See injective on Wiktionary
Download JSON data for injective meaning in All languages combined (8.9kB)
{
"derived": [
{
"_dis1": "0 0 0 0",
"word": "injective cogenerator"
},
{
"_dis1": "0 0 0 0",
"word": "injective dimension"
},
{
"_dis1": "0 0 0 0",
"word": "injective function"
},
{
"_dis1": "0 0 0 0",
"word": "injective hull"
},
{
"_dis1": "0 0 0 0",
"word": "injective map"
},
{
"_dis1": "0 0 0 0",
"word": "injective module"
},
{
"_dis1": "0 0 0 0",
"word": "injective object"
},
{
"_dis1": "0 0 0 0",
"word": "injective patch"
},
{
"_dis1": "0 0 0 0",
"word": "injective sheaf"
}
],
"etymology_text": "This term was introduced by Nicolas Bourbaki in his treatise Éléments de mathématique.",
"head_templates": [
{
"args": {
"1": "-"
},
"expansion": "injective (not comparable)",
"name": "en-adj"
}
],
"lang": "English",
"lang_code": "en",
"pos": "adj",
"related": [
{
"_dis1": "0 0 0 0",
"word": "injectal"
},
{
"_dis1": "0 0 0 0",
"word": "injectively"
},
{
"_dis1": "0 0 0 0",
"word": "bijective"
},
{
"_dis1": "0 0 0 0",
"word": "surjective"
}
],
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"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"
],
"id": "en-injective-en-adj-Lv-yL75F",
"links": [
[
"mathematics",
"mathematics"
],
[
"injection",
"injection"
],
[
"image",
"image"
],
[
"range",
"range"
],
[
"preimage",
"preimage"
],
[
"domain",
"domain"
]
],
"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"
],
"translations": [
{
"_dis1": "68 9 18 5",
"code": "ca",
"lang": "Catalan",
"sense": "inverse-deterministic",
"word": "injectiu"
},
{
"_dis1": "68 9 18 5",
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "inverse-deterministic",
"word": "內射的"
},
{
"_dis1": "68 9 18 5",
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "nèishède",
"sense": "inverse-deterministic",
"word": "内射的"
},
{
"_dis1": "68 9 18 5",
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "dānshède",
"sense": "inverse-deterministic",
"word": "单射的"
},
{
"_dis1": "68 9 18 5",
"code": "cs",
"lang": "Czech",
"sense": "inverse-deterministic",
"word": "prostý"
},
{
"_dis1": "68 9 18 5",
"code": "cs",
"lang": "Czech",
"sense": "inverse-deterministic",
"word": "injektivní"
},
{
"_dis1": "68 9 18 5",
"code": "da",
"lang": "Danish",
"sense": "inverse-deterministic",
"word": "injektiv"
},
{
"_dis1": "68 9 18 5",
"code": "fi",
"lang": "Finnish",
"sense": "inverse-deterministic",
"word": "injektiivinen"
},
{
"_dis1": "68 9 18 5",
"code": "fr",
"lang": "French",
"sense": "inverse-deterministic",
"word": "injectif"
},
{
"_dis1": "68 9 18 5",
"code": "de",
"lang": "German",
"sense": "inverse-deterministic",
"word": "injektiv"
},
{
"_dis1": "68 9 18 5",
"code": "el",
"lang": "Greek",
"roman": "amfimonótimi",
"sense": "inverse-deterministic",
"word": "αμφιμονότιμη"
},
{
"_dis1": "68 9 18 5",
"code": "is",
"lang": "Icelandic",
"sense": "inverse-deterministic",
"tags": [
"masculine"
],
"word": "eintækur"
},
{
"_dis1": "68 9 18 5",
"code": "ga",
"lang": "Irish",
"sense": "inverse-deterministic",
"word": "inteilgeach"
},
{
"_dis1": "68 9 18 5",
"alt": "にゅうしゃの",
"code": "ja",
"lang": "Japanese",
"roman": "nyuushyano",
"sense": "inverse-deterministic",
"word": "入射の"
},
{
"_dis1": "68 9 18 5",
"alt": "たんしゃの",
"code": "ja",
"lang": "Japanese",
"roman": "tannshano",
"sense": "inverse-deterministic",
"word": "単射の"
},
{
"_dis1": "68 9 18 5",
"code": "pl",
"lang": "Polish",
"sense": "inverse-deterministic",
"tags": [
"feminine"
],
"word": "różnowartościowa"
},
{
"_dis1": "68 9 18 5",
"code": "pt",
"lang": "Portuguese",
"sense": "inverse-deterministic",
"word": "injetivo"
},
{
"_dis1": "68 9 18 5",
"code": "ro",
"lang": "Romanian",
"sense": "inverse-deterministic",
"word": "injectiv"
},
{
"_dis1": "68 9 18 5",
"code": "ru",
"lang": "Russian",
"roman": "inʺjektívnyj",
"sense": "inverse-deterministic",
"word": "инъекти́вный"
},
{
"_dis1": "68 9 18 5",
"code": "es",
"lang": "Spanish",
"sense": "inverse-deterministic",
"word": "inyectivo"
},
{
"_dis1": "68 9 18 5",
"code": "sv",
"lang": "Swedish",
"sense": "inverse-deterministic",
"word": "injektiv"
}
]
},
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Algebra",
"orig": "en:Algebra",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"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.",
"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."
],
"id": "en-injective-en-adj-ea7SQ2vu",
"links": [
[
"algebra",
"algebra"
],
[
"module",
"module"
],
[
"ring",
"ring"
],
[
"generalizing",
"generalize"
],
[
"abstracted",
"abstract"
],
[
"short exact sequence",
"short exact sequence"
],
[
"splits",
"split"
]
],
"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"
],
"tags": [
"not-comparable"
],
"topics": [
"algebra",
"mathematics",
"sciences"
]
},
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Category theory",
"orig": "en:Category theory",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "14 29 45 12",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
}
],
"glosses": [
"Loosely, having a property analogous to that which characterizes projective 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."
],
"id": "en-injective-en-adj-jk717GXb",
"links": [
[
"category theory",
"category theory"
],
[
"object",
"object"
],
[
"category",
"category"
],
[
"monomorphism",
"monomorphism"
],
[
"morphism",
"morphism"
]
],
"qualifier": "most generally",
"raw_glosses": [
"(category theory, most generally, of a object Q in a category C) Loosely, having a property analogous to that which characterizes projective 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 a 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)."
],
"id": "en-injective-en-adj-hr07Pwns",
"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/"
},
{
"rhymes": "-ɛktɪv"
},
{
"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",
"tags": [
"US"
],
"text": "Audio (US)"
}
],
"wikipedia": [
"Nicolas Bourbaki"
],
"word": "injective"
}
{
"head_templates": [
{
"args": {
"1": "fr",
"2": "adjective form"
},
"expansion": "injective",
"name": "head"
}
],
"lang": "French",
"lang_code": "fr",
"pos": "adj",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "French entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
}
],
"form_of": [
{
"word": "injectif"
}
],
"glosses": [
"feminine singular of injectif"
],
"id": "en-injective-fr-adj-HxpIUBgn",
"links": [
[
"injectif",
"injectif#French"
]
],
"tags": [
"feminine",
"form-of",
"singular"
]
}
],
"sounds": [
{
"ipa": "/ɛ̃.ʒɛk.tiv/"
},
{
"homophone": "injectives"
}
],
"word": "injective"
}
{
"categories": [
"English 3-syllable words",
"English adjectives",
"English entries with incorrect language header",
"English lemmas",
"English terms with IPA pronunciation",
"English terms with audio links",
"English uncomparable adjectives",
"Rhymes:English/ɛktɪv",
"Rhymes:English/ɛktɪv/3 syllables"
],
"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.",
"head_templates": [
{
"args": {
"1": "-"
},
"expansion": "injective (not comparable)",
"name": "en-adj"
}
],
"lang": "English",
"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",
"mathematics"
],
[
"injection",
"injection"
],
[
"image",
"image"
],
[
"range",
"range"
],
[
"preimage",
"preimage"
],
[
"domain",
"domain"
]
],
"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": [
"(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.",
"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": [
[
"algebra",
"algebra"
],
[
"module",
"module"
],
[
"ring",
"ring"
],
[
"generalizing",
"generalize"
],
[
"abstracted",
"abstract"
],
[
"short exact sequence",
"short exact sequence"
],
[
"splits",
"split"
]
],
"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"
],
"tags": [
"not-comparable"
],
"topics": [
"algebra",
"mathematics",
"sciences"
]
},
{
"categories": [
"en:Category theory"
],
"glosses": [
"Loosely, having a property analogous to that which characterizes projective 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": [
[
"category theory",
"category theory"
],
[
"object",
"object"
],
[
"category",
"category"
],
[
"monomorphism",
"monomorphism"
],
[
"morphism",
"morphism"
]
],
"qualifier": "most generally",
"raw_glosses": [
"(category theory, most generally, of a object Q in a category C) Loosely, having a property analogous to that which characterizes projective 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 a 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/"
},
{
"rhymes": "-ɛktɪv"
},
{
"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",
"tags": [
"US"
],
"text": "Audio (US)"
}
],
"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"
}
{
"head_templates": [
{
"args": {
"1": "fr",
"2": "adjective form"
},
"expansion": "injective",
"name": "head"
}
],
"lang": "French",
"lang_code": "fr",
"pos": "adj",
"senses": [
{
"categories": [
"French 3-syllable words",
"French adjective forms",
"French entries with incorrect language header",
"French non-lemma forms",
"French terms with IPA pronunciation",
"French terms with homophones"
],
"form_of": [
{
"word": "injectif"
}
],
"glosses": [
"feminine singular of injectif"
],
"links": [
[
"injectif",
"injectif#French"
]
],
"tags": [
"feminine",
"form-of",
"singular"
]
}
],
"sounds": [
{
"ipa": "/ɛ̃.ʒɛk.tiv/"
},
{
"homophone": "injectives"
}
],
"word": "injective"
}
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.