  Membrane sigma-models have been used for the systematic description of closed
strings in non-geometric flux backgrounds. In particular, the conditions for
gauge invariance of the corresponding action functionals were related to the
Bianchi identities for the fluxes. In this contribution we demonstrate how to
express these Bianchi identities in terms of homotopy relations of the
underlying $L_\infty$-algebra for the case of the Courant sigma-model. We argue
that this result can be utilized in understanding the constraint structure of
Double Field Theory and the corresponding membrane sigma-model.
