Local maps of ringed topoi

For \(E = \PSh(\CRing^{\mathrm{fp},\op})\), the lax slice \(\Topos_{//E}\) is the category of ringed topoi. For \(E = \Shv_{\Zar}(\CRing^{\mathrm{fp},\op})\), the lax slice \(\Topos_{//E}\) is the full subcategory of the previous one spanned by the locally ringed topoi. Here, the fracture \(E^{\corp} = \Shv_{\Zar}(\CRing^{\mathrm{fp}, \ad, \op}) \to E\) determines the subcategory \((\Topos_{//E})^{\loc}\) consisting of the local morphisms of locally ringed topoi.