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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 Simplex category ： ウィキペディア英語版 Simplex category In mathematics, the simplex category (or simplicial category or nonempty finite ordinal category) is the category of non-empty finite ordinals and order preserving maps. It is used to define simplicial and cosimplicial objects. ==Formal definition== The simplex category is usually denoted by $\backslash Delta$. There are several equivalent descriptions of this category. $\backslash Delta$ can be described as the category of ''non-empty finite ordinals'' as objects, thought of as totally ordered sets, and ''order preserving functions'' as morphisms. The objects are commonly denoted $()\; =\; \backslash$ (so that $()$ is the ordinal $n+1$). The category is generated by coface and codegeneracy maps, which amount to inserting or deleting elements of the orderings. (See simplicial set for relations of these maps.) A simplicial object is a presheaf on $\backslash Delta$, that is a contravariant functor from $\backslash Delta$ to another category. For instance, simplicial sets are contravariant with the codomain category being the category of sets. A cosimplicial object is defined similarly as a covariant functor originating from $\backslash Delta$. 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「Simplex 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.