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

Fuente: arXiv
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Main Authors: Calderón, J. Miguel, Raggi-Cárdenas, Alberto Gerardo, Rosas, Itzel, Ruiz-Medina, Ramón H.
Format: Preprint
Published: 2025
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author Calderón, J. Miguel
Raggi-Cárdenas, Alberto Gerardo
Rosas, Itzel
Ruiz-Medina, Ramón H.
author_facet Calderón, J. Miguel
Raggi-Cárdenas, Alberto Gerardo
Rosas, Itzel
Ruiz-Medina, Ramón H.
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2508_10162
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Characterization of groupoid categories in terms of its category of $\mathcal{C}$-sets
Calderón, J. Miguel
Raggi-Cárdenas, Alberto Gerardo
Rosas, Itzel
Ruiz-Medina, Ramón H.
Category Theory
K-Theory and Homology
18A25, 18B40, 19A22
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.
title Characterization of groupoid categories in terms of its category of $\mathcal{C}$-sets
topic Category Theory
K-Theory and Homology
18A25, 18B40, 19A22
url https://arxiv.org/abs/2508.10162