  In a recent paper arXiv:0705.3190, we gave a general construction of a
para-cocyclic structure on a cosimplex, associated to a so called admissible
septuple -- consisting of two categories, three functors and two natural
transformations, subject to compatibility relations. The main examples of such
admissible septuples were induced by algebra homomorphisms. In this note we
provide more general examples coming from appropriate (`locally braided')
morphisms of monads.
