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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 Differential graded category ： ウィキペディア英語版 Differential graded category In mathematics, especially homological algebra, a differential graded category or DG category for short, is a category whose morphism sets are endowed with the additional structure of a differential graded ''Z''-module. In detail, this means that $Hom(A,B)$, the morphisms from any object ''A'' to another object ''B'' of the category is a direct sum $\backslash oplus\_Hom\_n(A,B)$ and there is a differential ''d'' on this graded group, i.e. for all ''n'' a linear map $d:\; Hom\_n(A,B)\; \backslash rightarrow\; Hom\_(A,B)$, which has to satisfy $d\; \backslash circ\; d\; =\; 0$. This is equivalent to saying that $Hom(A,B)$ is a cochain complex. Furthermore, the composition of morphisms $Hom(A,B)\; \backslash otimes\; Hom(B,C)\; \backslash rightarrow\; Hom(A,C)$ is required to be a map of complexes, and for all objects ''A'' of the category, one requires $d(id\_A)\; =\; 0$. == See also == * Differential algebra * Graded (mathematics) * Graded category 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「Differential graded 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.