预伽罗瓦范畴与弗拉伊塞定理
Pre-Galois categories and Fraïssé's theorem
AI总结：
本文引入预伽罗瓦范畴作为预坦纳卡范畴的组合类比，证明寡态群的光滑G-集范畴构成预伽罗瓦范畴且此类例子穷尽，从而重新表述弗拉伊塞定理，并借助置换类给出非预伽罗瓦的B-范畴例子。
摘要：
伽罗瓦范畴可被视为坦纳卡范畴的组合类比。我们引入预伽罗瓦范畴的概念，它可被视为预坦纳卡范畴的组合类比。给定一个寡态群 $G$，有限光滑 $G$-集的范畴 $\mathbf{S}(G)$ 是预伽罗瓦的。我们的主要定理（大致）表明这些例子是穷尽的；从某种意义上说，这一结果是弗拉伊塞定理的重新表述。我们还引入了一类更一般的 B-范畴，并利用置换类给出了一些不是预伽罗瓦的 B-范畴的例子。这项工作的动机来自对预坦纳卡范畴的某些应用。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
