English Dictionary

category theory

名詞

不可算名詞

(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.

日本語の意味

数学の一分野であり、具体的な空間や写像などの対象を抽象化して統一的な枠組みで扱い、さまざまな具体的数学分野における定理や構造の共通性を導き出す理論。 / 圏論

During the seminar, we discussed how category theory unifies results from algebra and topology by focusing on objects and morphisms.

セミナーでは、対象と射に注目することで代数や位相の結果を統一する圏論について議論しました。

意味（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.

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.