Example 7.16.

Every geometry listed in Section 7.2 gives a fractured topos by this construction. For instance, the classical Zariski geometry gives the pair

\[\Shv_{\Zar}((\CRing^{\mathrm{fp},\ad})\catop) \longrightarrow \Shv_{\Zar}((\CRing^{\mathrm{fp}})\catop),\]

which is the fractured topos underlying the topos-theoretic description of ordinary schemes above.