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arXiv · 2508.10162

Characterization of groupoid categories in terms of its category of $\mathcal{C}$-sets

J. Miguel Calderón·Alberto Gerardo Raggi-Cárdenas·Itzel Rosas·Ramón H. Ruiz-Medina
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Abstract

A $\mathcal{C}$-set is a functor from the category $\mathcal{C}$ to the category of finite sets and functions. The category of $\mathcal{C}$-sets, $\mathcal{C} - \operatorname*{set}$, is defined as the category whose objects are $\mathcal{C}$-sets, and whose morphisms are natural transformations between them. In this document we provide some concise characterizations of groupoids in terms of their category of $\mathcal{C}$-sets.

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J. Miguel Calderón, Alberto Gerardo Raggi-Cárdenas, Itzel Rosas, Ramón H. Ruiz-Medina. 2025-08-15. Characterization of groupoid categories in terms of its category of $\mathcal{C}$-sets. https://doi.org/10.1007/s10485-026-09854-2

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