scheme theory

This book develops Grothendieck's scheme theory as a method for studying algebraic geometry. […] In the preface of EGA [ Éléments de géométrie algébrique ], Grothendieck even claimed that a knowledge of classical algebraic geometry may hinder the reader from studying scheme theory.

With these ideas of scheme theory, perturbation, and abstraction, it becomes possible to see how metacognition might be interpreted in constructivist terms.