The following statement is quoted from "Verdier duality" in wiki:
If $X$ is a finite-dimensional locally compact space, and $D^b(X)$ the bounded derived category of sheaves of abelian groups over $X$, then the Verdier dual is a contravariant functor $D: D^b(X) \rightarrow D^b(X)$ defined by $D(\mathcal{F}) = RHom(\mathcal{F},\omega_X)$
It has the following properties:
$D^2(\mathcal{F})\cong \mathcal{F}$ for sheaves with constructible cohomology.
(Intertwining of functors $f_*$ and $f_!$) If $f$ is a continuous map from $X$ to $Y$ then there is an isomorphism $D(Rf_{\ast}(\mathcal{F})) \cong Rf_!D(\mathcal{F})$.
This is the page in wiki for "Verdier duality". I don't understand why $\mathcal{F}$ should have constructible cohomology (the first property). Can anyone help me? Thanks a lot!