Implementing the biset category of finite groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866913149132734464 |
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| author | Barakat, Mohamed Talleux, Marc Zickgraf, Fabian |
| author_facet | Barakat, Mohamed Talleux, Marc Zickgraf, Fabian |
| contents | We describe an implementation of the biset category of finite groups as a tower of standard categorical constructions, all of which are implemented in the software projec t CAP for algorithmic category theory. In particular, we describe the composition of bisets as a composition in a Kleisli category of some biadjunction monad. This composition relies on the universal property of the coequalizer completion of a group viewed as a groupoid on one object. Expressing this universal property offers an elegant categorical interpretation of the Schreier-Sims orbit algorithm. Indeed, the implementation relies on every aspect of the algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_18346 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Implementing the biset category of finite groups Barakat, Mohamed Talleux, Marc Zickgraf, Fabian Category Theory Group Theory We describe an implementation of the biset category of finite groups as a tower of standard categorical constructions, all of which are implemented in the software projec t CAP for algorithmic category theory. In particular, we describe the composition of bisets as a composition in a Kleisli category of some biadjunction monad. This composition relies on the universal property of the coequalizer completion of a group viewed as a groupoid on one object. Expressing this universal property offers an elegant categorical interpretation of the Schreier-Sims orbit algorithm. Indeed, the implementation relies on every aspect of the algorithm. |
| title | Implementing the biset category of finite groups |
| topic | Category Theory Group Theory |
| url | https://arxiv.org/abs/2604.18346 |