symmetric monoidal (∞,1)-category of spectra
The term highly structured spectrum refers to models for spectra by model categories which carry more structure than sequential spectra, such as to support a symmetric monoidal smash product of spectra (see there for more background). This includes excisive functors, orthogonal spectra, symmetric spectra and S-modules. For details see Introduction to Stable homotopy theory, Part 1-2 – Structured spectra.
Similarly a highly structured ring spectrum is a monoid in this context (a model for an A-infinity algebra/E-infinity algebra).
See at the following entries:
model structure on spectra, symmetric monoidal smash product of spectra
Anthony Elmendorf, Igor Kriz, Peter May, Modern foundations for stable homotopy theory (pdf)
Anthony Elmendorf, Igor Kriz, Michael Mandell, P. May, Rings, modules and algebras in stable homotopy theory (aka “EKMM”)
Michael Mandell, Peter May, Stefan Schwede, Brooke Shipley, Model categories of diagram spectra, Proceedings of the London Mathematical Society Volume 82, Issue 2, 2000 (pdf, doi:10.1112/S0024611501012692)
Stefan Schwede, p.214-216 of Symmetric spectra (2012)
Last revised on May 5, 2020 at 04:18:46. See the history of this page for a list of all contributions to it.