模糊Quantale范畴的性质-陕西师范大学学报期刊社网站

陕西师范大学学报（自然科学版）

数学与计算机科学

模糊Quantale范畴的性质

汪开云, 赵彬*

(陕西师范大学数学与信息科学学院, 陕西西安 710062)

汪开云,男,讲师,博士,研究方向为格上拓扑与模糊推理.E-mail:wangkaiyun_2006@126.com.

摘要:

引入了模糊Quantale的概念，证明了模糊Quantale范畴同构于L-代数范畴,于是从范畴论的角度说明L-代数也可以看成是Quantale的模糊化结构; 给出了模糊Quantale范畴中的极限的具体结构,同时证明了该范畴是完备范畴; 给出模糊Quantale范畴中逆系统的逆极限结构, 引入了两个逆系统之间映射的定义,由此导出两个逆系统的逆极限之间的极限映射.

关键词：

范畴; 模糊Quantale; L-代数; 极限

收稿日期：

2012-12-25

中图分类号：

O153.1

文献标识码：

文章编号：

1672-4291(2013)03-0001-06

基金项目：

国家自然科学基金资助项目(11171196,11001158).

Doi:

Some properties of the category of fuzzy Quantales

WANG Kai-yun, ZHAO Bin*

(College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China)

Abstract:

The concept of a fuzzy Quantale is introduced.It is shown that the category of fuzzy Quantales is isomorphic to the category of L-algebras. This result presents that L-algebras can also be treated as fuzzifications of Quantales from the viewpoint of category theory.The concrete structure of limit in the category of fuzzy Quantales is given, and the completeness of the category of fuzzy Quantales is obtained.The structure of inverse limit of an inverse system in the category of fuzzy Quantales is described.Then a mapping between two inverse systems is defined, and the concept of a limit mapping between the inverse limits of two inverse systems is induced.

KeyWords:

category; fuzzy Quantale; L-algebra; limit