  Consider a closed non-degenerate 3-form $\omega$ with an infinitesimal action
of a Lie algebra $\mathfrak{g}$. Motivated by the fact that the observables
associated to $\omega$ form a Lie 2-algebra, we introduce homotopy moment maps
defined on a Lie 2-algebra rather than just on the Lie algebra $\mathfrak{g}$.
  We formulate existence criteria and provide a construction for such homotopy
moment maps, by characterizing them in terms of cohomology.
