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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 Symmetric spectrum ： ウィキペディア英語版 Symmetric spectrum In algebraic topology, a symmetric spectrum ''X'' is a spectrum of pointed simplicial sets that comes with an action of the symmetric group $\backslash Sigma\_n$ on $X\_n$ such that the composition of structure maps :$S^1\; \backslash wedge\; \backslash dots\; \backslash wedge\; S^1\; \backslash wedge\; X\_n\; \backslash to\; S^1\; \backslash wedge\; \backslash dots\; \backslash wedge\; S^1\; \backslash wedge\; X\_\; \backslash to\; \backslash dots\; \backslash to\; S^1\; \backslash wedge\; X\_\; \backslash to\; X\_$ is equivariant with respect to $\backslash Sigma\_p\; \backslash times\; \backslash Sigma\_n$. A morphism between symmetric spectra is a morphism of spectra that is equivariant with respect to the actions of symmetric groups. The technical advantage of the category $\backslash mathcalp^\backslash Sigma$ of symmetric spectra is that it has a closed symmetric monoidal structure (with respect to smash product). It is also a simplicial model category. A symmetric ring spectrum is a monoid in $\backslash mathcalp^\backslash Sigma$; if the monoid is commutative, it's a commutative ring spectrum. The possibility of this definition of "ring spectrum" was one of motivations behind the category. A similar technical goal is also achieved by May's theory of S-modules, a competing theory. == References == *(Introduction to symmetric spectra I ) *M. Hovey, B. Shipley, and J. Smith, “Symmetric spectra”, Journal of the AMS 13 (1999), no. 1, 149 – 208. 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「Symmetric spectrum」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.