See exact sequence on Wiktionary
{ "forms": [ { "form": "exact sequences", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "exact sequence (plural exact sequences)", "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": "Algebra", "orig": "en:Algebra", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "derived": [ { "word": "long exact sequence" }, { "word": "short exact sequence" } ], "glosses": [ "A sequence of modules (or groups, vector spaces, etc.; most generally, objects of an abelian category) with adjacent objects connected by homomorphisms (generally, morphisms) such that the image of one homomorphism is the kernel of the next." ], "hypernyms": [ { "word": "chain complex" } ], "id": "en-exact_sequence-en-noun-PkKRzvQg", "links": [ [ "algebra", "algebra" ], [ "sequence", "sequence" ], [ "module", "module" ], [ "group", "group" ], [ "vector space", "vector space" ], [ "object", "object" ], [ "abelian category", "abelian category" ], [ "homomorphism", "homomorphism" ], [ "morphism", "morphism" ], [ "image", "image" ], [ "kernel", "kernel" ] ], "raw_glosses": [ "(algebra) A sequence of modules (or groups, vector spaces, etc.; most generally, objects of an abelian category) with adjacent objects connected by homomorphisms (generally, morphisms) such that the image of one homomorphism is the kernel of the next." ], "topics": [ "algebra", "mathematics", "sciences" ], "wikipedia": [ "exact sequence" ] } ], "word": "exact sequence" }
{ "derived": [ { "word": "long exact sequence" }, { "word": "short exact sequence" } ], "forms": [ { "form": "exact sequences", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "exact sequence (plural exact sequences)", "name": "en-noun" } ], "hypernyms": [ { "word": "chain complex" } ], "lang": "English", "lang_code": "en", "pos": "noun", "senses": [ { "categories": [ "English countable nouns", "English entries with incorrect language header", "English lemmas", "English multiword terms", "English nouns", "Pages with 1 entry", "Pages with entries", "en:Algebra" ], "glosses": [ "A sequence of modules (or groups, vector spaces, etc.; most generally, objects of an abelian category) with adjacent objects connected by homomorphisms (generally, morphisms) such that the image of one homomorphism is the kernel of the next." ], "links": [ [ "algebra", "algebra" ], [ "sequence", "sequence" ], [ "module", "module" ], [ "group", "group" ], [ "vector space", "vector space" ], [ "object", "object" ], [ "abelian category", "abelian category" ], [ "homomorphism", "homomorphism" ], [ "morphism", "morphism" ], [ "image", "image" ], [ "kernel", "kernel" ] ], "raw_glosses": [ "(algebra) A sequence of modules (or groups, vector spaces, etc.; most generally, objects of an abelian category) with adjacent objects connected by homomorphisms (generally, morphisms) such that the image of one homomorphism is the kernel of the next." ], "topics": [ "algebra", "mathematics", "sciences" ], "wikipedia": [ "exact sequence" ] } ], "word": "exact sequence" }
Download raw JSONL data for exact sequence meaning in All languages combined (1.5kB)
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-12-21 from the enwiktionary dump dated 2024-12-04 using wiktextract (d8cb2f3 and 4e554ae). 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.