Relativity of reductive chain complexes of non-abelian simplexes

Chain total double complexes with reductive differentials for non-abelian simplexes with associated spaces are considered. It is conjectured that corresponding relative cohomology is equivalent to the coset space of vanishing over non-vanishing functionals related to differentials of complexes. The conjecture is supported by the theorem for the case of spaces of correlation functions and generalized connections on vertex operator algebra bundles.