翻訳と辞書 Words near each other ・ ACY ・ Acy, Aisne ・ Acy, Louisiana ・ Acy-en-Multien ・ Acy-Romance ・ ACY1 ・ Acyanotic heart defect ・ Acyclania ・ Acyclania schadei ・ Acyclania tenebrosa ・ Acyclic ・ Acyclic coloring ・ Acyclic dependencies principle ・ Acyclic diene metathesis ・ Acyclic graph ・ Acyclic model ・ Acyclic object ・ Acyclic orientation ・ Acyclic space ・ Acygnatha ・ Acygonia ・ Acyl ・ Acyl azide ・ Acyl carrier protein ・ Acyl carrier protein synthase ・ Acyl chloride ・ Acyl CoA dehydrogenase ・ Acyl halide ・ Acyl-(acyl-carrier-protein) desaturase ・ Acyl-(acyl-carrier-protein)—phospholipid O-acyltransferase Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Acyclic model ： ウィキペディア英語版 Acyclic model In algebraic topology, a discipline within mathematics, the acyclic models theorem can be used to show that two homology theories are isomorphic. The theorem was developed by topologists Samuel Eilenberg and Saunders MacLane. They discovered that, when topologists were writing proofs to establish equivalence of various homology theories, there were numerous similarities in the processes. Eilenberg and MacLane then discovered the theorem to generalize this process. It can be used to prove the Eilenberg–Zilber theorem. ==Statement of the theorem== Let $\backslash mathcal$ be an arbitrary category and $\backslash mathcal(R)$ be the category of chain complexes of $R$-modules. Let $F,V\; :\; \backslash mathcal\; \backslash to\; \backslash mathcal(R)$ be covariant functors such that: * $F\_i\; =\; V\_i\; =\; 0$ for . * There are $\backslash mathcal\_k\; \backslash subseteq\; \backslash mathcal$ for $k\; \backslash ge\; 0$ such that $F\_k$ has a basis in $\backslash mathcal\_k$, so $F$ is a free functor. * $V$ is $k$- and $(k+1)$-acyclic at these models, which means that $H\_k(V(M))\; =\; 0$ for all $k>0$ and all $M\; \backslash in\; \backslash mathcal\_k\; \backslash cup\; \backslash mathcal\_$. Then the following assertions hold: * Every natural transformation $\backslash varphi\; :\; H\_0(F)\; \backslash to\; H\_0(V)$ is induced by a natural chain map $f\; :\; F\; \backslash to\; V$. * If $\backslash varphi,\backslash psi:\; H\_0(F)\backslash to\; H\_0(V)$ are natural transformations, $f,g:\; F\backslash to\; V$ are natural chain maps as before and $\backslash varphi^=\backslash psi^$ for all models $M\backslash in\backslash mathcal\_0$, then there is a natural chain homotopy between $f$ and $g$. * In particular the chain map $f$ is unique up to natural chain homotopy.〔 〕 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「Acyclic model」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.