  In arXiv:1606.07885, many different Grothendieck topologies were introduced
on the category of Azumaya algebras. Here we give a classification in terms of
sets of supernatural numbers. Then we discuss the associated categories of
sheaves and their topos-theoretic points, which are related to UHF-algebras.
The sheaf toposes that correspond to a single supernatural number have an
alternative description, involving actions of the associated projective general
linear group.
