See injective on Wiktionary
{
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"_dis1": "0 0 0 0",
"word": "injective cogenerator"
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"word": "injective dimension"
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"_dis1": "0 0 0 0",
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"_dis1": "0 0 0 0",
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"_dis1": "0 0 0 0",
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{
"_dis1": "0 0 0 0",
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{
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"etymology_text": "This term was introduced by Nicolas Bourbaki in his treatise Éléments de mathématique.",
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"Of, relating to, or being an injection: such that each element of the image (or range) is associated with at most one element of the preimage (or domain); inverse-deterministic"
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"(mathematics) Of, relating to, or being an injection: such that each element of the image (or range) is associated with at most one element of the preimage (or domain); inverse-deterministic"
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"_dis1": "68 10 17 5",
"code": "ca",
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"sense": "inverse-deterministic",
"word": "injectiu"
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{
"_dis1": "68 10 17 5",
"code": "cmn",
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"sense": "inverse-deterministic",
"word": "內射的"
},
{
"_dis1": "68 10 17 5",
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "nèishède",
"sense": "inverse-deterministic",
"word": "内射的"
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{
"_dis1": "68 10 17 5",
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"roman": "dānshède",
"sense": "inverse-deterministic",
"word": "单射的"
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"code": "cs",
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"word": "injektiv"
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"word": "injektiv"
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"_dis1": "68 10 17 5",
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"roman": "amfimonótimi",
"sense": "inverse-deterministic",
"word": "αμφιμονότιμη"
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"_dis1": "68 10 17 5",
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"sense": "inverse-deterministic",
"word": "inteilgeach"
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"_dis1": "68 10 17 5",
"alt": "にゅうしゃの",
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"roman": "nyuushyano",
"sense": "inverse-deterministic",
"word": "入射の"
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"alt": "たんしゃの",
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"word": "単射の"
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"word": "różnowartościowa"
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{
"_dis1": "68 10 17 5",
"code": "pt",
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"sense": "inverse-deterministic",
"word": "injetivo"
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"_dis1": "68 10 17 5",
"code": "ro",
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"sense": "inverse-deterministic",
"word": "injectiv"
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{
"_dis1": "68 10 17 5",
"code": "ru",
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"roman": "inʺjektívnyj",
"sense": "inverse-deterministic",
"word": "инъекти́вный"
},
{
"_dis1": "68 10 17 5",
"code": "es",
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"sense": "inverse-deterministic",
"word": "inyectivo"
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"Loosely, having a certain generalizing property, abstracted from the study of ℚ as a ℤ-module. Formally, such that any short exact sequence of (left) R-modules beginning with M splits, or any of several equivalent statements: See Injective module."
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"injectif",
"injectif#French"
]
],
"tags": [
"feminine",
"form-of",
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]
}
],
"sounds": [
{
"ipa": "/ɛ̃.ʒɛk.tiv/"
},
{
"homophone": "injectives"
}
],
"word": "injective"
}
{
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"Terms with Czech translations",
"Terms with Danish translations",
"Terms with Finnish translations",
"Terms with French translations",
"Terms with German translations",
"Terms with Greek translations",
"Terms with Icelandic translations",
"Terms with Irish translations",
"Terms with Japanese translations",
"Terms with Mandarin translations",
"Terms with Polish translations",
"Terms with Portuguese translations",
"Terms with Romanian translations",
"Terms with Russian translations",
"Terms with Spanish translations",
"Terms with Swedish translations"
],
"derived": [
{
"word": "injective cogenerator"
},
{
"word": "injective dimension"
},
{
"word": "injective function"
},
{
"word": "injective hull"
},
{
"word": "injective map"
},
{
"word": "injective module"
},
{
"word": "injective object"
},
{
"word": "injective patch"
},
{
"word": "injective sheaf"
}
],
"etymology_text": "This term was introduced by Nicolas Bourbaki in his treatise Éléments de mathématique.",
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"lang_code": "en",
"pos": "adj",
"related": [
{
"word": "injectal"
},
{
"word": "injectively"
},
{
"word": "bijective"
},
{
"word": "surjective"
}
],
"senses": [
{
"categories": [
"en:Mathematics"
],
"glosses": [
"Of, relating to, or being an injection: such that each element of the image (or range) is associated with at most one element of the preimage (or domain); inverse-deterministic"
],
"links": [
[
"mathematics",
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"raw_glosses": [
"(mathematics) Of, relating to, or being an injection: such that each element of the image (or range) is associated with at most one element of the preimage (or domain); inverse-deterministic"
],
"synonyms": [
{
"word": "one-to-one"
}
],
"tags": [
"not-comparable"
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
"en:Algebra"
],
"glosses": [
"Loosely, having a certain generalizing property, abstracted from the study of ℚ as a ℤ-module. Formally, such that any short exact sequence of (left) R-modules beginning with M splits, or any of several equivalent statements: See Injective module."
],
"links": [
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"qualifier": "module theory",
"raw_glosses": [
"(algebra, module theory, of a (left) module M over a ring R) Loosely, having a certain generalizing property, abstracted from the study of ℚ as a ℤ-module. Formally, such that any short exact sequence of (left) R-modules beginning with M splits, or any of several equivalent statements: See Injective module."
],
"raw_tags": [
"of a (left) module M over a ring R"
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"tags": [
"not-comparable"
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"topics": [
"algebra",
"mathematics",
"sciences"
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},
{
"categories": [
"en:Category theory"
],
"glosses": [
"Loosely, having a property analogous to that which characterizes injective modules (see above). Formally, such that, given a monomorphism f:X→Y in C, for every morphism g:X→Q there exists a morphism h:Y→Q such that h∘f=g; see Injective object."
],
"links": [
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"category theory",
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"monomorphism",
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"morphism",
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"qualifier": "most generally",
"raw_glosses": [
"(category theory, most generally, of an object Q in a category C) Loosely, having a property analogous to that which characterizes injective modules (see above). Formally, such that, given a monomorphism f:X→Y in C, for every morphism g:X→Q there exists a morphism h:Y→Q such that h∘f=g; see Injective object."
],
"raw_tags": [
"of an object Q in a category C"
],
"tags": [
"not-comparable"
],
"topics": [
"category-theory",
"computing",
"engineering",
"mathematics",
"natural-sciences",
"physical-sciences",
"sciences"
]
},
{
"glosses": [
"Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above)."
],
"links": [
[
"homological algebra",
"homological algebra"
],
[
"resolution",
"resolution"
]
],
"qualifier": "homological algebra",
"raw_glosses": [
"(homological algebra, of a resolution) Such that the objects (usually modules) involved in the resolution are injective (in the algebraic senses above)."
],
"raw_tags": [
"of a resolution"
],
"tags": [
"not-comparable"
]
}
],
"sounds": [
{
"ipa": "/ɪnˈd͡ʒɛktɪv/"
},
{
"audio": "en-us-injective.ogg",
"mp3_url": "https://upload.wikimedia.org/wikipedia/commons/transcoded/0/01/En-us-injective.ogg/En-us-injective.ogg.mp3",
"ogg_url": "https://upload.wikimedia.org/wikipedia/commons/0/01/En-us-injective.ogg"
},
{
"rhymes": "-ɛktɪv"
}
],
"translations": [
{
"code": "ca",
"lang": "Catalan",
"sense": "inverse-deterministic",
"word": "injectiu"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "inverse-deterministic",
"word": "內射的"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "nèishède",
"sense": "inverse-deterministic",
"word": "内射的"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "dānshède",
"sense": "inverse-deterministic",
"word": "单射的"
},
{
"code": "cs",
"lang": "Czech",
"sense": "inverse-deterministic",
"word": "prostý"
},
{
"code": "cs",
"lang": "Czech",
"sense": "inverse-deterministic",
"word": "injektivní"
},
{
"code": "da",
"lang": "Danish",
"sense": "inverse-deterministic",
"word": "injektiv"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "inverse-deterministic",
"word": "injektiivinen"
},
{
"code": "fr",
"lang": "French",
"sense": "inverse-deterministic",
"word": "injectif"
},
{
"code": "de",
"lang": "German",
"sense": "inverse-deterministic",
"word": "injektiv"
},
{
"code": "el",
"lang": "Greek",
"roman": "amfimonótimi",
"sense": "inverse-deterministic",
"word": "αμφιμονότιμη"
},
{
"code": "is",
"lang": "Icelandic",
"sense": "inverse-deterministic",
"tags": [
"masculine"
],
"word": "eintækur"
},
{
"code": "ga",
"lang": "Irish",
"sense": "inverse-deterministic",
"word": "inteilgeach"
},
{
"alt": "にゅうしゃの",
"code": "ja",
"lang": "Japanese",
"roman": "nyuushyano",
"sense": "inverse-deterministic",
"word": "入射の"
},
{
"alt": "たんしゃの",
"code": "ja",
"lang": "Japanese",
"roman": "tannshano",
"sense": "inverse-deterministic",
"word": "単射の"
},
{
"code": "pl",
"lang": "Polish",
"sense": "inverse-deterministic",
"tags": [
"feminine"
],
"word": "różnowartościowa"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "inverse-deterministic",
"word": "injetivo"
},
{
"code": "ro",
"lang": "Romanian",
"sense": "inverse-deterministic",
"word": "injectiv"
},
{
"code": "ru",
"lang": "Russian",
"roman": "inʺjektívnyj",
"sense": "inverse-deterministic",
"word": "инъекти́вный"
},
{
"code": "es",
"lang": "Spanish",
"sense": "inverse-deterministic",
"word": "inyectivo"
},
{
"code": "sv",
"lang": "Swedish",
"sense": "inverse-deterministic",
"word": "injektiv"
}
],
"wikipedia": [
"Nicolas Bourbaki"
],
"word": "injective"
}
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"lang": "French",
"lang_code": "fr",
"pos": "adj",
"senses": [
{
"categories": [
"French 3-syllable words",
"French adjective forms",
"French entries with incorrect language header",
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"Pages with 2 entries",
"Pages with entries"
],
"form_of": [
{
"word": "injectif"
}
],
"glosses": [
"feminine singular of injectif"
],
"links": [
[
"injectif",
"injectif#French"
]
],
"tags": [
"feminine",
"form-of",
"singular"
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}
],
"sounds": [
{
"ipa": "/ɛ̃.ʒɛk.tiv/"
},
{
"homophone": "injectives"
}
],
"word": "injective"
}
Download raw JSONL data for injective meaning in All languages combined (7.9kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-28 from the enwiktionary dump dated 2024-11-21 using wiktextract (65a6e81 and 0dbea76). 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.