We know that the category of Boolean algebras and homomorphisms is the ind-completion of $\mathsf{FinBA}$, the full subcategory of $\mathsf{BA}$ of finite Boolean algebras. I am wondering if the same holds for the category $\mathsf{HA}$ of Heyting algebras and Heyting morphisms.
Since Heyting algebras are models of an algebraic theory we know that it has filtered colimits. But I don't know how to prove that every Heyting algebra is the colimit of the diagram of its finite subalgebras.