Yep, though Grothendieck's perspective was more abstract. To him, affine schemes succinctly described coslice categories over a ring (with only localization map

Yep, though Grothendieck's perspective was more abstract. To him, affine schemes succinctly described coslice categories over a ring (with only localization maps). Adding equivalences back into the mix leads to his theory of stacks/descent. Adding more general localizations leads to his étale, fppf, fpqc results. His work has a more categorical than ring theoretic flavor.