翻訳と辞書 Words near each other ・ Category O ・ Category of abelian groups ・ Category of being ・ Category of elements ・ Category of finite-dimensional Hilbert spaces ・ Category of groups ・ Category of magmas ・ Category of manifolds ・ Category of medial magmas ・ Category of metric spaces ・ Category of modules ・ Category of preordered sets ・ Category of relations ・ Category of rings ・ Category of sets ・ Category of small categories ・ Category of topological spaces ・ Category of topological vector spaces ・ Category performance ratio ・ Category theory ・ Category utility ・ Categoría Primera A ・ Categoría Primera B ・ Categoría Primera C ・ Catellani Reaction ・ Catellibacterium ・ Catello Amarante ・ Catello Cimmino ・ Catello di Rosso Gianfigliazzi ・ Catello Manzi Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Category of small categories ： ウィキペディア英語版 Category of small categories In mathematics, specifically in category theory, the category of small categories, denoted by Cat, is the category whose objects are all small categories and whose morphisms are functors between categories. Cat may actually be regarded as a 2-category with natural transformations serving as 2-morphisms. The category Cat is itself a large category, and therefore not an object of itself. In order to avoid problems analogous to Russell's paradox one cannot form the “category of all categories”. But it is possible to form a quasicategory of all categories. ==Properties== The category Cat has a forgetful functor ''U'' into the quiver category Quiv: :''U'' : Cat → Quiv This functor forgets the identity morphisms of a given category, and it forgets morphism compositions. The left adjoint of this functor is a functor ''F'' taking Quiv to the corresponding free categories: :''F'' : Quiv → Cat 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「Category of small categories」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.