模糊Quantale范畴的性质

Some properties of the category of fuzzy Quantales

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.

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.