Let $𝕀$ be the category of finite sets and injections. The Schanuel topos is the category of pullback-preserving functors ${𝕀}^{\text{op}}\to \text{𝐒𝐞𝐭}$.

Equivalently, it is the category of nominal sets, which are sets equipped with an action by the group of permutations on a countable set of names $𝔸$, such that every element has finite support.