# nLab model structure on S-modules

Contents

model category

## Model structures

for ∞-groupoids

### for $(\infty,1)$-sheaves / $\infty$-stacks

#### Stable homotopy theory

stable homotopy theory

Introduction

# Contents

## Idea

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).

model structure on spectra

## References

The construction originates in

Review includes

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

Last revised on March 10, 2019 at 14:40:14. See the history of this page for a list of all contributions to it.