  A DFT algebroid is a special case of the metric (or Vaisman) algebroid, shown
to be relevant in understanding the symmetries of double field theory. In
particular, a DFT algebroid is a structure defined on a vector bundle over
doubled spacetime equipped with the C-bracket of double field theory. In this
paper we give the definition of a DFT algebroid as a curved $L_\infty$-algebra
and show how implementation of the strong constraint of double field theory can
be formulated as an $L_\infty$-algebra morphism. Our results provide a useful
step towards coordinate invariant descriptions of double field theory and the
construction of the corresponding sigma-model.
