A complete Heyting algebra is a Heyting algebra which is also a complete lattice; that is, it is a poset with arbitrary limits and colimits, that is also cartesian closed. By the adjoint functor theorem, one can demonstrate that every frame is a complete Heyting algebra, and vice versa, so far as the underlying poset goes. However, morphisms of frames needn’t preserve exponential objects or infinitary meets, as would most naturally be required of morphisms of complete Heyting algebras. Also,...