nLab
smashing localization

Contents

Contents

Idea

If a Bousfield localization of spectra L EL_E at a spectrum EE preserves all direct sums, then it is given by smash product with the EE-localization of the sphere spectrum

L EXXL ES L_E X \simeq X \wedge L_E S

and is hence called a smashing localization.

Smashing localizations hence in particular

  1. preserve (∞,1)-colimits;

  2. are monoidal (∞,1)-functors except possibly for preservation of the tensor unit.

see e.g. (GGN 13, p. 8) for discussion.

Examples

Counter-examples

References

Last revised on September 20, 2018 at 12:25:18. See the history of this page for a list of all contributions to it.