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Recognition of connective commutative algebra spectra through an idempotent quasiadjunction

Renato Vasconcellos Vieira

Algebraic & Geometric Topology 23 (2023) 295–338
Abstract

A recognition principle for –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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