The fundamental theorem of topos theory states that the slice categories $\mathcal{E}/A$ of a (Grothendieck) topos $\mathcal{E}$ are again (Grothendieck) toposes.
If $\mathcal{E}$ is of the form $\mathrm{Sh}(C, J)$ for some subcanonical site $(C,J)$, then if $A$ is some object of $\mathcal{E}$, can we write $\mathcal{E}/A$ as sheaves on $C/A$ (identifying $C$ with the representable sheaves) with an appropriate choice of topology on $C/A$?