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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 be a category and let be a class of morphisms of . An object of is said to be ''''-injective if for every morphism and every morphism in there exists a morphism extending (the domain of) , i.e. . The morphism in the above definition is not required to be uniquely determined by and . In a locally small category, it is equivalent to require that the hom functor -morphisms to epimorphisms (surjections). The classical choice for 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
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