  We show how the BV-BFV formalism provides natural solutions to descent
equations, and discuss how it relates to the emergence of holographic
counterparts of given gauge theories. Furthermore, by means of an AKSZ-type
construction we reproduce the Chern-Simons to Wess-Zumino-Witten correspondence
from infinitesimal local data, and show an analogous correspondence for BF
theory. We discuss how holographic correspondences relate to choices of
polarisation relevant for quantisation, proposing a semi-classical
interpretation of the quantum holographic principle.
