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In algebra, given a ring ''R'', the category of left modules over ''R'' is the category whose objects are all left modules over ''R'' and whose morphism are all module homomorphisms between left ''R''-modules. The category of right modules is defined in the similar way. Note: Some authors use the term module category for the category of modules; this term is non-standard as well as ambiguous since it could also refer to a category with a monoidal-category action.〔(【引用サイトリンク】title=module category in nLab )〕 == Properties == The category of left modules (or that of right modules) is an abelian category. The category has enough projectives〔trivially since any module is a quotient of a free module.〕 and enough injectives. Mitchell's embedding theorem states every abelian category arises as a full subcategory of the category of modules. Projective limits and inductive limits exist in the category of (say left) modules. Over a commutative ring, together with the tensor product of modules ⊗, the category of modules is a symmetric monoidal 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「Category of modules」の詳細全文を読む スポンサード リンク
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