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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Adjoint functors ： ウィキペディア英語版 Adjoint functors In mathematics, specifically category theory, adjunction is a possible relationship between two functors. Adjunction is ubiquitous in mathematics, as it specifies intuitive notions of optimization and efficiency. In the most concise symmetric definition, an adjunction between categories ''C'' and ''D'' is a pair of functors, :$F:\; \backslash mathcal\; \backslash rightarrow\; \backslash mathcal$   and   $G:\; \backslash mathcal\; \backslash rightarrow\; \backslash mathcal$ and a family of bijections :$\backslash mathrm\_\_\{\backslash mathcal\{D\}\}(Y,GX)$ which is natural in the variables ''X'' and ''Y''. The functor ''F'' is called a left adjoint functor, while ''G'' is called a right adjoint functor. The relationship “''F'' is left adjoint to ''G''” (or equivalently, “''G'' is right adjoint to ''F''”) is sometimes written :$F\backslash dashv\; G.$ This definition and others are made precise below. == Introduction == “The slogan is ‘Adjoint functors arise everywhere’.” (Saunders Mac Lane, ''Categories for the working mathematician'') The long list of examples in this article is only a partial indication of how often an interesting mathematical construction is an adjoint functor. As a result, general theorems about left/right adjoint functors, such as the equivalence of their various definitions or the fact that they respectively preserve colimits/limits (which are also found in every area of mathematics), can encode the details of many useful and otherwise non-trivial results. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Adjoint functors」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.