  In this short paper we prove a derived version of the Riemann-Hilbert
correspondence of Deligne and Simpson. Our generalization is twofold: on one
side we consider families of representations of the full homotopy type of a
smooth analytic space $X$ in the stable $\infty$-category of complexes of
coherent sheaves and of perfect complexes; on the other side, we allow the base
parametrizing such families to be derived $\mathbb C$-analytic spaces.
