  This is a continuation of prior work of the author on cosection localization
for d-manifolds. We construct reduced virtual fundamental classes for derived
manifolds with surjective cosections and cosection localized virtual
fundamental classes for $(-2)$-shifted symplectic derived schemes in larger
generality. Moreover, using recent results of Oh-Thomas, we show that the
algebraic and differential geometric constructions of reduced and cosection
localized virtual fundamental classes of $(-2)$-shifted symplectic derived
schemes yield the same result in homology. We obtain applications towards the
construction and integrality of reduced invariants in Donaldson-Thomas theory
of Calabi-Yau fourfolds.
