Pre-Galois categories and Fraïssé's theorem
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866910342357975040 |
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| author | Harman, Nate Snowden, Andrew |
| author_facet | Harman, Nate Snowden, Andrew |
| contents | Galois categories can be viewed as the combinatorial analog of Tannakian categories. We introduce the notion of pre-Galois category, which can be viewed as the combinatorial analog of pre-Tannakian categories. Given an oligomorphic group $G$, the category $\mathbf{S}(G)$ of finitary smooth $G$-sets is pre-Galois. Our main theorem (approximately) says that these examples are exhaustive; this result is, in a sense, a reformulation of Fraïssé's theorem. We also introduce a more general class of B-categories, and give some examples of B-categories that are not pre-Galois using permutation classes. This work is motivated by certain applications to pre-Tannakian categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_13784 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Pre-Galois categories and Fraïssé's theorem Harman, Nate Snowden, Andrew Representation Theory Category Theory Galois categories can be viewed as the combinatorial analog of Tannakian categories. We introduce the notion of pre-Galois category, which can be viewed as the combinatorial analog of pre-Tannakian categories. Given an oligomorphic group $G$, the category $\mathbf{S}(G)$ of finitary smooth $G$-sets is pre-Galois. Our main theorem (approximately) says that these examples are exhaustive; this result is, in a sense, a reformulation of Fraïssé's theorem. We also introduce a more general class of B-categories, and give some examples of B-categories that are not pre-Galois using permutation classes. This work is motivated by certain applications to pre-Tannakian categories. |
| title | Pre-Galois categories and Fraïssé's theorem |
| topic | Representation Theory Category Theory |
| url | https://arxiv.org/abs/2301.13784 |