See homomorphism on Wiktionary
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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#58;A#92;rightarrowB is a collection of homomorphisms h#95;U#58;A(U)#92;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 #92;Phi from G to H is called a Lie group homomorphism if (1) #92;Phi is a group homomorphism and (2) #92;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." ], "hyponyms": [ { "_dis1": "77 23", "sense": "structure-preserving map between algebraic structures", "word": "automorphism" }, { "_dis1": "77 23", "sense": "structure-preserving map between algebraic structures", "word": "endomorphism" }, { "_dis1": "77 23", "sense": "structure-preserving map between algebraic structures", "word": "epimorphism" }, { "_dis1": "77 23", "sense": "structure-preserving map between algebraic structures", "word": "isomorphism" }, { "_dis1": "77 23", "sense": "structure-preserving map between algebraic structures", "word": "linear map" }, { "_dis1": "77 23", "sense": "structure-preserving map between algebraic structures", "word": "monomorphism" } ], "id": 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"notion in mathematics", "tags": [ "common-gender" ], "word": "homomorfi" }, { "_dis1": "88 12", "code": "nl", "lang": "Dutch", "sense": "notion in mathematics", "tags": [ "neuter" ], "word": "homomorfisme" }, { "_dis1": "88 12", "code": "fi", "lang": "Finnish", "sense": "notion in mathematics", "word": "homomorfismi" }, { "_dis1": "88 12", "code": "fr", "lang": "French", "sense": "notion in mathematics", "tags": [ "masculine" ], "word": "homomorphisme" }, { "_dis1": "88 12", "code": "ka", "lang": "Georgian", "roman": "homomorpizmi", "sense": "notion in mathematics", "word": "ჰომომორფიზმი" }, { "_dis1": "88 12", "code": "de", "lang": "German", "sense": "notion in mathematics", "tags": [ "masculine" ], "word": "Homomorphismus" }, { "_dis1": "88 12", "code": "el", "lang": "Greek", "roman": "omomorfismós", "sense": "notion in mathematics", "tags": [ "masculine" ], "word": "ομομορφισμός" }, { "_dis1": "88 12", "code": "hi", "lang": "Hindi", "roman": "samākāritā", "sense": "notion in mathematics", "word": "समाकारिता" }, { "_dis1": "88 12", "code": "hu", "lang": "Hungarian", "sense": "notion in mathematics", "word": "homomorfizmus" }, { "_dis1": "88 12", "code": "is", "lang": "Icelandic", "sense": "notion in mathematics", "tags": [ "feminine" ], "word": "mótun" }, { "_dis1": "88 12", "code": "is", "lang": "Icelandic", "sense": "notion in mathematics", "tags": [ "feminine" ], "word": "sammótun" }, { "_dis1": "88 12", "code": "ga", "lang": "Irish", "sense": "notion in mathematics", "tags": [ "feminine" ], "word": "homamorfacht" }, { "_dis1": "88 12", "code": "it", "lang": "Italian", "sense": "notion in mathematics", "tags": [ "masculine" ], "word": "omomorfismo" }, { "_dis1": "88 12", "code": "lt", "lang": "Lithuanian", "sense": "notion in mathematics", "word": "homomorfizmas" }, { "_dis1": "88 12", "code": "fa", "lang": "Persian", "sense": "notion in mathematics", "word": "همریختی" }, { "_dis1": "88 12", "code": "pl", "lang": "Polish", "sense": "notion in mathematics", "tags": [ "masculine" ], "word": "homomorfizm" }, { "_dis1": "88 12", "code": "pt", "lang": "Portuguese", "sense": "notion in mathematics", "tags": [ "masculine" ], "word": "homomorfismo" }, { "_dis1": "88 12", "code": "pa", "lang": "Punjabi", "roman": "homomaurphizam", "sense": "notion in mathematics", "word": "ਹੋਮੋਮੌਰਫਿਜ਼ਮ" }, { "_dis1": "88 12", "code": "ru", "lang": "Russian", "roman": "gomomorfízm", "sense": "notion in mathematics", "tags": [ "masculine" ], "word": "гомоморфи́зм" }, { "_dis1": "88 12", "code": "sh", "lang": "Serbo-Croatian", "sense": "notion in mathematics", "tags": [ "masculine" ], "word": "homomorfizam" }, { "_dis1": "88 12", "code": "sl", "lang": "Slovene", "sense": "notion in mathematics", "tags": [ "masculine" ], "word": "homomorfizem" }, { "_dis1": "88 12", "code": "es", "lang": "Spanish", "sense": "notion in mathematics", "tags": [ "masculine" ], "word": "homomorfismo" }, { "_dis1": "88 12", "code": "sv", "lang": "Swedish", "sense": "notion in mathematics", "tags": [ "common-gender" ], "word": "homomorfi" }, { "_dis1": "88 12", "code": "sv", "lang": "Swedish", "sense": "notion in mathematics", "tags": [ "common-gender" ], "word": "homomorfism" }, { "_dis1": "88 12", "code": "uk", "lang": "Ukrainian", "roman": "homomorfizm", "sense": "notion in mathematics", "tags": [ "masculine" ], "word": "гомоморфізм" }, { "_dis1": "88 12", "code": "vi", "lang": "Vietnamese", "sense": "notion in mathematics", "word": "phép đồng cấu" } ] }, { "categories": [ { "kind": "topical", "langcode": "en", "name": "Biology", "orig": "en:Biology", "parents": [ "Sciences", "All topics", "Fundamental" ], "source": "w" }, { "_dis": "50 50", "kind": "other", "name": "English entries with incorrect language header", "parents": [ "Entries with incorrect language header", "Entry maintenance" ], "source": "w+disamb" }, { "_dis": "46 54", "kind": "other", "name": "English terms prefixed with homo-", "parents": [], "source": "w+disamb" }, { "_dis": "51 49", 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"other", "name": "Terms with Lithuanian translations", "parents": [], "source": "w+disamb" }, { "_dis": "37 63", "kind": "other", "name": "Terms with Persian translations", "parents": [], "source": "w+disamb" }, { "_dis": "38 62", "kind": "other", "name": "Terms with Polish translations", "parents": [], "source": "w+disamb" }, { "_dis": "40 60", "kind": "other", "name": "Terms with Portuguese translations", "parents": [], "source": "w+disamb" }, { "_dis": "38 62", "kind": "other", "name": "Terms with Punjabi translations", "parents": [], "source": "w+disamb" }, { "_dis": "39 61", "kind": "other", "name": "Terms with Russian translations", "parents": [], "source": "w+disamb" }, { "_dis": "37 63", "kind": "other", "name": "Terms with Serbo-Croatian translations", "parents": [], "source": "w+disamb" }, { "_dis": "37 63", "kind": "other", "name": "Terms with Slovene translations", "parents": [], "source": "w+disamb" }, { "_dis": "41 59", "kind": "other", "name": "Terms with Spanish translations", "parents": [], "source": "w+disamb" }, { "_dis": "38 62", "kind": "other", "name": "Terms with Swedish translations", "parents": [], "source": "w+disamb" }, { "_dis": "38 62", "kind": "other", "name": "Terms with Ukrainian translations", "parents": [], "source": "w+disamb" }, { "_dis": "37 63", "kind": "other", "name": "Terms with Vietnamese translations", "parents": [], "source": "w+disamb" }, { "_dis": "43 57", "kind": "topical", "langcode": "en", "name": "Logic", "orig": "en:Logic", "parents": [ "Formal sciences", "Philosophy", "Sciences", "All topics", "Fundamental" ], "source": "w+disamb" } ], "examples": [ { "text": "Coordinate term: homology" } ], "glosses": [ "A similar appearance of two unrelated organisms or structures, as for example with fish and whales." ], "id": "en-homomorphism-en-noun-en:biology", "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": [ { "audio": "LL-Q1860 (eng)-Flame, not lame-homomorphism.wav", "mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/0/05/LL-Q1860_%28eng%29-Flame%2C_not_lame-homomorphism.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-homomorphism.wav.mp3", "ogg_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/0/05/LL-Q1860_%28eng%29-Flame%2C_not_lame-homomorphism.wav/LL-Q1860_%28eng%29-Flame%2C_not_lame-homomorphism.wav.ogg" } ], "wikipedia": [ "homomorphism" ], "word": "homomorphism" }
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mathematics", "tags": [ "masculine" ], "word": "гомоморфізм" }, { "code": "vi", "lang": "Vietnamese", "sense": "notion in mathematics", "word": "phép đồng cấu" } ], "wikipedia": [ "homomorphism" ], "word": "homomorphism" }
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