Formal plethories

Abstract

Unstable operations in a generalized cohomology theory E give rise to a functor from the category of algebras over E to itself which is a colimit of representable functors and a comonoid with respect to composition of such functors. In this paper I set up a framework to study the algebra of such functors, which I call formal plethories, in the case where $E_{\ast }$ is a Prüfer ring. I show that the "logarithmic" functors of primitives and indecomposables give linear approximations of formal plethories by bimonoids in the 2-monoidal category of bimodules over a ring.

61 pages, to appear in Adv. Math

Cited by in corpus (2)

• Commutative ring objects in pro-categories and generalized Moore spectra
• The plethory of operations in complex topological K-theory