Groupoids of left quotients

2011/08/29 by Nassraddin Ghroda, Ghroda, N.
Computer Science · Decision Sciences · Mathematics · #Advanced Algebra and Logic #Category Theory (math.CT) #FOS: Mathematics #Fuzzy and Soft Set Theory #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1108.5663

openalex publication_date 2011/08/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A subcategory C of a groupoid \mathbbG is a left order in \mathbbG, if every element of \mathbbG can be written as a^-1b where a, b ∈ C. A subsemigroupoid \mathfrakC of a groupoid \mathbbG is a left q-order in \mathbbG, if every element of \mathbbG can be written as a^-1b where a, b ∈ \mathfrakC. 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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