模糊L−关系范畴的范畴性质  

The categorical properties of fuzzy L-relations category

作　　者：周鑫 刘淼 汤建钢 ZHOU Xin;LIU Miao;TANG Jian-gang(School of Mathematics and Statistics,Yili Normal University,Yining 835000,Xinjiang,China;Institute of Applied Mathematics,Yili Normal University,Yining 835000,Xinjiang,China)

机构地区：[1]伊犁师范大学数学与统计学院,新疆伊宁835000 [2]伊犁师范大学应用数学研究所,新疆伊宁835000

出　　处：《云南大学学报（自然科学版）》2023年第4期779-786,共8页Journal of Yunnan University(Natural Sciences Edition)

基　　金：新疆维吾尔自治区自然科学基金(2020D01C269);新疆维吾尔自治区高校科研计划(XJEDU2021Y042);新疆伊犁州科技计划(YZ2022Y010);伊犁师范大学博士科研启动基金(2021YSBS011);伊犁师范大学科研创新团队(CXZK2021014);伊犁师范大学“学实高层次人才岗位”项目(YSXSGG22002).

摘　　要：运用范畴论的观点和语言,结合模糊关系范畴L-Rel的范畴性质,讨论了模糊L-关系范畴L-Rel的相关范畴性质.首先,给出了L-Rel中2个对象的积和余积的结构.进而,定义出双函子■和†-函子,得到L-Rel是L-对称幺半范畴.最后,指出了L-Rel是一个2-范畴.Using the viewpoint and language of category theory and combining the categorical properties of fuzzy relations category L-Rel,we discussed the categorical properties of fuzzy L-relations category L-Rel.Furthermore,we proved the category L-Rel is a †-symmetric monoidal category which is constructed by bifunctor 8 and L-functor.Finally,we showed the category L-Rel is a 2-category.

关 键 词：模糊关系 范畴 积 †-对称幺半范畴 2-范畴 

分 类 号：O159[理学—数学]