See Hopf algebra in All languages combined, or Wiktionary
{
"etymology_text": "Named after Heinz Hopf.",
"forms": [
{
"form": "Hopf algebras",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "Hopf algebra (plural Hopf algebras)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Pages with 1 entry",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Pages with entries",
"parents": [],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"glosses": [
"A structure that is simultaneously a unital associative algebra and a counital coassociative coalgebra, equipped with an antiautomorphism satisfying a certain property."
],
"id": "en-Hopf_algebra-en-noun-6kpsBMTg",
"links": [
[
"mathematics",
"mathematics"
],
[
"structure",
"structure"
],
[
"simultaneous",
"simultaneous"
],
[
"unital",
"unital"
],
[
"associative",
"associative"
],
[
"algebra",
"algebra"
],
[
"counital",
"counital"
],
[
"coassociative",
"coassociative"
],
[
"coalgebra",
"coalgebra"
],
[
"antiautomorphism",
"antiautomorphism"
]
],
"raw_glosses": [
"(mathematics) A structure that is simultaneously a unital associative algebra and a counital coassociative coalgebra, equipped with an antiautomorphism satisfying a certain property."
],
"topics": [
"mathematics",
"sciences"
],
"wikipedia": [
"Heinz Hopf",
"Hopf algebra"
]
}
],
"word": "Hopf algebra"
}
{
"etymology_text": "Named after Heinz Hopf.",
"forms": [
{
"form": "Hopf algebras",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "Hopf algebra (plural Hopf algebras)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English eponyms",
"English lemmas",
"English multiword terms",
"English nouns",
"Pages with 1 entry",
"Pages with entries",
"en:Mathematics"
],
"glosses": [
"A structure that is simultaneously a unital associative algebra and a counital coassociative coalgebra, equipped with an antiautomorphism satisfying a certain property."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"structure",
"structure"
],
[
"simultaneous",
"simultaneous"
],
[
"unital",
"unital"
],
[
"associative",
"associative"
],
[
"algebra",
"algebra"
],
[
"counital",
"counital"
],
[
"coassociative",
"coassociative"
],
[
"coalgebra",
"coalgebra"
],
[
"antiautomorphism",
"antiautomorphism"
]
],
"raw_glosses": [
"(mathematics) A structure that is simultaneously a unital associative algebra and a counital coassociative coalgebra, equipped with an antiautomorphism satisfying a certain property."
],
"topics": [
"mathematics",
"sciences"
],
"wikipedia": [
"Heinz Hopf",
"Hopf algebra"
]
}
],
"word": "Hopf algebra"
}
Download raw JSONL data for Hopf algebra meaning in English (1.3kB)
This page is a part of the kaikki.org machine-readable English 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.