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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 Subdivided interval categories ： ウィキペディア英語版 Subdivided interval categories In category theory (mathematics) there exists an important collection of categories denoted $()$ for natural numbers $n\backslash in\backslash mathbb$. The objects of $()$ are the integers $0,1,2,\backslash ldots,n$, and the morphism set $Hom(i,j)$ for objects $i,j\backslash in()$ is empty if $j$ and consists of a single element if $i\backslash leq\; j$. Subdivided interval categories are very useful in defining simplicial sets. The category whose objects are the subdivided interval categories and whose morphisms are functors is often written $\backslash Delta$ and is called the simplicial indexing category. A simplicial set is just a contravariant functor $X:\backslash Delta^\backslash rightarrow\; Sets$. ==Examples== The category 𝟘 is an empty interval, that is, an empty category, having any objects or morphisms. It is an initial object in the category of all categories. The category (), also denoted as 𝟙, is a one-object, one-morphism category. It is the terminal object in the category of all categories. The category (), also denoted as 𝟚 has two objects and a single (non-identity) morphism between them. If $\backslash mathcal$ is any category, then $\backslash mathcal^$ is the category of morphisms and commutative squares in $\backslash mathcal.$ The category (), also denoted as 𝟛 has three objects and three non-identity morphisms. 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「Subdivided interval categories」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.