In this talk I will extend the cohomological setting developed by Batalin, Fradkin and Vilkovisky (BFV), which produces a resolution of coisotropic reduction in terms of hamiltonian dg manifolds, to the case of nested coisotropic embeddings inside a symplectic manifold. I will use this extension to prove that "resolution commutes with reduction" for a general class of nested coisotropic embeddings. This talk is based on  arXiv:2410.23184, a joint work with M. Schiavina.