See free category in All languages combined, or Wiktionary
{ "forms": [ { "form": "free categories", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "free category (plural free categories)", "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": "Category theory", "orig": "en:Category theory", "parents": [ "Mathematics", "Formal sciences", "Sciences", "All topics", "Fundamental" ], "source": "w" } ], "glosses": [ "A category that is induced by a multidigraph thus: it has as its objects the vertices of the multidigraph and its morphisms are paths in the multidigraph; composition of morphisms is concatenation of paths, as long as the end of one path coincides with the beginning of the other path; an identity morphism of an object is an “empty path” at that vertex." ], "hyponyms": [ { "word": "free monoid" } ], "id": "en-free_category-en-noun-YJqtgZBN", "links": [ [ "category theory", "category theory" ], [ "category", "category" ], [ "multidigraph", "multidigraph" ], [ "vertices", "vertex" ] ], "raw_glosses": [ "(category theory) A category that is induced by a multidigraph thus: it has as its objects the vertices of the multidigraph and its morphisms are paths in the multidigraph; composition of morphisms is concatenation of paths, as long as the end of one path coincides with the beginning of the other path; an identity morphism of an object is an “empty path” at that vertex." ], "topics": [ "category-theory", "computing", "engineering", "mathematics", "natural-sciences", "physical-sciences", "sciences" ], "wikipedia": [ "free category" ] } ], "word": "free category" }
{ "forms": [ { "form": "free categories", "tags": [ "plural" ] } ], "head_templates": [ { "args": {}, "expansion": "free category (plural free categories)", "name": "en-noun" } ], "hyponyms": [ { "word": "free monoid" } ], "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:Category theory" ], "glosses": [ "A category that is induced by a multidigraph thus: it has as its objects the vertices of the multidigraph and its morphisms are paths in the multidigraph; composition of morphisms is concatenation of paths, as long as the end of one path coincides with the beginning of the other path; an identity morphism of an object is an “empty path” at that vertex." ], "links": [ [ "category theory", "category theory" ], [ "category", "category" ], [ "multidigraph", "multidigraph" ], [ "vertices", "vertex" ] ], "raw_glosses": [ "(category theory) A category that is induced by a multidigraph thus: it has as its objects the vertices of the multidigraph and its morphisms are paths in the multidigraph; composition of morphisms is concatenation of paths, as long as the end of one path coincides with the beginning of the other path; an identity morphism of an object is an “empty path” at that vertex." ], "topics": [ "category-theory", "computing", "engineering", "mathematics", "natural-sciences", "physical-sciences", "sciences" ], "wikipedia": [ "free category" ] } ], "word": "free category" }
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This page is a part of the kaikki.org machine-readable English 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.