  Within unfolded dynamics approach, we represent actions and conserved charges
as elements of cohomology of the $L_\infty$ algebra underlying the unfolded
formulation of a given dynamical system. The unfolded off-shell constraints for
symmetric fields of all spins in Minkowski space are shown to have the form of
zero curvature and covariant constancy conditions for 1-forms and 0-forms
taking values in an appropriate star product algebra. Unfolded formulation of
Yang-Mills and Einstein equations is presented in a closed form.
