摘要
本文给出了相容定向完备范畴的概念及在此结构下的way-below关系与连续性,讨论了相容定向完备范畴上的way-below关系的一些性质,证明了在相容连续范畴中way-below关系满足强插值性质.最后给出了相容连续范畴的一个刻画定理,即相容定向完备范畴L是相容连续的当且仅当对任意的x∈obL,↓x是连续的.
In this paper,we introduce the concepts of the consistently directed complete categories and the relation of way-below in this structure.After that a concept of continuous and the properties of the way below relation on consistently directed complete categories are discussed.It is proved that the way-below relation satisfies the strong interpolation property in a consistently continuous category.At last,it is showed that a consistently directed complete category L is consistently continuous if and only if for all x∈obL,↓x is a continuous.
出处
《吉林师范大学学报（自然科学版）》
2013年第3期33-35,共3页
Journal of Jilin Normal University:Natural Science Edition
基金
国家自然科学基金资助项目(911171156)
安徽省自然科学研究项目(KJ2012Z358)
关键词
相容定向完备范畴
连续
WAY-BELOW关系
插值性质
consistently directed complete category
continuous
the way below relation
interpolation property
