  Given a $\mathfrak{g}$-action on a Poisson manifold $(M, \pi)$ and an
equivariant map $J: M \rightarrow \mathfrak{h}^*,$ for $\mathfrak{h}$ a
$\mathfrak{g}$-module, we obtain, under natural compatibility and regularity
conditions previously considered by Cattaneo-Zambon, a homotopy Poisson algebra
generalizing the classical BFV algebra described by Kostant-Sternberg in the
usual hamiltonian setting. As an application of our methods, we also derive
homological models for the reduced spaces associated to quasi-Poisson and
hamiltonian quasi-Poisson spaces.
