有界完备的domain范畴是monadic范畴  

The category of bounded completeκ-domains is monadic

作　　者：张巍[1] 

机构地区：[1]四川大学数学学院,成都610064

出　　处：《四川大学学报（自然科学版）》2011年第6期1276-1280,共5页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(10771147)

摘　　要：一个连续格就是一个完备的连续偏序集,一个有界完备domain则是一个有定向并与非空交的连续偏序集.1975年,Day证明了连续格范畴是集合范畴和T_0拓扑空间范畴上的monadic范畴.本文作者把这一结论推广到了有界完备domain范畴:对任意无限基数κ,作者引入了有界完备的κ-domain以及相应的Scottκ拓扑的概念。并证明了有界完备的κ-domain范畴是集合范畴和T_0的κ拓扑空间范畴上的monadic范畴.A continuous lattice is a complete continuous partially ordered set （poset）, while a bounded complete domain is a continuous poser that has directed joins and nonempty meets. In 1975,Day proved that the category of continuous lattices is monadic over the category of sets and that of To spaces. In this paper this conclusion is extended to bounded complete e-domains for any infinite cardinal κ. First, the concepts of bounded complete κ-domain and Scott κ topology are introduced; Then, it is showed that the category of bounded complete κ-domains is monadic over the category of sets and that of To g-spaces.

关 键 词：monadic范畴 有界完备的κ—domain κ—dcpo κ-空间 

分 类 号：O153.1[理学—数学]