Structured $(\infty,1)$-topos $(X,O_{G,X})$ where (1) $X$ is an $(\infty,1)$-topos (2) $G=(\underline G, Ad_G)$ is a *geometry*, i.e. $\underline G$ is an essentially small $(\infty,1)$-category with finite limits, which is idempotent complete, $Ad_G$ is an admissible structure in $\underline G$. (3) $O_{G,X}:G\to X$ is a *$G$-structure (aka "structure sheaf") on $X$*, i.e. a functor which is (3a) left exact (3b) induces a jointly epimorphic family in the image of $O_{G,X}$ (i.e. every covering sieve consisting of admissible morphisms on an object of $X$ induces an effective epimorphism out of the product of the images...)