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We construct semiorthogonal decompositions of Donaldson-Thomas (DT)categories for reduced curve classes on local surfaces into products ofquasi-BPS categories and Pandharipande-Thomas (PT) categories, giving acategorical analogue of the numerical DT/PT correspondence for Calabi-Yau3-folds. The main ingredient is a categorical wall-crossing formula for DT/PTquivers (which appear as Ext-quivers in the DT/PT wall-crossing) proved in ourprevious paper. We also study quasi-BPS categories of points on local surfacesand propose conjectural computations of their K-theory analogous to formulasalready known for the three dimensional affine space.

The categorical DT/PT correspondence and quasi-BPS categories for local surfaces