From coextensive varieties to the Gaeta topos

Abstract

In this paper, we show that in every coextensive variety V, the assignment that maps each algebra to its set of central elements is both functorial and representable. Furthermore, we prove that the full subcategory of finitely presented algebras in V is coextensive. Finally, we establish that if V is additionally (0, 1)-dense, the Gaeta topos classifies central-free V-models.