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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 Graded category ： ウィキペディア英語版 Graded category A graded category is a mathematical concept. If $\backslash mathcal$ is a category, then a $\backslash mathcal$-graded category is a category $\backslash mathcal$ together with a functor $F:\backslash mathcal\; \backslash rightarrow\; \backslash mathcal$. Monoids and groups can be thought of as categories with a single element. A monoid-graded or group-graded category is therefore one in which to each morphism is attached an element of a given monoid (resp. group), its grade. This must be compatible with composition, in the sense that compositions have the product grade. ==Definition== There are various different definitions of a graded category, up to the most abstract one given above. A more concrete definition of a semigroup-graded Abelian category is as follows: Let $\backslash mathcal$ be an Abelian category and $\backslash mathbb$ a semigroup. Let $\backslash mathcal=\backslash$ be a set of functors from $\backslash mathcal$ to itself. If * $S\_$ is the identity functor on $\backslash mathcal$, * $S\_S\_=S\_$ for all $g,h\backslash in\; \backslash mathbb$ and * $S\_$ is a full and faithful functor for every $g\backslash in\; \backslash mathbb$ we say that $(\backslash mathcal,\backslash mathcal)$ is a $\backslash mathbb$-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「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.