Categorical wall-crossing formula for Donaldson-Thomas theory on the resolved conifold

We prove a wall-crossing formula for categorical Donaldson-Thomas invariants on the resolved conifold, which categorifies the Nagao-Nakajima wall-crossing formula for numerical DT invariants on it. The categorified Hall products are used to describe the wall-crossing formula as semiorthogonal decompositions. A successive application of the categorical wall-crossing formula yields semiorthogonal decompositions of categorical Pandharipande-Thomas stable pair invariants on the resolved conifold, which categorify the product expansion formula of the generating series of numerical PT invariants on it.