Regular categories, oligomorphic monoids, and tensor categories
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913281507065856 |
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| author | Snowden, Andrew |
| author_facet | Snowden, Andrew |
| contents | Knop constructed a tensor category associated to a finitely-powered regular category equipped with a degree function. In recent work with Harman, we constructed a tensor category associated to an oligomorphic group equipped with a measure. In this paper, we explain how Knop's approach fits into our theory. The first, and most important, step describes finitely-powered regular categories in terms of oligomorphic monoids; this may be of independent interest. We go on to examine some aspects of this construction when the regular category one starts with is the category of $G$-sets for an oligomorphic group $G$, which yields some interesting examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_16267 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regular categories, oligomorphic monoids, and tensor categories Snowden, Andrew Representation Theory Category Theory Knop constructed a tensor category associated to a finitely-powered regular category equipped with a degree function. In recent work with Harman, we constructed a tensor category associated to an oligomorphic group equipped with a measure. In this paper, we explain how Knop's approach fits into our theory. The first, and most important, step describes finitely-powered regular categories in terms of oligomorphic monoids; this may be of independent interest. We go on to examine some aspects of this construction when the regular category one starts with is the category of $G$-sets for an oligomorphic group $G$, which yields some interesting examples. |
| title | Regular categories, oligomorphic monoids, and tensor categories |
| topic | Representation Theory Category Theory |
| url | https://arxiv.org/abs/2403.16267 |