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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 Distributor (category theory) ： ウィキペディア英語版 Profunctor In category theory, a branch of mathematics, profunctors are a generalization of relations and also of bimodules. They are related to the notion of correspondences. == Definition == A profunctor (also named distributor by the French school and module by the Sydney school) $\backslash ,\backslash phi$ from a category $C$ to a category $D$, written :$\backslash phi\; \backslash colon\; C\backslash nrightarrow\; D$, is defined to be a functor :$\backslash phi\; \backslash colon\; D^$ where $D^\backslash mathrm$ denotes the opposite category of $D$ and $\backslash mathbf$ denotes the category of sets. Given morphisms $f\backslash colon\; d\backslash to\; d\text{'},\; g\backslash colon\; c\backslash to\; c\text{'}$ respectively in $D,\; C$ and an element $x\backslash in\backslash phi(d\text{'},c)$, we write $xf\backslash in\; \backslash phi(d,c),\; gx\backslash in\backslash phi(d\text{'},c\text{'})$ to denote the actions. Using the cartesian closure of $\backslash mathbf$, the category of small categories, the profunctor $\backslash phi$ can be seen as a functor :$\backslash hat\; \backslash colon\; C\backslash to\backslash hat$ where $\backslash hat$ denotes the category $\backslash mathrm^\{D^\backslash mathrm\{op\}\}$ of presheaves over $D$. A correspondence from $C$ to $D$ is a profunctor $D\backslash nrightarrow\; C$. 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「Profunctor」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.