Joint with Sarah Whitehouse

Tall-Wraith monoids were introduced in The Hunting of the Hopf Ring to describe the algebraic structure on the set of unstable operations of a suitable generalised cohomology theory. In this paper we begin the study of Tall-Wraith monoids in an algebraic and categorical setting. We show that for V a variety of algebras, applying the free V-algebra functor to a monoid in Set produces a Tall-Wraith monoid. We also study the example of the Tall-Wraith monoid defined by the self set-maps of a finite ring, an example closely related to the original motivation for Tall-Wraith monoids.

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• In a 2-up version as PDF or PS
• In a 1-up version as PDF or PS
• On the arxiv as 1102.3549.