Guitart states in "Toute theorie est algebrique et topologique" (Proposition 17) without proof (at least, I don't understand the hints there) that the category $\mathbf{Sch}$ of schemes is the category of models of a large mixed sketch. Presumably, it is built using Burroni's sketch of $\mathbf{Top}$.

Questions.

1. Can someone explain more how that sketch for $\mathbf{Sch}$ looks like?
2. Perhaps a first step would be to find sketches for the categories $\mathbf{RS}$ and $ \mathbf{LRS}$ of (locally) ringed spaces, but do they exist? I suspect that for this we first need to find a categorical characterization of local homeomorphisms ($\equiv$ sheaves) internal to $\mathbf{Top}$?
3. Is there a large limit sketch for the category of affine schemes, i.e. $\mathbf{CRing}^{\mathrm{op}}$? That would be a huge surprise. In case it helps, $\mathbf{CRing}^{\mathrm{op}}$ is not Isbell-compact. Is there, at least, a large mixed sketch for affine schemes?