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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 factorization system ： ウィキペディア英語版 factorization system In mathematics, it can be shown that every function can be written as the composite of a surjective function followed by an injective function. Factorization systems are a generalization of this situation in category theory. ==Definition== A factorization system (''E'', ''M'') for a category C consists of two classes of morphisms ''E'' and ''M'' of C such that: #''E'' and ''M'' both contain all isomorphisms of C and are closed under composition. #Every morphism ''f'' of C can be factored as $f=m\backslash circ\; e$ for some morphisms $e\backslash in\; E$ and $m\backslash in\; M$. #The factorization is ''functorial'': if $u$ and $v$ are two morphisms such that $vme=m\text{'}e\text{'}u$ for some morphisms $e,\; e\text{'}\backslash in\; E$ and $m,\; m\text{'}\backslash in\; M$, then there exists a unique morphism $w$ making the following diagram commute: ''Remark:'' $(u,v)$ is a morphism from $me$ to $m\text{'}e\text{'}$ in the arrow category. 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「factorization system」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.