nLab model structure on S-modules

Idea

A model structure on spectra for S-modules.

The category of S-modules (EKMM 97) is a presentation of the symmetric monoidal (∞,1)-category of spectra, with the special property that it implements the smash product of spectra such as to yield itself a symmetric monoidal model category of spectra: the model structure on symmetric spectra. This implies in particular that with respect to this symmetric smash product of spectra an E-∞ ring is presented simply as a plain commutative monoid in S-modules.

Properties

Relation to the model structure on symmetric spectra

There is a Quillen equivalence to the model structure on symmetric spectra (Schwede 01).

Relation to model structure on orthogonal structure

Comparison to the model structure on orthogonal spectra is due to (Mandell 04).

Related concepts

model structure on spectra

• sequential spectrum, model structure on sequential spectra

with symmetric monoidal smash product of spectra

• symmetric spectrum, model structure on symmetric spectra

• orthogonal spectrum, model structure on orthogonal spectra

• S-module, model structure on S-modules

• excisive functor, model structure on excisive functors

• Model categories of diagram spectra

References

The construction originates in

• Anthony Elmendorf, Igor Kriz, Michael Mandell, Peter May, Rings, modules and algebras in stable homotopy theory, AMS 1997, 2014

Review includes

• Anthony Elmendorf, Igor Kriz, Peter May, sections 2 and 3 of Modern foundations for stable homotopy theory (pdf)

Comparison to the model structure on symmetric spectra is due to

• Stefan Schwede, S-modules and symmetric spectra, Math. Ann. 319, 517–532 (2001) (pdf)

Comparison to the model structure on orthogonal spectra is due to

• Michael Mandell, Equivariant orthogonal spectra and S-modules (pdf)