تقرير
The category of partial group actions: quotients, (co)limits and groupoids
| العنوان: | The category of partial group actions: quotients, (co)limits and groupoids |
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| المؤلفون: | Jerez, Emmanuel |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Group Theory, Primary 16W22, 20C99 Secondary 18A30, 18A32, 43A65, 18B40 |
| الوصف: | We consider the category of partial actions, where the group and the set upon which the group acts can vary. Within this framework, we develop a theory of quotient partial actions and prove that this category is both (co)complete and encompasses the category of groupoids as a full subcategory. In particular, we establish the existence of a pair of adjoint functors, denoted as $\Phi : \textbf{Grpd} \to \textbf{PA}$ and $\Psi : \textbf{PA} \to \textbf{Grpd}$, with the property that $\Psi \Phi \cong 1_{\textbf{Grpd} }$. Next, for a given groupoid $\Gamma$, we provide a characterization of all partial actions that allow the recovery of the groupoid $\Gamma$ through $\Psi$. This characterization is expressed in terms of certain normal subgroups of a universal group constructed from $\Gamma.$ Comment: The previous version was an incorrect file that was uploaded. I have corrected some typographical errors and improved the proof of Proposition 2.18 |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2311.06223 |
| رقم الأكسشن: | edsarx.2311.06223 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |