nLab
model structure on S-modules

Contents

Context

Model category theory

model category

Definitions

Morphisms

Universal constructions

Refinements

Producing new model structures

Presentation of (,1)(\infty,1)-categories

Model structures

for \infty-groupoids

for ∞-groupoids

for nn-groupoids

for \infty-groups

for \infty-algebras

general

specific

for stable/spectrum objects

for (,1)(\infty,1)-categories

for stable (,1)(\infty,1)-categories

for (,1)(\infty,1)-operads

for (n,r)(n,r)-categories

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

Stable homotopy theory

Contents

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).

model structure on spectra

with symmetric monoidal smash product of 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.