  We show the existence of semiorthogonal decompositions of Donaldson-Thomas
categories for $(-1)$-shifted cotangent derived stacks associated with
$\Theta$-stratifications on them. Our main result gives an analogue of window
theorem for categorical DT theory, which has applications to d-critical
analogue of D/K equivalence conjecture, i.e. existence of fully-faithful
functors (equivalences) under d-critical flips (flops). As an example of
applications, we show the existence of fully-faithful functors of DT categories
for Pandharipande-Thomas stable pair moduli spaces under wall-crossing at
super-rigid rational curves for any relative reduced curve classes.
