Graded extention of categorical groups of the type (Π, A)

In this paper, we present the concept of strict factor set on the group Γ with coefficients in categorical groups of the type (Π, A). We define the element h ∈ H3 Γ and give a new interpretation of cohomology groups with third-dimensional operator Γ. The element h determines a 1-1 correspondence between classes of factor sets on Γ with coefficients in (Π, A) and group H3 Γ (Π, A).