  We define a generalized form of $L_\infty$-algebras called
$EL_\infty$-algebras. As we show, these provide the natural algebraic framework
for generalized geometry and the symmetries of double field theory as well as
the gauge algebras arising in the tensor hierarchies of gauged supergravity.
Our perspective shows that the kinematical data of the tensor hierarchy is an
adjusted higher gauge theory, which is important for developing finite gauge
transformations as well as non-local descriptions. Mathematically,
$EL_\infty$-algebras provide small resolutions of the operad $\mathcal{L}ie$,
and they shed some light on Loday's problem of integrating Leibniz algebras.
