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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 Accessible category ： ウィキペディア英語版 Accessible category The theory of accessible categories originates from the work of Grothendieck completed by 1969 (Grothendieck (1972)) and Gabriel-Ulmer (1971). It has been further developed in 1989 by Michael Makkai and Robert Paré, with motivation coming from model theory, a branch of mathematical logic.〔J. Rosicky ("On combinatorial model categories" ), ''Arxiv'', 16 August 2007. Retrieved on 19 January 2008.〕 Accessible categories have also applications in homotopy theory.〔〔J. Rosicky, Injectivity and accessible categories〕 Grothendieck also continued the development of the theory for homotopy-theoretic purposes in his (still partly unpublished) 1991 manuscript Les dérivateurs (Grothendieck (1991)). Some properties of accessible categories depend on the set universe in use, particularly on the cardinal properties.〔J. Adamek and J. Rosicky, Locally Presentable and Accessible Categories, Cambridge University Press 1994〕 ==Definition== Let $K$ be an infinite regular cardinal and let $C$ be a category. An object $X$ of $C$ is called $K$-presentable if the Hom functor $Hom(X,-)$ preserves $K$-directed colimits. The category $C$ is called $K$-accessible provided that : * $C$ has $K$-directed colimits * $C$ has a set $P$ of $K$-presentable objects such that every object of $C$ is a $K$-directed colimit of objects of $P$ A category $C$ is called accessible if $C$ is $K$-accessible for some infinite regular cardinal $K$. A $\backslash aleph\_0$-presentable object is usually called finitely presentable, and an $\backslash aleph\_0$-accessible category is often called finitely accessible. 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「Accessible 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.