Groupoids of left quotients

Details Groupoids of left quotients Groupoids of left quotients

2011-08-29

arxiv.org/abs/1108.5663v1

Mathematics

Category Theory

Scientific paper

A subcategory $\textbf{C}$ of a groupoid $\mathbb{G}$ is a left order in $\mathbb{G}$, if every element of $\mathbb{G}$ can be written as $a^{-1}b$ where $a, b \in \textbf{C}$. A subsemigroupoid $\mathfrak{C}$ of a groupoid $\mathbb{G}$ is a left q-order in $\mathbb{G}$, if every element of $\mathbb{G}$ can be written as $a^{-1}b$ where $a, b \in \mathfrak{C}$. We give a characterization of left orders (q-orders) in groupoids. In addition, we describe the relationship between left I-orders in primitive inverse semigroups and left orders (q-orders) in groupoids.

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