|
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 along with a forgetful functor that maps to the category of sets and has the following three properties: * admits initial (or weak) structures with respect to * Constant functions in lift to -morphisms * Fibers 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
|