Adams-type maps are not stable under composition

Abstract

We give a simple counterexample to the plausible conjecture that Adams-type maps of ring spectra are stable under composition. We then show that over a field, this failure is quite extreme, as any map to an E ∞ \mathbb {E}_{\infty } - k k -algebra is a transfinite composition of Adams-type maps.

Dirac geometry II: coherent cohomology

“… 7 Equivalently, we assume that is descent-flat in the terminology of [5], where it is proved that this property of is not stable under composition. …”