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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 Topological category ： ウィキペディア英語版 Topological category In category theory, a discipline in mathematics, the notion of topological category has a number of different, inequivalent definitions. In one approach, a topological category is a category that is enriched over the category of compactly generated Hausdorff spaces. They can be used as a foundation for higher category theory, where they can play the role of (∞,1)-categories. An important example of a topological category in this sense is given by the category of CW complexes, where each set Hom(''X'',''Y'') of continuous maps from ''X'' to ''Y'' is equipped with the compact-open topology. In another approach, a topological category is defined as a category $C$ along with a forgetful functor $T:\; C\; \backslash to\; \backslash mathbf$ that maps to the category of sets and has the following three properties: * $C$ admits initial (or weak) structures with respect to $T$ * Constant functions in $\backslash mathbf$ lift to $C$-morphisms * Fibers $T^\; x,\; x\; \backslash in\; \backslash mathbf$ are small (they are sets and not proper classes). An example of a topological category in this sense is the categories of all topological spaces with continuous maps, where one uses the standard forgetful functor. ==See also== *Infinity category *Simplicial 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「Topological 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.