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arXiv · 2011.06924

On a connection between fuzzy subgroups and $F$-inverse covers of inverse monoids

Elton Pasku
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Abstract

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.

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Elton Pasku. 2020-11-12. On a connection between fuzzy subgroups and $F$-inverse covers of inverse monoids. https://arxiv.org/abs/2011.06924

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