E-quantale范畴

The category of E-quantales

引入了E-quantale的定义及其一些相关概念,讨论了E-quantale的一些重要性质。证明了Quantale的幂集和E-quantale的乘积均可构成E-quantale,给出了Quantale的一种自然扩张,由E-quantale可以扩张成一个Quantale。在Quantale子范畴和E-quantale范畴之间定义了一个嵌入函子K,并在函子K与遗忘函子U之间构造了一个自然变换,证明了在一定条件下一个E-quantale和某个单位Quantale的幂集同构。

The definition of an E-quantale is introduced,and some properies of E-quantale is obtained. It is proved that the power set of Quantale and the product of E-quantales are E-quantales. Finally,an embedding functor K from the subcategory of Quantales to the category of E-quantale is introducted,and a natural transformation from functor K and forgotten functor U is constructed. Moreover,under some conditions an E-quantale is isomorphic to the power set of a unital Quantale.