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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 Tower (mathematics) ： ウィキペディア英語版 Tower (mathematics) In category theory, a branch of abstract mathematics, a tower is defined as follows. Let $\backslash mathcal\; I$ be the poset :$\backslash cdots\backslash rightarrow\; 2\backslash rightarrow\; 1\backslash rightarrow\; 0$ of whole numbers in reverse order, regarded as a category. A (countable) tower of objects in a category $\backslash mathcal\; A$ is a functor from $\backslash mathcal\; I$ to $\backslash mathcal\; A$. In other words, a tower (of $\backslash mathcal\; A$) is a family of objects $\backslash \_$ in $\backslash mathcal\; A$ where there exists a map :$A\_i\backslash rightarrow\; A\_j$ if $i>j$ and the composition :$A\_i\backslash rightarrow\; A\_j\backslash rightarrow\; A\_k$ is the map $A\_i\backslash rightarrow\; A\_k$ == Example == Let $M\_i=M$ for some $R$-module $M$. Let $M\_i\backslash rightarrow\; M\_j$ be the identity map for $i>j$. Then $\backslash$ forms a tower of modules. 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「Tower (mathematics)」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.