The existence of a (co)moment is an important prerequisite for many constructions in symplectic geometry. The recent discovery of a multisymplectic comoment, that is a morphismof L_infinity algebras, opened the pathway to reduction and quantization procedures in the multisymplectic realm. In this talk we will review the notion of multisymplectic comoment andgive a geometric characterization of its existence. We will then look at the case of actions on n-dimensional spheres and discuss what can still be done, when no homotopy comoment exists.
