Recognition of connective commutative algebra spectra through an idempotent quasiadjunction

Vasconcellos Vieira, Renato

doi:10.2140/agt.2023.23.295

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Recognition of connective commutative algebra spectra through an idempotent quasiadjunction

Renato Vasconcellos Vieira

Algebraic & Geometric Topology 23 (2023) 295–338

DOI: 10.2140/agt.2023.23.295

Abstract

A recognition principle for $\infty$ –loop pairs of spaces of connective commutative algebra spectra over connective commutative ring spectra is proved. This is done by generalizing the classical recognition principle for connective commutative ring spectra using relative operads. The machinery of weak Quillen quasiadjunctions, a generalization of Quillen adjunctions, is used to handle the model theoretical aspects of the proof.

Keywords

spectra, ring spectra, algebra spectra, loop space machines, operads, stable homotopy theory, infinite loop spaces, localization, model categories

Mathematical Subject Classification

Primary: 55P43, 55P48

Secondary: 55P42, 55P47, 55P60, 55P65

References

Publication

Received: 25 February 2021

Revised: 1 August 2021

Accepted: 12 October 2021

Published: 27 March 2023

Authors

Renato Vasconcellos Vieira
Instituto de Ciências Matemáticas e de Computação Universidade de São Paulo São Carlos Brazil

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Volume 23, issue 1 (2023)