# nLab pre-spectrum

Contents

### Context

#### Stable Homotopy theory

stable homotopy theory

Introduction

# Contents

## Idea

In stable homotopy theory, the stable homotopy category Ho(Spectra) or the stable $(\infty,1)$-category Spectra of spectra is often conceived of as a localization (the homotopy category of a Bousfield localization of model categories or the reflective sub-$(\infty,1)$-category) of an ambient auxiliary category or $(\infty,1)$-category of “pre-spectra”. The localization by spectrification then turns a pre-spectrum into a genuine spectrum.

In the simplest and historically first model, pre-spectra are sequential spectra and the genuine spectra among these are the Omega-spectra.

More generally, highly structured spectra such as symmetric spectra, orthogonal spectra or S-modules are all, a priori, pre-spectra.

## References

See the references at spectrum.

Last revised on June 9, 2022 at 02:50:01. See the history of this page for a list of all contributions to it.