  In this paper we give an explicit description of the left adjoint of the
forgetful functor from the algebraic category of G\"odel algebras (i.e.,
prelinear Heyting algebras) to the algebraic category of bounded prelinear
Hilbert algebras. We apply this result in order to study possible descriptions
of the coproduct of two finite algebras in the algebraic category of prelinear
Hilbert algebras.
