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Let 
$\mathcal {F}$ be a polystable sheaf on a smooth minimal projective surface of Kodaira dimension 0. Then the differential graded (DG) Lie algebra 
$R\operatorname {Hom}(\mathcal {F},\mathcal {F})$ of derived endomorphisms of 
$\mathcal {F}$ is formal. The proof is based on the study of equivariant 
$L_{\infty }$ minimal models of DG Lie algebras equipped with a cyclic structure of degree 2 which is non-degenerate in cohomology, and does not rely (even for K3 surfaces) on previous results on the same subject.
