  In this paper, we prove that there is a canonical homotopy $(n+1)$-algebra
structure on the shifted operadic deformation complex
$Def(e_n\to\mathcal{P})[-n]$ for any operad $\mathcal{P}$ and a map of operads
$f\colon e_n\to\mathcal{P}$. This result generalizes the result of [T2], where
the case $\mathcal{P}=\mathrm{End}_{Op}(X)$ was considered. Another more
computational proof of the same statement was recently sketched in [CW].
  Our method combines the one of [T2] with the categorical algebra on the
category of symmetric sequences, introduced in [R] and further developed in
[KM] and [Fr1]. We define suitable deformation functors on $n$-coalgebras,
which are considered as the "non-commutative" base of deformation, prove their
representability, and translate properties of the functors to the corresponding
properties of the representing objects. A new point, which makes the method
more powerful, is to consider the argument of our deformation theory as an
object of the category of symmetric sequences of dg vector spaces, not as just
a single dg vector space.
