  We show that an $L_\infty$-algebra can be extended to a graded Hopf algebra
with a codifferential. Then we twist this extended $L_\infty$-algebra with a
Drinfel'd twist, simultaneously twisting its modules. Taking the
$L_\infty$-algebra as its own (Hopf) module, we obtain the recently proposed
braided $L_\infty$-algebra. The Hopf algebra morphisms are identified with the
strict $L_\infty$-morphisms, while the braided $L_\infty$-morphisms define a
more general $L_\infty$-action of twisted $L_\infty$-algebras.
