Operadic right modules via the dendroidal formalism

In this work we study the homotopy theory of the category RMod₏ of right modules over a simplicial operad P via the formalism of forest spaces fSpaces, as introduced by Heuts, Hinich and Moerdijk. In particular, we show that, for P is closed and -free, there exists a Quillen equivalence between the projective model structure on RMod₏, and the contravariant model structure on the slice category fSpaces/₍₏ over the dendroidal nerve of P. As an application, we comment on how this result can be used to compute derived mapping spaces of between operadic right modules.