Characterization of groupoid categories in terms of its category of $\mathcal{C}$-sets
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866913023271108608 |
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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 |
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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 |