See left inverse on Wiktionary
{
"antonyms": [
{
"word": "right inverse"
}
],
"forms": [
{
"form": "left inverses",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "left inverse (plural left inverses)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"text": "In order for a function to have a left inverse it must be injective.",
"type": "example"
}
],
"glosses": [
"A related function that, given the output of the original function, returns the input that produced that output."
],
"id": "en-left_inverse-en-noun-yL79eHO-",
"links": [
[
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"mathematics"
],
[
"function",
"function"
]
],
"raw_glosses": [
"(mathematics) A related function that, given the output of the original function, returns the input that produced that output."
],
"topics": [
"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": "26 74",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "15 85",
"kind": "other",
"name": "Entries with translation boxes",
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"source": "w+disamb"
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{
"_dis": "29 71",
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{
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},
{
"_dis": "19 81",
"kind": "other",
"name": "Terms with German translations",
"parents": [],
"source": "w+disamb"
}
],
"glosses": [
"For a given morphism f : X → Y, its right inverse (if it has one) is a morphism s : Y → X such that s∘f= mbox id_X."
],
"hypernyms": [
{
"_dis1": "15 85",
"word": "inverse"
}
],
"id": "en-left_inverse-en-noun-s8pIGGQE",
"links": [
[
"category theory",
"category theory"
],
[
"morphism",
"morphism"
]
],
"raw_glosses": [
"(category theory) For a given morphism f : X → Y, its right inverse (if it has one) is a morphism s : Y → X such that s∘f= mbox id_X."
],
"topics": [
"category-theory",
"computing",
"engineering",
"mathematics",
"natural-sciences",
"physical-sciences",
"sciences"
],
"translations": [
{
"_dis1": "20 80",
"code": "de",
"lang": "German",
"sense": "Translations",
"tags": [
"neuter"
],
"word": "Linksinverses"
}
]
}
],
"word": "left inverse"
}
{
"antonyms": [
{
"word": "right inverse"
}
],
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English lemmas",
"English multiword terms",
"English nouns",
"Entries with translation boxes",
"Pages with 1 entry",
"Pages with entries",
"Terms with German translations",
"Translation table header lacks gloss"
],
"forms": [
{
"form": "left inverses",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "left inverse (plural left inverses)",
"name": "en-noun"
}
],
"hypernyms": [
{
"word": "inverse"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"English terms with usage examples",
"en:Mathematics"
],
"examples": [
{
"text": "In order for a function to have a left inverse it must be injective.",
"type": "example"
}
],
"glosses": [
"A related function that, given the output of the original function, returns the input that produced that output."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"function",
"function"
]
],
"raw_glosses": [
"(mathematics) A related function that, given the output of the original function, returns the input that produced that output."
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
"en:Category theory"
],
"glosses": [
"For a given morphism f : X → Y, its right inverse (if it has one) is a morphism s : Y → X such that s∘f= mbox id_X."
],
"links": [
[
"category theory",
"category theory"
],
[
"morphism",
"morphism"
]
],
"raw_glosses": [
"(category theory) For a given morphism f : X → Y, its right inverse (if it has one) is a morphism s : Y → X such that s∘f= mbox id_X."
],
"topics": [
"category-theory",
"computing",
"engineering",
"mathematics",
"natural-sciences",
"physical-sciences",
"sciences"
]
}
],
"translations": [
{
"code": "de",
"lang": "German",
"sense": "Translations",
"tags": [
"neuter"
],
"word": "Linksinverses"
}
],
"word": "left inverse"
}
Download raw JSONL data for left inverse meaning in All languages combined (1.8kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-11-06 from the enwiktionary dump dated 2024-10-02 using wiktextract (fbeafe8 and 7f03c9b). 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.