nLab highly structured spectrum

Idea

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

• symmetric spectrum, model structure on symmetric spectra

• orthogonal spectrum, model structure on orthogonal spectra

• S-module, model structure on S-modules

Related concepts

• brave new algebra

References

• 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)