  We show the existence of semiorthogonal decompositions (SOD) of
Pandharipande-Thomas (PT) stable pair moduli spaces on Calabi-Yau 3-folds with
irreducible curve classes, assuming relevant moduli spaces are non-singular.
The above result is motivated by categorifications of wall-crossing formula of
PT invariants in the derived category, and also a d-critical analogue of
Bondal-Orlov, Kawamata's D/K equivalence conjecture. We also give SOD of stable
pair moduli spaces on K3 surfaces, which categorifies Kawai-Yoshioka's formula
proving Katz-Klemm-Vafa formula for PT invariants on K3 surfaces with
irreducible curve classes.
