  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 Fra\"iss\'e'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.
