  This paper is on elimination of defining equations of the cyclotomic
analogues, introduced by the first author, of Drinfeld's scheme of associators.
We show that the mixed pentagon equation implies the octagon equation for N=2
and the particular distribution relation. We also explain that Broadhurst
duality is compatible with the torsor structure. We develop a formalism of
infinitesimal module categories and use it for deriving a proof left implicit
in the first named author's earlier work.
