The Leibniz PROP is a crossed presimplicial algebra
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915294109237248 |
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| author | Aşkaroğulları, Murat Can Kaygun, Atabey |
| author_facet | Aşkaroğulları, Murat Can Kaygun, Atabey |
| contents | We prove that the Leibniz PROP is isomorphic (as $\Bbbk$-linear categories) to the symmetric crossed presimplicial algebra $\Bbbk[(Δ^+)^{op} \mathbb{S}]$ where $Δ^+$ is the skeletal category of finite well-ordered sets with surjections, but the distributive law between $(Δ^+)^{op}$ and the symmetric groups $\mathbb{S} = \bigsqcup_{n\geq 1} S_n$ is not the standard one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10925 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Leibniz PROP is a crossed presimplicial algebra Aşkaroğulları, Murat Can Kaygun, Atabey Category Theory 17A32, 18M85, 18M32 We prove that the Leibniz PROP is isomorphic (as $\Bbbk$-linear categories) to the symmetric crossed presimplicial algebra $\Bbbk[(Δ^+)^{op} \mathbb{S}]$ where $Δ^+$ is the skeletal category of finite well-ordered sets with surjections, but the distributive law between $(Δ^+)^{op}$ and the symmetric groups $\mathbb{S} = \bigsqcup_{n\geq 1} S_n$ is not the standard one. |
| title | The Leibniz PROP is a crossed presimplicial algebra |
| topic | Category Theory 17A32, 18M85, 18M32 |
| url | https://arxiv.org/abs/2404.10925 |