nLab n-truncated structured (infinity,1)-topos

A structured (infinity,1)-topos $\mathcal{O}_{\mathcal{X}} : \mathcal{G} \to \mathcal{X}$ is called $n$-truncated if the image of each object of the geometry (for structured (infinity,1)-toposes) $\mathcal{G}$ is an n-truncated object of $\mathcal{X}$.

See derived scheme and derived Deligne-Mumford stack for discussion of examples of $n$-truncated structured $(\infty,1)$-toposes.