This work represents the concept of an n-groupoid Γ
n and ncharacters χn on n-groupoids as complex-valued maps from spaces of different classes of morphisms satisfying the condition χn(ψ◦kϕ) = χn(ψ)+χn(ϕ)
for any possible compositions. A sequence of spaces of n-characters and
morphisms between them is constructed and its accuracy is shown. This
construction has important application for describing the derivations in a
group algebras. In particular, this approach allows us to study the algebra of external derivations from a new point of view, and also to construct
some interesting examples. The work was carried out under the guidance of
Arutyunov A. A.. And it is based on the Mishchenko A. S. ideas.