弱幂等Quantale范畴与相关范畴的关系

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.

Relationships between Category of Weakly Idempotent Quantales and Related Categories

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.