Joint with Sarah Whitehouse

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.

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• Published version in Homology, Homotopy and Applications, Volume 11(2), 2009, p75-132.
• On the arXiv as 0711.3722
• In a 2-up version as PDF or PS