Abstract
We introduce the notions of generalized join-hemimorphism and
generalized Boolean relation as an extension of the notions of
join-hemimorphism and Boolean relation, respectively. We prove a
duality between these two notions. We will also define a
generalization of the notion of Boolean algebra with operators by
considering a finite family of Boolean algebras endowed with a
generalized join-hemimorphism. Finally, we define suitable
notions of subalgebra, congruences, Boolean equivalence, and open
filters.