关于逆幺半群的模糊子群与$F$ -逆覆盖的关系
On a connection between fuzzy subgroups and $F$-inverse covers of inverse monoids
摘要：
定义了模糊子群范畴$\mathfrak{F}\mathfrak{G}$和逆幺半群的$F$ -逆覆盖范畴$\mathfrak{F}\mathfrak{C}$，证明了$\mathfrak{F}\mathfrak{G}$完全嵌入到$\mathfrak{F}\mathfrak{C}$中.这表明，至少从范畴的观点来看，模糊子群属于标准数学，就像它们属于模糊数学一样。
英文摘要：
We define two categories, the category $\mathfrak{F}\mathfrak{G}$ of fuzzy subgroups, and the category $\mathfrak{F}\mathfrak{C}$ of $F$-inverse covers of inverse monoids, and prove that $\mathfrak{F}\mathfrak{G}$ fully embeds into $\mathfrak{F}\mathfrak{C}$. This shows that, at least from a categorical viewpoint, fuzzy subgroups belong to the standard mathematics as much as they do to the fuzzy one.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
