  Given two Lie $\infty$-algebras $E$ and $V$, any Lie $\infty$-action of $E$
on $V$ defines a Lie $\infty$-algebra structure on $E\oplus V$. Some
compatibility between the action and the Lie $\infty$-structure on $V$ is
needed to obtain a particular Loday $\infty$-algebra, the non-abelian
hemisemidirect product. These are the coherent actions. For coherent actions it
is possible to define non-abelian homotopy embedding tensors as Maurer-Cartan
elements of a convenient Lie $\infty$-algebra. Generalizing the classical case,
we see that a non-abelian homotopy embedding tensor defines a Loday
$\infty$-structure on $V$ and is a morphism between this new Loday
$\infty$-algebra and $E$.
