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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 Local system ： ウィキペディア英語版 Local system In mathematics, local coefficients is an idea from algebraic topology, a kind of half-way stage between homology theory or cohomology theory with coefficients in the usual sense, in a fixed abelian group ''A'', and general sheaf cohomology which, roughly speaking, allows coefficients to vary from point to point in a topological space ''X''. Such a concept was introduced by Norman Steenrod. ==Formal definition== Let ''X'' be a locally path connected topological space, and ''M'' a module over some ring ''R''. A local coefficient system of ''R''-modules ''E'' with fiber ''M'' is a fiber bundle with fiber ''M'' with an action of the fundamental groupoid of the base ''X'', that is, for each path $\backslash gamma\; :\; ()\backslash to\; X$, a morphism $\backslash gamma\_$ *: E_\to E_ that depends only on the homotopy class with fixed extremities of the path, is the identity on constant paths and such that composition of paths corresponds to compositions of morphisms. In sheaf theory terms, a constant sheaf has locally constant functions as its sections. Consider instead a sheaf ''F'', such that locally on ''X'' it is a constant sheaf. That means that in some neighbourhood of any ''x'' in ''X'', it is isomorphic to a constant sheaf. Then ''F'' may be used as a system of ''local coefficients'' on ''X''. 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「Local system」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.