模糊<i>L</i>−关系范畴的范畴性质

模糊L−关系范畴的范畴性质

摘要: 运用范畴论的观点和语言，结合模糊关系范畴 L - \textRel 的范畴性质，讨论了模糊 L - 关系范畴 \mathcalL - \textRel 的相关范畴性质. 首先，给出了 \mathcalL - \textRel 中2个对象的积和余积的结构. 进而，定义出双函子 \otimes 和 \dagger −函子，得到 \mathcalL - \textRel 是 \dagger - 对称幺半范畴. 最后，指出了 \mathcalL - \textRel 是一个2−范畴.

Abstract: Using the viewpoint and language of category theory and combining the categorical properties of fuzzy relations category L \text- \textRel , we discussed the categorical properties of fuzzy L-relations category \mathcalL \text- \textRel . Furthermore, we proved the category \mathcalL \text- \textRel is a \dagger -symmetric monoidal category which is constructed by bifunctor \otimes and \dagger -functor. Finally, we showed the category \mathcalL \text- \textRel is a 2-category.