  In this paper we show how the theory of monads can be used to deduce in a
uniform manner several duality theorems involving categories of relations on
one side and categories of algebras with homomorphisms preserving only some
operations on the other. Furthermore, we investigate the monoidal structure
induced by Cartesian product on the relational side and show that in some cases
the corresponding operation on the algebraic side represents bimorphisms.

Logic