  This is the fifth article in the Derived Langlands series which consists of
one monograph and four articles. In this article I describe the Hopf algebra
and Positive Selfadjoint Hopfalgebra (PSH) aspects to classification of a
number of new classes of presentations and admissibility which have appeared
earlier in the series. The paper begins with a very estensive. partly
hypothetical, of the synthesis of the entire series. Many of the proofs and
ideas in this series are intended to be suggestive rather than the finished
definitive product for extenuating circumstances explained therein.
