category theory

English

Wikibooks

Noun

category theory (uncountable)

1. (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.
   • 1984, Robert Goldblatt, Topoi, the categorial analysis of logic, page 3:

     As mentioned earlier set theory provides a general conceptual framework for mathematics. 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.

Hypernyms

• mathematics, theory

Translations

branch of mathematics

• Chinese:

  Mandarin: 範疇論／范畴论 (zh) (fànchóulùn)

• Czech: teorie kategorií f
• Finnish: kategoriateoria
• French: théorie des catégories (fr) f
• German: Kategorientheorie f
• Icelandic: ríkjafræði f
• Malay: teori kategori
• Romanian: teoria categoriei f
• Russian: теория категорий f (teorija kategorij)
• Spanish: teoría de categorías f
• Swedish: kategoriteori (sv) c
• Turkish: kategori teorisi, ulam kuramı