  In this note we give the Kolyvagin recursion in cyclotomic Euler systens a
new and universal interpretation with the help of the double complex method
introduced by Anderson and further developed by Das and Ouyang. Namely, we show
that the recursion satisfied by Kolyvagin classes is the specialization of a
universal recursion independent of the chosen field satisfied by universal
Kolyvagin classes in the group cohomology of the universal ordinary
distribution a la Kubert. Further, we show by a method involving a variant of
the diagonal shift operation introduced by Das that certain group cohomology
classes belonging (up to sign) to a basis previously constructed by Ouyang also
satisfy the universal recursion.
