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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 Cofree coalgebra ： ウィキペディア英語版 Cofree coalgebra In algebra, the cofree coalgebra of a vector space or module is a coalgebra analog of the free algebra of a vector space. The cofree coalgebra of any vector space over a field exists, though it is more complicated than one might expect by analogy with the free algebra. ==Definition== If ''V''  is a vector space over a field F, then the cofree coalgebra ''C'' (''V''), of ''V'', is a coalgebra together with a linear map ''C'' (''V'')→''V'', such that any linear map from a coalgebra ''X'' to ''V'' factors through a coalgebra homomorphism from ''X'' to ''C'' (''V''). In other words, the functor ''C''  is right adjoint to the forgetful functor from coalgebras to vector spaces. The cofree coalgebra of a vector space always exists, and is unique up to canonical isomorphism. Cofree cocommutative coalgebras are defined in a similar way, and can be constructed as the largest cocommutative coalgebra in the cofree coalgebra. 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「Cofree coalgebra」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.