  If quantum mechanics were to be applicable to macroscopic objects, classical
mechanics would have to be a limiting case of quantum mechanics. Then the
category Set that packages classical mechanics has to be in some sense a
'limiting case' of the category Hilb packaging quantum mechanics. Following
from this assumption, quantum-classical correspondence can be considered as a
mapping of the category Hilb to the category Set, i.e., a functor from Hilb to
Set, taking place in the macroscopic limit. As a procedure, which takes us from
an object of the category Hilb (i.e., a Hilbert space) in the macroscopic limit
to an object of the category Set (i.e., a set of values that describe the
configuration of a system), this functor must take a finite number of steps in
order to make the equivalence of Hilb and Set verifiable. However, as it is
shown in the present paper, such a constructivist requirement cannot be met in
at least one case of an Ising model of a spin glass. This could mean that it is
impossible to demonstrate the emergence of classicality totally from the
formalism of standard quantum mechanics.
