Z-Quantale的表示定理

Representation Theorems for Z-Quantales

考虑Z-Quantale的表示问题.首先,证明任意单位Z-Quantale都同构于由其强Z-自连续映射所构成的Z-Quantale;其次,证明对于任意单位Z-Quantale都存在其上的一个关系Z-Quantale与其同构;最后,讨论单位Z-Quantale范畴与关系Z-Quantale范畴之间的关系,证明单位Z-Quantale范畴与关系Z-Quantale范畴等价.

We considered representation problems of Z-Quantales.Firstly,we proved that any unital Z-Quantale was isomorphic to the Z-Quantale formed by its strong self-continuous maps.Secondly,we proved that any unital Z-Quantale was isomorphic to a relation Z-Quantale.Finally,we discussed the relationship between the category of unital Z-Quantales and the category of relation Z-Quantales,and proved that the category of unital Z-Quantales was equivalent to the category of relation Z-Quantales.