  The idea of the work is to find an invariant way to pass from deformation
theory to cohomology, which does not use any explicit cocycles. The appropriate
cohomology theory is based on considering sheaves on a certain site. An
advantage of the approach is that it enables one to give a simultanious
treatement to all types of algebras. As an application, we prove the PBW
theorem in cases where it is not yet known.
