See category theory on Wiktionary
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Now, since category theory, through the notion of topos, has succeeded in axiomatising set-theory, the outcome is an entirely new categorial foundation of mathematics! The category-theorists attitude that \"function\" rather than \"set membership\" can be seen as the fundamental mathematical concept has been entirely vindicated. The pre-eminent role of set theory in contemporary mathematics is suddenly challenged. A revolution has occurred in the history of mathematical ideas (albeit a peaceful one) that will undoubtedly influence the direction of the path to the future.", "type": "quote" } ], "glosses": [ "A branch of mathematics which deals with spaces and maps between them in abstraction, taking similar theorems from various disparate more concrete branches of mathematics and unifying them." ], "hypernyms": [ { "word": "mathematics" }, { "word": "theory" } ], "id": "en-category_theory-en-noun-01kYRen7", "links": [ [ "mathematics", "mathematics" ], [ "abstraction", "abstraction" ], [ "theorems", "theorems" ] ], "raw_glosses": [ "(mathematics) A branch of mathematics which deals with spaces and maps between them in abstraction, taking similar theorems from various disparate more concrete branches of mathematics and unifying them." ], "tags": [ "uncountable" ], "topics": [ "mathematics", "sciences" ], "translations": [ { "code": "cmn", "lang": "Chinese Mandarin", "roman": "fànchóulùn", "sense": "branch of mathematics", "word": "範疇論 /范畴论" }, { "code": "cs", "lang": "Czech", "sense": "branch of mathematics", "tags": [ "feminine" ], "word": "teorie kategorií" }, { "code": "fi", "lang": "Finnish", "sense": "branch of mathematics", "word": "kategoriateoria" }, { "code": "fr", "lang": "French", "sense": "branch of mathematics", "tags": [ "feminine" ], "word": "théorie des catégories" }, { "code": "de", "lang": "German", "sense": "branch of mathematics", "tags": [ "feminine" ], "word": "Kategorientheorie" }, { "code": "is", "lang": "Icelandic", "sense": "branch of mathematics", "tags": [ "feminine" ], "word": "ríkjafræði" }, { "alt": "けんろん", "code": "ja", "lang": "Japanese", "roman": "kenron", "sense": "branch of mathematics", "word": "圏論" }, { "alt": "範疇論", "code": "ko", "lang": "Korean", "roman": "beomjuron", "sense": "branch of mathematics", "word": "범주론" }, { "code": "ms", "lang": "Malay", "sense": "branch of mathematics", "word": "teori kategori" }, { "code": "ro", "lang": "Romanian", "sense": "branch of mathematics", "tags": [ "feminine" ], "word": "teoria categoriei" }, { "code": "ru", "lang": "Russian", "roman": "teorija kategorij", "sense": "branch of mathematics", "tags": [ "feminine" ], "word": "теория категорий" }, { "code": "es", "lang": "Spanish", "sense": "branch of mathematics", "tags": [ "feminine" ], "word": "teoría de categorías" }, { "code": "sv", "lang": "Swedish", "sense": "branch of mathematics", "tags": [ "common-gender" ], "word": "kategoriteori" }, { "code": "tr", "lang": "Turkish", "sense": "branch of mathematics", "word": "kategori teorisi" }, { "code": "tr", "lang": "Turkish", "sense": "branch of mathematics", "word": "ulam kuramı" } ], "wikipedia": [ "category theory" ] } ], "word": "category theory" }
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This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2025-03-01 from the enwiktionary dump dated 2025-02-21 using wiktextract (7c21d10 and f2e72e5). 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.
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