  Pre-Tannakian categories are a natural class of tensor categories that can be
viewed as generalizations of algebraic groups. We define a pre-Tannkian
category to be discrete if it is generated by an \'etale commutative algebra;
these categories generalize finite groups. The main theorem of this paper
establishes a rough classification of these categories: we show that any
discrete pre-Tannakian $\mathcal{C}$ category is associated to an oligomorphic
group $G$, via a construction we recently introduced. In certain cases, such as
when $\mathcal{C}$ has enough projectives, we completely describe $\mathcal{C}$
in terms of $G$.
