  We consider some generalization of the theory of quantum states and
demonstrate that the consideration of quantum states as sheaves can provide, in
principle, more deep understanding of some well-known phenomena. The key
ingredients of the proposed construction are the families of sections of
sheaves with values in the proper category of the functional realizations of
infinite-dimensional Hilbert spaces with special (multiscale) filtrations
decomposed into the (entangled) orbits generated by actions/representations of
internal hidden symmetries. In such a way, we open a possibility for the exact
description and reinterpretation of a lot of quantum phenomena.
