Dimension and partial groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915855277752320 |
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| author | Hackney, Philip Molinier, Rémi |
| author_facet | Hackney, Philip Molinier, Rémi |
| contents | A partial group with $n+1$ elements is, when regarded as a symmetric simplicial set, of dimension at most $n$. This dimension is $n$ if and only if the partial group is a group. As a consequence of the first statement, finite partial groups are genuinely finite, despite being seemingly specified by infinitely much data. In particular, finite partial groups have only finitely many im-partial subgroups. We also consider dimension of partial groupoids. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dimension and partial groups Hackney, Philip Molinier, Rémi Group Theory Algebraic Topology Category Theory 18N50, 20D20, 20N99 (Primary) 18F20, 20L05, 55U10 (Secondary) A partial group with $n+1$ elements is, when regarded as a symmetric simplicial set, of dimension at most $n$. This dimension is $n$ if and only if the partial group is a group. As a consequence of the first statement, finite partial groups are genuinely finite, despite being seemingly specified by infinitely much data. In particular, finite partial groups have only finitely many im-partial subgroups. We also consider dimension of partial groupoids. |
| title | Dimension and partial groups |
| topic | Group Theory Algebraic Topology Category Theory 18N50, 20D20, 20N99 (Primary) 18F20, 20L05, 55U10 (Secondary) |
| url | https://arxiv.org/abs/2406.19854 |