论文标题
完全规律性的分类评论
A categorical review of complete regularity
论文作者
论文摘要
我们使用Ultrafter-Convergence Axiomatics用于拓扑空间，以详细介绍一个温和的分类介绍，首先是基于Barr的基于设定的关系T-Algebras，然后是Burroni的T类t-preorters在C类C中内部的T-Preorders，此处称为C中的T-preorders，在C中称为C中的T-preorders，以替代超级属性的C上，以替换超级属性。在这些设置中，人们不仅发现紧凑性和豪斯多夫分离的概念最初是由于鬃毛引起的，而且是完全规律性的。基于Burroni的某种隐藏结果，本文的主要定理在C和T的适度假设下建立了完全规则的T空间类别的外部纤维化表征，其反射性Hausdorff T空间的反射性子类别。
We use the ultrafilter-convergence axiomatics for topological spaces to motivate in detail a gentle categorical introduction, first to Barr's Set-based relational T-algebras, and then to Burroni's T-preorders internal to a category C, here called T-spaces in C, for a monad T on C that substitutes the ultrafilter monad on Set. Within these settings one finds not only the notions of compactness and Hausdorff separation, originally due to Manes, but also that of complete regularity. Based on a somewhat hidden result by Burroni, the main theorem of this paper establishes an external fibrational characterization of the category of completely regular T-spaces with its reflexive subcategory of compact Hausdorff T-spaces, under modest assumptions on C and T.
