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Adams-type maps are not stable under composition
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 of \(\mathbb{E}_{\infty}\)-algebras is a transfinite composition of Adams-type maps.
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Published in: | arXiv.org 2022-02 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Online Access: | Get full text |
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Summary: | 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 of \(\mathbb{E}_{\infty}\)-algebras is a transfinite composition of Adams-type maps. |
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ISSN: | 2331-8422 |