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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 Bousfield localization ： ウィキペディア英語版 Bousfield localization In category theory, a branch of mathematics, a (left) Bousfield localization of a model category replaces the model structure with another model structure with the same cofibrations but with more weak equivalences. Bousfield localization is named after Aldridge Bousfield, who first introduced this technique in the context of localization of topological spaces and spectra.〔Aldridge Bousfield, ''(The localization of spectra with respect to homology )'', Topology vol 18 (1979)〕〔Aldridge Bousfield, ''The localization of spaces with respect to homology'', Topology vol. 14 (1975)〕 ==Model category structure of the Bousfield localization== Given a class ''C'' of morphisms in a model category ''M'' the left Bousfield localization is a new model structure on the same category as before. Its equivalences, cofibrations and fibrations, respectively, are * the ''C''-local equivalences * the original cofibrations of ''M'' and (necessarily, since cofibrations and weak equivalences determine the fibrations) * the maps having the right lifting property with respect to the cofibrations in ''M'' which are also ''C''-local equivalences. In this definition, a ''C''-local equivalence is a map $f:\; X\; \backslash to\; Y$ which, roughly speaking, does not make a difference when mapping to a ''C''-local object. More precisely, $f^$ * : map (Y, W) \to map (X, W) is required to be a weak equivalence (of simplicial sets) for any ''C''-local object ''W''. An object ''W'' is called ''C''-local if it is fibrant (in ''M'') and :$s^$ * : map (B, W) \to map (A, W) is a weak equivalence for ''all'' maps $f:\; A\; \backslash to\; B$ in ''C''. The notation $map(-,\; -)$ is, for a general model category (not necessarily enriched over simplicial sets) a certain simplicial set whose set of path components agrees with morphisms in the homotopy category of ''M'': :$\backslash pi\_0\; (map(X,\; Y))\; =\; Hom\_(X,\; Y).$ If ''M'' is a simplicial model category (such as, say, simplicial sets or topological spaces), then "map" above can be taken to be the derived simplicial mapping space of ''M''. This description does not make any claim about the existence of this model structure, for which see below. Dually, there is a notion of ''right Bousfield localization'', whose definition is obtained by replacing cofibrations by fibrations (and reversing directions of all arrows). 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「Bousfield localization」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.