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In mathematics, an inverse system in a category ''C'' is a functor from a small cofiltered category ''I'' to ''C''. An inverse system is sometimes called a ''pro-object'' in ''C''. The dual concept is a direct system. ==The category of inverse systems== Pro-objects in ''C'' form a category ''pro-C''. The general definition was given by Alexander Grothendieck in 1959, in ''TDTE''. Two inverse systems :''F'':I C'' and ''G'':J C'' determine a functor :''I''op x ''J'' ''Sets'', namely the functor :. The set of homomorphisms between ''F'' and ''G'' in ''pro-C'' is defined to be the colimit of this functor in the first variable, followed by the limit in the second variable. If ''C'' has all inverse limits, then the limit defines a functor ''pro-C''''C''. In practice, e.g. if ''C'' is a category of algebraic or topological objects, this functor is not an equivalence of categories. 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「inverse system」の詳細全文を読む スポンサード リンク
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