  We introduce a foundational sheaf theoretical scheme for the comprehension of
quantum event structures, in terms of localization systems consisting of
Boolean coordinatization coverings induced by measurement. The scheme is based
on the existence of a categorical adjunction between presheaves of Boolean
event algebras and Quantum event algebras. On the basis of this adjoint
correspondence we prove the existence of an object of truth values in the
category of quantum logics, characterized as subobject classifier. This
classifying object plays the equivalent role that the two-valued Boolean truth
values object plays in classical event structures. We construct the object of
quantum truth values explicitly and argue that it constitutes the appropriate
choice for the valuation of propositions describing the behavior of quantum
systems.
