  This paper proves certain facts concerning the equivariance of quantization
of pi-finite spaces. We argue that these facts establish an analogy between
this quantization procedure and the geometric quantization of a symplectic
vector space. Specifically, we observe that symmetries of a given
polarization/Lagrangian always induce coherent symmetries of the quantization.
On the other hand, symmetries of the entire phase space a priori only induce
projective symmetries. For certain three-dimensional theories, this
projectivity appears via a twice-categorified analogue of
Blattner-Kostant-Sternberg kernels in geometric quantization and the associated
integral transforms.
