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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 Traced monoidal category ： ウィキペディア英語版 Traced monoidal category In category theory, a traced monoidal category is a category with some extra structure which gives a reasonable notion of feedback. A traced symmetric monoidal category is a symmetric monoidal category C together with a family of functions :$\backslash mathrm^U\_:\backslash mathbf(X\backslash otimes\; U,Y\backslash otimes\; U)\backslash to\backslash mathbf(X,Y)$ called a ''trace'', satisfying the following conditions (where we sometimes denote an identity morphism by the corresponding object, e.g., using ''U'' to denote $\backslash text\_U$): * naturality in ''X'': for every $f:X\backslash otimes\; U\backslash to\; Y\backslash otimes\; U$ and $g:X\text{'}\backslash to\; X$, ::$\backslash mathrm^U\_(f)g=\backslash mathrm^U\_(f(g\backslash otimes\; U))$ * naturality in ''Y'': for every $f:X\backslash otimes\; U\backslash to\; Y\backslash otimes\; U$ and $g:Y\backslash to\; Y\text{'}$, ::$g\backslash mathrm^U\_(f)=\backslash mathrm^U\_((g\backslash otimes\; U)f)$ * dinaturality in ''U'': for every $f:X\backslash otimes\; U\backslash to\; Y\backslash otimes\; U\text{'}$ and $g:U\text{'}\backslash to\; U$ ::$\backslash mathrm^U\_((Y\backslash otimes\; g)f)=\backslash mathrm^\_(f(X\backslash otimes\; g))$ * vanishing I: for every $f:X\backslash otimes\; I\backslash to\; Y\backslash otimes\; I$, ::$\backslash mathrm^I\_(f)=f$ * vanishing II: for every $f:X\backslash otimes\; U\backslash otimes\; V\backslash to\; Y\backslash otimes\; U\backslash otimes\; V$ ::$\backslash mathrm^\_(f)=\backslash mathrm^U\_(\backslash mathrm^V\_(f))$ * superposing: for every $f:X\backslash otimes\; U\backslash to\; Y\backslash otimes\; U$ and $g:W\backslash to\; Z$, ::$g\backslash otimes\; \backslash mathrm^U\_(f)=\backslash mathrm^U\_(g\backslash otimes\; f)$ * yanking: ::$\backslash mathrm^X\_(\backslash gamma\_)=X$ (where $\backslash gamma$ is the symmetry of the monoidal category). == Properties == * Every compact closed category admits a trace. * Given a traced monoidal category C, the ''Int construction'' generates the free (in some bicategorical sense) compact closure Int(C) of C. 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「Traced monoidal 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.