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In category theory, the notion of a projective object generalizes the notion of a projective module. An object ''P'' in a category C is projective if the hom functor : preserves epimorphisms. That is, every morphism ''f:P→X'' factors through every epi ''Y→X''. Let be an abelian category. In this context, an object is called a ''projective object'' if : is an exact functor, where is the category of abelian groups. The dual notion of a projective object is that of an injective object: An object in an abelian category is ''injective'' if the functor from to is exact. ==Enough projectives== Let be an abelian category. is said to have enough projectives if, for every object of , there is a projective object of and an exact sequence : In other words, the map is "epi", or an epimorphism. 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「projective object」の詳細全文を読む スポンサード リンク
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