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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 Injective object ： ウィキペディア英語版 Injective object In mathematics, especially in the field of category theory, the concept of injective object is a generalization of the concept of injective module. This concept is important in homotopy theory and in theory of model categories. The dual notion is that of a projective object. ==Definition== Let $\backslash mathfrak$ be a category and let $\backslash mathcal$ be a class of morphisms of $\backslash mathfrak$. An object $Q$ of $\backslash mathfrak$ is said to be ''$\backslash mathcal$''-injective if for every morphism $f:\; A\; \backslash to\; Q$ and every morphism $h:\; A\; \backslash to\; B$ in $\backslash mathcal$ there exists a morphism $g:\; B\; \backslash to\; Q$ extending (the domain of) $f$, i.e. $g\; \backslash circ\; h\; =\; f$. The morphism $g$ in the above definition is not required to be uniquely determined by $h$ and $f$. In a locally small category, it is equivalent to require that the hom functor $Hom\_$-morphisms to epimorphisms (surjections). The classical choice for $\backslash mathcal$ is the class of monomorphisms, in this case, the expression injective object is used. 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「Injective object」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.