguation of Terms with Ukrainian translations: 38 62 Disambiguation of Terms with Vietnamese translations: 37 63 Topics: biology, natural-sciences
The following are not (yet) sense-disambiguated
Derived forms: boundary homomorphism, connecting homomorphism, graph homomorphism, homomorphous, ring homomorphism, semigroup homomorphism Related terms: morphism, convergent evolution [biology, natural-sciences]

Inflected forms

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  "derived": [
    {
      "_dis1": "0 0",
      "word": "boundary homomorphism"
    },
    {
      "_dis1": "0 0",
      "word": "connecting homomorphism"
    },
    {
      "_dis1": "0 0",
      "word": "graph homomorphism"
    },
    {
      "_dis1": "0 0",
      "word": "homomorphous"
    },
    {
      "_dis1": "0 0",
      "word": "ring homomorphism"
    },
    {
      "_dis1": "0 0",
      "word": "semigroup 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."
        },
        {
          "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": "quote"
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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": "77 23",
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          "_dis1": "88 12",
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          "roman": "homomorpizmi",
          "sense": "notion in mathematics",
          "word": "ჰომომორფიზმი"
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          "sense": "notion in mathematics",
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          "text": "Coordinate term: homology"
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      "glosses": [
        "A similar appearance of two unrelated organisms or structures, as for example with fish and whales."
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      ],
      "raw_glosses": [
        "(biology) A similar appearance of two unrelated organisms or structures, as for example with fish and whales."
      ],
      "senseid": [
        "en:biology"
      ],
      "topics": [
        "biology",
        "natural-sciences"
      ]
    }
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  "wikipedia": [
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  "word": "homomorphism"
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{
  "categories": [
    "English countable nouns",
    "English entries with incorrect language header",
    "English lemmas",
    "English nouns",
    "English terms prefixed with homo-",
    "Entries with translation boxes",
    "Pages with 1 entry",
    "Pages with entries",
    "Terms with Arabic translations",
    "Terms with Armenian translations",
    "Terms with Czech translations",
    "Terms with Danish translations",
    "Terms with Dutch translations",
    "Terms with Finnish translations",
    "Terms with French translations",
    "Terms with Georgian translations",
    "Terms with German translations",
    "Terms with Greek translations",
    "Terms with Hindi translations",
    "Terms with Hungarian translations",
    "Terms with Icelandic translations",
    "Terms with Irish translations",
    "Terms with Italian translations",
    "Terms with Lithuanian translations",
    "Terms with Persian translations",
    "Terms with Polish translations",
    "Terms with Portuguese translations",
    "Terms with Punjabi translations",
    "Terms with Russian translations",
    "Terms with Serbo-Croatian translations",
    "Terms with Slovene translations",
    "Terms with Spanish translations",
    "Terms with Swedish translations",
    "Terms with Ukrainian translations",
    "Terms with Vietnamese translations",
    "en:Logic"
  ],
  "derived": [
    {
      "word": "boundary homomorphism"
    },
    {
      "word": "connecting homomorphism"
    },
    {
      "word": "graph homomorphism"
    },
    {
      "word": "homomorphous"
    },
    {
      "word": "ring homomorphism"
    },
    {
      "word": "semigroup homomorphism"
    }
  ],
  "etymology_templates": [
    {
      "args": {
        "1": "en",
        "2": "homo",
        "3": "morphism"
      },
      "expansion": "homo- + morphism",
      "name": "prefix"
    }
  ],
  "etymology_text": "From homo- + morphism.",
  "forms": [
    {
      "form": "homomorphisms",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "homomorphism (plural homomorphisms)",
      "name": "en-noun"
    }
  ],
  "hyponyms": [
    {
      "sense": "structure-preserving map between algebraic structures",
      "word": "automorphism"
    },
    {
      "sense": "structure-preserving map between algebraic structures",
      "word": "endomorphism"
    },
    {
      "sense": "structure-preserving map between algebraic structures",
      "word": "epimorphism"
    },
    {
      "sense": "structure-preserving map between algebraic structures",
      "word": "isomorphism"
    },
    {
      "sense": "structure-preserving map between algebraic structures",
      "word": "linear map"
    },
    {
      "sense": "structure-preserving map between algebraic structures",
      "word": "monomorphism"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "related": [
    {
      "word": "morphism"
    },
    {
      "topics": [
        "biology",
        "natural-sciences"
      ],
      "word": "convergent evolution"
    }
  ],
  "senses": [
    {
      "categories": [
        "English terms with quotations",
        "en:Algebra",
        "en:Functions"
      ],
      "examples": [
        {
          "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": "quote"
        },
        {
          "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.",
          "type": "quote"
        }
      ],
      "glosses": [
        "A structure-preserving map between two algebraic structures of the same type, such as groups, rings, or vector spaces."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "map",
          "map#English"
        ],
        [
          "algebraic structure",
          "algebraic structure"
        ],
        [
          "groups",
          "group#English"
        ],
        [
          "rings",
          "ring#English"
        ],
        [
          "vector space",
          "vector space"
        ]
      ],
      "raw_glosses": [
        "(algebra) A structure-preserving map between two algebraic structures of the same type, such as groups, rings, or vector spaces."
      ],
      "senseid": [
        "en:mathematics"
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    },
    {
      "categories": [
        "en:Biology"
      ],
      "examples": [
        {
          "text": "Coordinate term: homology"
        }
      ],
      "glosses": [
        "A similar appearance of two unrelated organisms or structures, as for example with fish and whales."
      ],
      "links": [
        [
          "biology",
          "biology"
        ],
        [
          "appearance",
          "appearance"
        ]
      ],
      "raw_glosses": [
        "(biology) A similar appearance of two unrelated organisms or structures, as for example with fish and whales."
      ],
      "senseid": [
        "en:biology"
      ],
      "topics": [
        "biology",
        "natural-sciences"
      ]
    }
  ],
  "sounds": [
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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": "hi",
      "lang": "Hindi",
      "roman": "samākāritā",
      "sense": "notion in mathematics",
      "word": "समाकारिता"
    },
    {
      "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"
}

Download raw JSONL data for homomorphism meaning in English (8.6kB)


This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). 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.