二元模糊关系范畴的对称幺半范畴性

Symmetric monoid categorization of binary fuzzy relation category

摘要: 结合模糊关系范畴的概念给出了二元模糊关系范畴 \mathbbL_bRel 的概念. 首先，讨论了范畴 \mathbbL_bRel 的积和余积的结构. 其次，定义了张量积函子 \otimes ，得到了 \mathbbL_bRel 是对称幺半范畴. 进而，给出了范畴 \mathbbL_bRel 中的幺半群和余幺半群结构. 最后，以二元模糊关系范畴 \mathbbL_bRel 作为纽带，构造了一个从模糊集范畴 \mathbbLS et 到模糊关系范畴 Rel_\mathbbL\mathbbL 的忠实函子.

Abstract: The concept of binary fuzzy relation category \mathbbL_bRel was given by combining the concept of fuzzy relation category. Firstly, we discussed the structure of product and coproduct in the category \mathbbL_bRel . Secondly, we defined the tensor functor and obtained that the category \mathbbL_bRel is a symmetric monoid category. Furthermore, we gave the structure of monoid and comonoid in the category \mathbbL_bRel . Finally, we constructed a functor from fuzzy set category \mathbbLS et to fuzzy relation category Rel_\mathbbL\mathbbL by using binary fuzzy relation category \mathbbL_bRel .