Pro-C groups and Pro-C pseudo simplicial groups

Using the homotopy groups of pseudosimplicial groups, Inasaridze, [11], construct nonabelian derived functors with values in the category of groupsWe gave some basic information. Using the Inasaridze, [11], define pseudosimplicial groups. We show that the category of crossed module is equivalent to the category of Pro-C pseudosimplicial groups with Moore complexes of lenght 1. Also we define pseudo Pro-C 2-crossed module and we prove that the category of pseudo Pro-C 2-crossed module is equivalent to the category of pseudo simplicial groups with Moore complex of lenght 2. Using the Inasaridze, [11],[12] constructed homotopy groups of Pro-C pseudosimplicial groups and non abelian derived functors with values in the category of group. We define Profinite pseudosimplicial algebra considering Profinite pseudosimplicial algebras. We show that the category of crossed module is equivalent to the category of Profinite pseudosimplicial algebras with Moore complexes of lenght 1. Also we define Profinite pseudo 2-crossed module and we prove that the category of Profinite pseudo 2-crossed module is equivalent to the category of Profinite pseudo simplicial algebras with Moore complex of lenght 2.