Title: The Hunting of the Hopf Ring
Authors: Andrew Stacey and Sarah Whitehouse
MSC: 55S25 (primary); 55N20, 16W99 (secondary)
arXiv: 0711.3722
Addresses of authors:
  Andrew Stacey
  Institutt for matematiske fag
  NTNU
  7491 Trondheim
  Norway
  andrew.stacey@math.ntnu.no

  Sarah Whitehouse
  Department of Pure Mathematics
  University of Sheffield
  Sheffield S3 7RH
  UK
  S.Whitehouse@sheffield.ac.uk

Abstract:
We provide a new algebraic description of the structure on the set of all
unstable cohomology operations for a suitable generalised cohomology theory,
E^*. Our description is as a graded and completed version of a Tall-Wraith
monoid. The E^*-cohomology of a space X is a module for this Tall-Wraith
monoid.  We also show that the corresponding Hopf ring of unstable
co-operations is a module for the Tall-Wraith monoid of unstable operations.
Further examples are provided by considering operations from one theory to
another.