See isomorphism on Wiktionary
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"Terms with Hindi translations",
"Terms with Hungarian translations",
"Terms with Icelandic translations",
"Terms with Italian translations",
"Terms with Kazakh translations",
"Terms with Mandarin translations",
"Terms with Portuguese translations",
"Terms with Russian translations",
"Terms with Serbo-Croatian translations",
"Terms with Spanish translations",
"Terms with Tagalog translations",
"Terms with Ukrainian translations"
],
"derived": [
{
"word": "Curry-Howard isomorphism"
},
{
"word": "natural isomorphism"
},
{
"word": "quasi-isomorphism"
},
{
"word": "ring isomorphism"
}
],
"etymology_templates": [
{
"args": {
"1": "en",
"2": "iso",
"3": "morphism"
},
"expansion": "iso- + -morphism",
"name": "confix"
}
],
"etymology_text": "From iso- + -morphism.",
"forms": [
{
"form": "isomorphisms",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "~"
},
"expansion": "isomorphism (countable and uncountable, plural isomorphisms)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "isomorphic"
},
{
"word": "isomorphous"
},
{
"urls": [
"https://www.encyclopediaofmath.org/index.php/Isomorphism"
],
"word": "Isomorphism on Encyclopedia of Mathematics"
},
{
"urls": [
"https://ncatlab.org/nlab/show/isomorphism"
],
"word": "isomorphism on nLab"
},
{
"urls": [
"http://mathworld.wolfram.com/Isomorphism.html"
],
"word": "Isomorphism on Wolfram MathWorld"
},
{
"urls": [
"http://mathworld.wolfram.com/GraphIsomorphism.html"
],
"word": "Graph Isomorphism on Wolfram MathWorld"
},
{
"urls": [
"http://mathworld.wolfram.com/NaturalIsomorphism.html"
],
"word": "Natural Isomorphism on Wolfram MathWorld"
}
],
"senses": [
{
"categories": [
"English terms with quotations",
"en:Biology"
],
"glosses": [
"Similarity of form",
"the similarity in form of organisms, which may be due to convergent evolution or shared genetic background, e.g. an algae species in which the haploid and diploid life stages are indistinguishable based on morphology."
],
"links": [
[
"biology",
"biology"
],
[
"similarity",
"similarity"
],
[
"form",
"form"
],
[
"organism",
"organism"
],
[
"convergent evolution",
"convergent evolution"
],
[
"haploid",
"haploid"
],
[
"diploid",
"diploid"
]
],
"raw_glosses": [
"Similarity of form",
"(biology) the similarity in form of organisms, which may be due to convergent evolution or shared genetic background, e.g. an algae species in which the haploid and diploid life stages are indistinguishable based on morphology."
],
"tags": [
"countable",
"uncountable"
],
"topics": [
"biology",
"natural-sciences"
]
},
{
"categories": [
"English terms with quotations",
"en:Chemistry"
],
"examples": [
{
"ref": "1874, C. Rammelsberg, “Crystallographic and chemical relations of the natural sulphides, arsenides, and sulpharsenides”, in The Chemical News and Journal of Physical Science, page 197:",
"text": "The isomorphism of compounds does not prove the isomorphism of their respective constituents.",
"type": "quote"
}
],
"glosses": [
"Similarity of form",
"the similarity in the crystal structures of similar chemical compounds."
],
"links": [
[
"chemistry",
"chemistry"
],
[
"crystal",
"crystal"
],
[
"chemical",
"chemical"
],
[
"compound",
"compound"
]
],
"raw_glosses": [
"Similarity of form",
"(chemistry) the similarity in the crystal structures of similar chemical compounds."
],
"tags": [
"countable",
"uncountable"
],
"topics": [
"chemistry",
"natural-sciences",
"physical-sciences"
]
},
{
"categories": [
"English terms with quotations",
"en:Sociology"
],
"glosses": [
"Similarity of form",
"the similarity in the structure or processes of different organizations."
],
"links": [
[
"sociology",
"sociology"
],
[
"processes",
"processes"
],
[
"organization",
"organization"
]
],
"raw_glosses": [
"Similarity of form",
"(sociology) the similarity in the structure or processes of different organizations."
],
"tags": [
"countable",
"uncountable"
],
"topics": [
"human-sciences",
"sciences",
"social-science",
"sociology"
]
},
{
"categories": [
"English terms with quotations"
],
"examples": [
{
"ref": "1984, Brigitte Asbach-Schnitker, “Introduction”, in Mercury or The Secret and Swift Messenger, →ISBN:",
"text": "The postulated isomorphism between words and things constitutes the characterizing feature of all philosophically based universal languages.",
"type": "quote"
}
],
"glosses": [
"Similarity of form"
],
"tags": [
"countable",
"uncountable"
]
},
{
"categories": [
"en:Functions"
],
"glosses": [
"A one-to-one correspondence",
"A bijection f such that both f and its inverse f⁻¹ are homomorphisms, that is, structure-preserving mappings."
],
"links": [
[
"bijection",
"bijection"
],
[
"inverse",
"inverse function"
],
[
"homomorphism",
"homomorphism"
]
],
"qualifier": "group algebra",
"raw_glosses": [
"A one-to-one correspondence",
"(group algebra) A bijection f such that both f and its inverse f⁻¹ are homomorphisms, that is, structure-preserving mappings."
],
"tags": [
"countable",
"uncountable"
]
},
{
"categories": [
"en:Computer science"
],
"glosses": [
"A one-to-one correspondence",
"a one-to-one correspondence between all the elements of two sets, e.g. the instances of two classes, or the records in two datasets."
],
"links": [
[
"computer science",
"computer science"
],
[
"one-to-one",
"one-to-one"
],
[
"correspondence",
"correspondence"
],
[
"element",
"element"
],
[
"set",
"set"
],
[
"instance",
"instance"
],
[
"class",
"class"
],
[
"record",
"record"
],
[
"dataset",
"dataset"
]
],
"raw_glosses": [
"A one-to-one correspondence",
"(computer science) a one-to-one correspondence between all the elements of two sets, e.g. the instances of two classes, or the records in two datasets."
],
"tags": [
"countable",
"uncountable"
],
"topics": [
"computer",
"computing",
"engineering",
"mathematics",
"natural-sciences",
"physical-sciences",
"science",
"sciences"
]
},
{
"categories": [
"en:Category theory"
],
"glosses": [
"A one-to-one correspondence",
"A morphism which has a two-sided inverse; the composition of the morphism and such an inverse yields either one of two identity morphisms (depending on the order of composition)."
],
"links": [
[
"category theory",
"category theory"
],
[
"morphism",
"morphism"
]
],
"raw_glosses": [
"A one-to-one correspondence",
"(category theory) A morphism which has a two-sided inverse; the composition of the morphism and such an inverse yields either one of two identity morphisms (depending on the order of composition)."
],
"tags": [
"countable",
"uncountable"
],
"topics": [
"category-theory",
"computing",
"engineering",
"mathematics",
"natural-sciences",
"physical-sciences",
"sciences"
]
}
],
"sounds": [
{
"audio": "en-us-isomorphism.ogg",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/a/ae/En-us-isomorphism.ogg/En-us-isomorphism.ogg.mp3",
"ogg_url": "https://upload.wikimedia.org/wikipedia/commons/a/ae/En-us-isomorphism.ogg"
}
],
"synonyms": [
{
"sense": "in category theory",
"word": "iso"
}
],
"translations": [
{
"code": "bg",
"lang": "Bulgarian",
"roman": "izomorfízǎm",
"sense": "the similarity in form of organisms of different ancestry",
"tags": [
"masculine"
],
"word": "изоморфи́зъм"
},
{
"code": "cs",
"lang": "Czech",
"sense": "the similarity in form of organisms of different ancestry",
"tags": [
"masculine"
],
"word": "izomorfismus"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "the similarity in form of organisms of different ancestry",
"word": "isomorfismi"
},
{
"code": "fr",
"lang": "French",
"sense": "the similarity in form of organisms of different ancestry",
"tags": [
"masculine"
],
"word": "isomorphisme"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "the similarity in form of organisms of different ancestry",
"word": "izomorfizmus"
},
{
"code": "it",
"lang": "Italian",
"sense": "the similarity in form of organisms of different ancestry",
"tags": [
"masculine"
],
"word": "isomorfismo"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "the similarity in form of organisms of different ancestry",
"tags": [
"masculine"
],
"word": "isomorfismo"
},
{
"code": "ru",
"lang": "Russian",
"roman": "izomorfízm",
"sense": "the similarity in form of organisms of different ancestry",
"tags": [
"masculine"
],
"word": "изоморфи́зм"
},
{
"code": "sh",
"lang": "Serbo-Croatian",
"sense": "the similarity in form of organisms of different ancestry",
"tags": [
"masculine"
],
"word": "izomorfizam"
},
{
"code": "es",
"lang": "Spanish",
"sense": "the similarity in form of organisms of different ancestry",
"tags": [
"masculine"
],
"word": "isomorfismo"
},
{
"code": "tl",
"lang": "Tagalog",
"sense": "the similarity in form of organisms of different ancestry",
"word": "kasanyuan"
},
{
"code": "uk",
"lang": "Ukrainian",
"roman": "izomorfízm",
"sense": "the similarity in form of organisms of different ancestry",
"tags": [
"masculine"
],
"word": "ізоморфі́зм"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "tónggòu",
"sense": "bidirectionally structure-preserving bijection",
"word": "同構 /同构"
},
{
"code": "cs",
"lang": "Czech",
"sense": "bidirectionally structure-preserving bijection",
"tags": [
"masculine"
],
"word": "izomorfismus"
},
{
"code": "da",
"lang": "Danish",
"sense": "bidirectionally structure-preserving bijection",
"tags": [
"common-gender"
],
"word": "isomorfi"
},
{
"code": "nl",
"lang": "Dutch",
"sense": "bidirectionally structure-preserving bijection",
"tags": [
"neuter"
],
"word": "isomorfisme"
},
{
"code": "eo",
"lang": "Esperanto",
"sense": "bidirectionally structure-preserving bijection",
"word": "izomorfio"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "bidirectionally structure-preserving bijection",
"word": "isomorfismi"
},
{
"code": "de",
"lang": "German",
"sense": "bidirectionally structure-preserving bijection",
"tags": [
"masculine"
],
"word": "Isomorphismus"
},
{
"code": "hi",
"lang": "Hindi",
"roman": "tulyākāritā",
"sense": "bidirectionally structure-preserving bijection",
"word": "तुल्याकारिता"
},
{
"code": "hi",
"lang": "Hindi",
"roman": "samākŕtiktā",
"sense": "bidirectionally structure-preserving bijection",
"word": "समाकृतिकता"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "bidirectionally structure-preserving bijection",
"word": "izomorfia"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "bidirectionally structure-preserving bijection",
"tags": [
"feminine"
],
"word": "einsmótun"
},
{
"code": "kk",
"lang": "Kazakh",
"roman": "izomorfizm",
"sense": "bidirectionally structure-preserving bijection",
"word": "изоморфизм"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "bidirectionally structure-preserving bijection",
"tags": [
"masculine"
],
"word": "isomorfismo"
},
{
"code": "ru",
"lang": "Russian",
"roman": "izomorfizm",
"sense": "bidirectionally structure-preserving bijection",
"tags": [
"masculine"
],
"word": "изоморфизм"
},
{
"code": "es",
"lang": "Spanish",
"sense": "bidirectionally structure-preserving bijection",
"tags": [
"masculine"
],
"word": "isomorfismo"
}
],
"word": "isomorphism"
}
Download raw JSONL data for isomorphism meaning in All languages combined (11.2kB)
{
"called_from": "page/1498/20230118",
"msg": "''Similarity of form'[...]' gloss has examples we want to keep, but there are subglosses.",
"path": [
"isomorphism"
],
"section": "English",
"subsection": "noun",
"title": "isomorphism",
"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 2025-02-22 from the enwiktionary dump dated 2025-02-02 using wiktextract (9e2b7d3 and f2e72e5). 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.