  We identify the type of $\mathbb{C}[[\hbar]]$-linear structure inherent in
the $\infty$-categories which arise in the theory of Deformation Quantization
modules. Using this structure, we show that the $\infty$-category of
quasicoherent cohomologically complete DQ-modules is a deformation of the
$\infty$-category of quasicoherent sheaves. We also obtain integral
representation results for DQ-modules similar to the ones of To\"en and
Ben-Zvi-Nadler-Francis, stating that suitably linear functors between
$\infty$-categories of DQ-modules are integral transforms.
