Abstract
For an object
A
of a category of interest
C
we construct the group with operations
B(A)
and the semidirect product
B(A)⋉A
and prove that there exists an actor of
A
in
C
if and only if
B(A)⋉A∈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
Ω
2
={+,∗,
∗
∘
}
.