  We construct semiorthogonal decompositions of Donaldson-Thomas (DT)
categories for reduced curve classes on local surfaces into products of
quasi-BPS categories and Pandharipande-Thomas (PT) categories, giving a
categorical analogue of the numerical DT/PT correspondence for Calabi-Yau
3-folds. The main ingredient is a categorical wall-crossing formula for DT/PT
quivers (which appear as Ext-quivers in the DT/PT wall-crossing) proved in our
previous paper. We also study quasi-BPS categories of points on local surfaces
and propose conjectural computations of their K-theory analogous to formulas
already known for the three dimensional affine space.
