  In this paper we provided an explicit construction for the left adjoint of
the forgetful functor from the category of Heyting algebras to that of Hilbert
algebras. This functor factorizes through the free implicative semilattice
extension of a Hilbert algebra of Celani and Jansana [On the free implicative
semilattice extension of a Hilbert algebra}. Mathematical Logic Quarterly 58, 3
(2012), 188--207].
