The full simplicially enriched subcategory spanned by Stein manifolds has a Grothendieck topology on the category of homotopy components: namely a cover of a Stein manifold $S$ is a family of holomorphic maps $\{X_\alpha\to S\}_\alpha$ such that we can deform each of them (by a homotopy within $Map(X_\alpha,S)$) to a biholomorphic map onto a Stein open subset in $S$, such that these Stein open subsets cover $S$.

This simplicial site is called the simplicial Stein site$Stein_\Delta$.