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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 Presheaf (category theory) ： ウィキペディア英語版 Presheaf (category theory) In category theory, a branch of mathematics, a presheaf on a category $C$ is a functor $F\backslash colon\; C^\backslash mathrm\backslash to\backslash mathbf$. If $C$ is the poset of open sets in a topological space, interpreted as a category, then one recovers the usual notion of presheaf on a topological space. A morphism of presheaves is defined to be a natural transformation of functors. This makes the collection of all presheaves into a category, and is an example of a functor category. It is often written as $\backslash widehat\; =\; \backslash mathbf^$ is sometimes called a profunctor. A presheaf that is naturally isomorphic to the contravariant hom-functor Hom(–,''A'') for some object ''A'' of C is called a representable presheaf. Some authors refer to a functor $F\backslash colon\; C^\backslash mathrm\backslash to\backslash mathbf$ as a $\backslash mathbf$-valued presheaf. == Examples == * A simplicial set is a Set-valued presheaf on the simplex category $C=\backslash Delta$. 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「Presheaf (category theory)」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.