See cohomology in All languages combined, or Wiktionary
Download JSON data for cohomology meaning in English (4.0kB)
{
"etymology_templates": [
{
"args": {
"1": "en",
"2": "co",
"3": "homology"
},
"expansion": "co- + homology",
"name": "prefix"
}
],
"etymology_text": "co- + homology",
"forms": [
{
"form": "cohomologies",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "~"
},
"expansion": "cohomology (countable and uncountable, plural cohomologies)",
"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": [
{
"ref": "2001, William Dwyer, Hans-Werner Henn, Homotopy Theoretic Methods in Group Cohomology, Springer Science & Business, page 55",
"text": "In section 1 we start off by recalling some fundamental results in cohomology of groups, in particular the Evens–Venkov result on finite generation of the cohomology ring (Theorem 2) and Quillen's landmark result which describes H*BG up to F-isomorphism (Theorem 5).",
"type": "quotation"
}
],
"glosses": [
"A method of contravariantly associating a family of invariant quotient groups to each algebraic or geometric object of a category, including categories of geometric and algebraic objects."
],
"id": "en-cohomology-en-noun-TKQSf~Kr",
"links": [
[
"mathematics",
"mathematics"
],
[
"contravariant",
"contravariant"
],
[
"invariant",
"invariant"
],
[
"quotient group",
"quotient group"
],
[
"category",
"category"
]
],
"raw_glosses": [
"(mathematics) A method of contravariantly associating a family of invariant quotient groups to each algebraic or geometric object of a category, including categories of geometric and algebraic objects."
],
"tags": [
"countable",
"uncountable"
],
"topics": [
"mathematics",
"sciences"
],
"translations": [
{
"_dis1": "100 0",
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "shàngtóngdiào",
"sense": "theory",
"word": "上同调"
},
{
"_dis1": "100 0",
"code": "fi",
"lang": "Finnish",
"sense": "theory",
"word": "kohomologia"
},
{
"_dis1": "100 0",
"code": "de",
"lang": "German",
"sense": "theory",
"tags": [
"feminine"
],
"word": "Kohomologie"
},
{
"_dis1": "100 0",
"code": "pt",
"lang": "Portuguese",
"sense": "theory",
"tags": [
"feminine"
],
"word": "cohomologia"
},
{
"_dis1": "100 0",
"code": "es",
"lang": "Spanish",
"sense": "theory",
"tags": [
"feminine"
],
"word": "cohomología"
}
]
},
{
"categories": [
{
"kind": "topical",
"langcode": "en",
"name": "Mathematics",
"orig": "en:Mathematics",
"parents": [
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
},
{
"_dis": "38 62",
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "42 58",
"kind": "other",
"name": "English entries with language name categories using raw markup",
"parents": [
"Entries with language name categories using raw markup",
"Entry maintenance"
],
"source": "w+disamb"
},
{
"_dis": "42 58",
"kind": "other",
"name": "English terms prefixed with co-",
"parents": [],
"source": "w+disamb"
},
{
"_dis": "36 64",
"kind": "other",
"name": "English terms suffixed with -ology",
"parents": [],
"source": "w+disamb"
}
],
"glosses": [
"A system of quotient groups associated to a topological space."
],
"id": "en-cohomology-en-noun-p1Y2U84o",
"links": [
[
"mathematics",
"mathematics"
],
[
"quotient group",
"quotient group"
],
[
"topological space",
"topological space"
]
],
"raw_glosses": [
"(mathematics) A system of quotient groups associated to a topological space."
],
"tags": [
"countable",
"uncountable"
],
"topics": [
"mathematics",
"sciences"
],
"translations": [
{
"_dis1": "0 100",
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "shàngtóngdiào",
"sense": "system",
"word": "上同调"
},
{
"_dis1": "0 100",
"code": "fi",
"lang": "Finnish",
"sense": "system",
"word": "kohomologia"
},
{
"_dis1": "0 100",
"code": "es",
"lang": "Spanish",
"sense": "system",
"tags": [
"feminine"
],
"word": "cohomología"
}
]
}
],
"wikipedia": [
"cohomology"
],
"word": "cohomology"
}
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English entries with language name categories using raw markup",
"English lemmas",
"English nouns",
"English terms prefixed with co-",
"English terms suffixed with -ology",
"English uncountable nouns"
],
"etymology_templates": [
{
"args": {
"1": "en",
"2": "co",
"3": "homology"
},
"expansion": "co- + homology",
"name": "prefix"
}
],
"etymology_text": "co- + homology",
"forms": [
{
"form": "cohomologies",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {
"1": "~"
},
"expansion": "cohomology (countable and uncountable, plural cohomologies)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
"English terms with quotations",
"en:Mathematics"
],
"examples": [
{
"ref": "2001, William Dwyer, Hans-Werner Henn, Homotopy Theoretic Methods in Group Cohomology, Springer Science & Business, page 55",
"text": "In section 1 we start off by recalling some fundamental results in cohomology of groups, in particular the Evens–Venkov result on finite generation of the cohomology ring (Theorem 2) and Quillen's landmark result which describes H*BG up to F-isomorphism (Theorem 5).",
"type": "quotation"
}
],
"glosses": [
"A method of contravariantly associating a family of invariant quotient groups to each algebraic or geometric object of a category, including categories of geometric and algebraic objects."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"contravariant",
"contravariant"
],
[
"invariant",
"invariant"
],
[
"quotient group",
"quotient group"
],
[
"category",
"category"
]
],
"raw_glosses": [
"(mathematics) A method of contravariantly associating a family of invariant quotient groups to each algebraic or geometric object of a category, including categories of geometric and algebraic objects."
],
"tags": [
"countable",
"uncountable"
],
"topics": [
"mathematics",
"sciences"
]
},
{
"categories": [
"en:Mathematics"
],
"glosses": [
"A system of quotient groups associated to a topological space."
],
"links": [
[
"mathematics",
"mathematics"
],
[
"quotient group",
"quotient group"
],
[
"topological space",
"topological space"
]
],
"raw_glosses": [
"(mathematics) A system of quotient groups associated to a topological space."
],
"tags": [
"countable",
"uncountable"
],
"topics": [
"mathematics",
"sciences"
]
}
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "shàngtóngdiào",
"sense": "theory",
"word": "上同调"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "theory",
"word": "kohomologia"
},
{
"code": "de",
"lang": "German",
"sense": "theory",
"tags": [
"feminine"
],
"word": "Kohomologie"
},
{
"code": "pt",
"lang": "Portuguese",
"sense": "theory",
"tags": [
"feminine"
],
"word": "cohomologia"
},
{
"code": "es",
"lang": "Spanish",
"sense": "theory",
"tags": [
"feminine"
],
"word": "cohomología"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "shàngtóngdiào",
"sense": "system",
"word": "上同调"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "system",
"word": "kohomologia"
},
{
"code": "es",
"lang": "Spanish",
"sense": "system",
"tags": [
"feminine"
],
"word": "cohomología"
}
],
"wikipedia": [
"cohomology"
],
"word": "cohomology"
}
This page is a part of the kaikki.org machine-readable English dictionary. This dictionary is based on structured data extracted on 2024-04-30 from the enwiktionary dump dated 2024-04-21 using wiktextract (210104c 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.