弱幂等Quantale范畴与相关范畴的关系

Relationships between Category of Weakly IdempotentQuantales and Related Categories

首先引入弱幂等Quantale及Quantale上弱幂等核映射的概念,给出Quantale的最大弱幂等商的等价刻画;然后证明弱幂等Quantale范畴是Quantale范畴的反射子范畴,幂等Quantale范畴是弱幂等Quantale范畴的反射子范畴;最后得到幂等Quantale范畴是Quantale范畴的反射子范畴.

Firstly,by introducing the concepts of a weakly idempotent quantale and a weakly idempotent nucleus on a quantale,we gave an equivalent characterization for the largest weakly idempotent quantale quotient.Secondly,we proved that the category of weakly idempotent quantales was a reflective subcategory of the category of quantales,the category of idempotent quantales was a reflective subcategory of the category of weakly idempotent quantales.Finally,we obtained that the category of idempotent quantales was a reflective subcategory of the category of quantales.