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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 dagger category ： ウィキペディア英語版 dagger category In mathematics, a dagger category (also called involutive category or category with involution 〔〔) is a category equipped with a certain structure called ''dagger'' or ''involution''. The name dagger category was coined by Selinger.〔 == Formal definition == A dagger category is a category $\backslash mathcal$ equipped with an involutive functor $\backslash dagger\backslash colon\; \backslash mathcal^\backslash rightarrow\backslash mathcal$ that is the identity on objects, where $\backslash mathcal^$ is the opposite category. In detail, this means that it associates to every morphism $f\backslash colon\; A\backslash to\; B$ in $\backslash mathcal$ its adjoint $f^\backslash dagger\backslash colon\; B\backslash to\; A$ such that for all $f\backslash colon\; A\backslash to\; B$ and $g\backslash colon\; B\backslash to\; C$, * $\backslash mathrm\_A=\backslash mathrm\_A^\backslash dagger\backslash colon\; A\backslash rightarrow\; A$ * $(g\backslash circ\; f)^\backslash dagger=f^\backslash dagger\backslash circ\; g^\backslash dagger\backslash colon\; C\backslash rightarrow\; A$ * $f^=f\backslash colon\; A\backslash rightarrow\; B\backslash ,$ Note that in the previous definition, the term "adjoint" is used in a way analogous to (and inspired by) the linear-algebraic sense, not in the category-theoretic sense. Some sources 〔 define a category with involution to be a dagger category with the additional property that its set of morphisms is partially ordered and that the order of morphisms is compatible with the composition of morphisms, that is ''a''<''b'' implies 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「dagger category」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.