Definition 7.23.
We define the subcategory
\[\Sch_{\Gg} \quad \subseteq \quad \Topos^{\loc}_{//E}\]
of \(\Gg\)-schemes as the full subcategory on those objects which are locally in the image of \(\Spec_{\Gg}\). Concretely, a \(\Gg\)-scheme admits a jointly surjective family of étale morphisms from affine objects \(\Spec_{\Gg}(A)\) with \(A\in\Pro(C)\).