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For X a compact oriented topological manifold and k a field, Verdier duality on locally constant sheaves of k-modules on X can be encoded in a non-commutative symplectic structure, called Calabi—Yau structure. Brav—Dyckerhoff also introduced a relative notion of such, which allows one to recover Verdier duality for manifolds with boundaries. If now X is equipped with a (nice enough) finite stratification P, we show that there exists a Calabi—Yau structure on the k-linear stable infinity-category of constructible sheaves on (X,P). In this case, even if X itself has no boundary, we will get a relative Calabi—Yau structure, where the role of the boundary is replaced by the tubular neighborhoods of the strata. This is joint work with Merlin Christ.