nLab pre-spectrum




In stable homotopy theory, the stable homotopy category Ho(Spectra) or the stable ( , 1 ) (\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- ( , 1 ) (\infty,1) -category) of an ambient auxiliary category or ( , 1 ) (\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.


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.