  For an object $A$ of a category of interest $\mathbb{C}$ we construct the
group with operations ${\mathfrak{B}}(A)$ and the semidirect product
${\mathfrak{B}}(A)\ltimes A$ and prove that there exists an actor of $A$ in
$\mathbb{C}$ if and only if ${\mathfrak{B}}(A)\ltimes A \in \mathbb{C}$. The
cases of groups, Lie, Leibniz, associative, commutative associative,
alternative algebras, crossed and precrossed modules are considered. The paper
contains some results for the case $\Omega_2 = \{+,*,*^{\circ}\}$.
