  In this paper we propose a procedure for a noncommutative derived Poisson
reduction, in the spirit of the Kontsevich-Rosenberg principle: "a
noncommutative structure of some kind on $A$ should give an analogous
commutative structure on all schemes ${\mathrm{Rep}}_n(A)$". We use double
Poisson structures as noncommutative Poisson structures and noncommutative
Hamiltonian spaces -- as first introduced by M. Van den Bergh -- to define
(derived) zero loci of Hamiltonian actions and a noncommutative
Chevalley-Eilenberg and BRST constructions, showing how we recover the
corresponding commutative constructions using the representation functor. In a
dedicated final short section we highlight how the categorical properties of
the representation functor lead to the natural introduction of new interesting
notions, such as noncommutative group schemes, group actions, or Poisson-group
schemes, which could help to understand the previous results in a different
light, and in future research generalise them into a broader, clearer
correspondence between noncommutative and commutative equivariant geometry.
