# nLab smashing localization

Contents

### Context

#### Stable Homotopy theory

stable homotopy theory

Introduction

# Contents

## Idea

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

$L_E X \simeq X \wedge L_E S$

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.

## 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.