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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 Burnside category ： ウィキペディア英語版 Burnside category In category theory and homotopy theory the Burnside category of a finite group ''G'' is a category whose objects are finite ''G''-sets and whose morphisms are (equivalence classes of) spans of ''G''-equivariant maps. It is a categorification of the Burnside ring of ''G''. ==Definitions== Let ''G'' be a finite group (in fact everything will work verbatim for a profinite group). Then for any two finite ''G''-sets ''X'' and ''Y'' we can define an equivalence relation among spans of ''G''-sets of the form $X\backslash leftarrow\; U\; \backslash rightarrow\; Y$ where two spans $X\backslash leftarrow\; U\; \backslash rightarrow\; Y$ and $X\backslash leftarrow\; W\; \backslash rightarrow\; Y$are equivalent if and only if there is a ''G''-equivariant bijection of ''U'' and ''W'' commuting with the projection maps to ''X'' and ''Y''. This set of equivalence classes form naturally a monoid under disjoint union, we indicate with $A(G)(X,Y)$ the group completion of that monoid. Taking pullbacks induces natural maps $A(G)(X,Y)\backslash times\; A(G)(Y,Z)\backslash rightarrow\; A(G)(X,Z)$. Finally we can define the Burnside category ''A(G)'' of ''G'' as the category whose objects are finite ''G''-sets and the morphisms spaces are the groups $A(G)(X,Y)$. 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「Burnside category」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.