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