Contents

model category

for ∞-groupoids

Contents

Idea

The category of symmetric spectra 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 symmetric spectra.

Properties

Relation to model structure on $\mathcal{S}$-modules

There is also a Quillen equivalence to the model structure on S-modules (Schwede 01)

model structure on spectra

References

The projective and injective model structure on symmetric spectra are due to

The “S-model structure” (also called “flat model structure” in Schwede 12, part III) is due to

• Brooke Shipley, A Convenient Model Category for Commutative Ring Spectra, 2003 (web)