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In this paper we prove a duality for constructible sheaves on conicallysmooth stratified spaces. Here we consider sheaves with values in a stable andbicomplete $\infty$-category equipped with a closed symmetric monoidalstructure, and in this setting constructible means locally constant alongstrata and with dualizable stalks. The crucial point where we need to employthe geometry of conically smooth structures is in showing that Lurie's versionof Verdier duality restricts to an equivalence between constructible sheavesand cosheaves: this requires a computation of the exit path $\infty$-categoryof a compact stratified space, that we obtain via resolution of singularities.

Verdier duality on conically smooth stratified spaces