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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 extranatural transformation ： ウィキペディア英語版 extranatural transformation In mathematics, specifically in category theory, an extranatural transformation〔Eilenberg and Kelly, A generalization of the functorial calculus, J. Algebra 3 366–375 (1966)〕 is a generalization of the notion of natural transformation. ==Definition== Let $F:A\backslash times\; B^\backslash mathrm\backslash times\; B\backslash rightarrow\; D$ and $G:A\backslash times\; C^\backslash mathrm\backslash times\; C\backslash rightarrow\; D$ two functors of categories. A family $\backslash eta\; (a,b,c):F(a,b,b)\backslash rightarrow\; G(a,c,c)$ is said to be natural in ''a'' and extranatural in ''b'' and ''c'' if the following holds: *$\backslash eta(-,b,c)$ is a natural transformation (in the usual sense). * (extranaturality in b) $\backslash forall\; (g:b\backslash rightarrow\; b^\backslash prime)\backslash in\; \backslash mathrm\backslash ,\; B$, $\backslash forall\; a\backslash in\; A$, $\backslash forall\; c\backslash in\; C$ the following diagram commutes :: $\backslash begin$ F(a,b',b) & \xrightarrow & F(a,b',b') \\ _|\qquad & & _|\qquad \\ F(a,b,b) & \xrightarrow & G(a,c,c) \end * (extranaturality in c) $\backslash forall\; (h:c\backslash rightarrow\; c^\backslash prime)\backslash in\; \backslash mathrm\backslash ,\; C$, $\backslash forall\; a\backslash in\; A$, $\backslash forall\; b\backslash in\; B$ the following diagram commutes :: $\backslash begin$ F(a,b,b) & \xrightarrow & G(a,c',c') \\ _|\qquad & & _|\qquad \\ G(a,c,c) & \xrightarrow & G(a,c,c') \end 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「extranatural transformation」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.