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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2021
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2107.09576 |
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| _version_ | 1866917622219538432 |
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| author | Verme, Giulia dal Weigel, Thomas |
| author_facet | Verme, Giulia dal Weigel, Thomas |
| contents | In this paper a Bass-Serre theory in the groupoid setting is developed and a structure theorem is established. Any groupoid action without inversion of edges on a forest induces a graph of groupoids, while any graph of groupoids satisfying certain hypothesis admits a canonical associated groupoid, called the fundamental groupoid, and a forest, called the Bass-Serre forest, such that the fundamental groupoid acts on the Bass-Serre forest. The structure theorem states that these processes are mutually inverse. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2107_09576 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Bass-Serre theory for groupoids Verme, Giulia dal Weigel, Thomas Group Theory Category Theory In this paper a Bass-Serre theory in the groupoid setting is developed and a structure theorem is established. Any groupoid action without inversion of edges on a forest induces a graph of groupoids, while any graph of groupoids satisfying certain hypothesis admits a canonical associated groupoid, called the fundamental groupoid, and a forest, called the Bass-Serre forest, such that the fundamental groupoid acts on the Bass-Serre forest. The structure theorem states that these processes are mutually inverse. |
| title | Bass-Serre theory for groupoids |
| topic | Group Theory Category Theory |
| url | https://arxiv.org/abs/2107.09576 |