nLab Rings, modules and algebras in stable homotopy theory


This page collects material related to

on higher algebra (brave new algebra) in stable homotopy theory, i.e. on ring spectra, module spectra etc.

(Sometimes referred to as EKMM for short, after the initials of its authors.)

This was the first account to give a symmetric monoidal category of spectra (here modered as “S-modules”), in which A A_\infty and E E_\infty-ring spectra could be defined as ordinary monoids and their modules.


Chapter I. Prologue: the category of 𝕃\mathbb{L}-spectra

Chapter II. Structured ring and module spectra

Chapter III. The homotopy theory of RR-Modules

Chapter IV. The algebraic theory of RR-modules

Chapter V. RR-Ring spectra and the specialization to MUMU

Chapter VI. Algebraic K-theory of SS-algebras

Chapter VII. RR-algebras and topological model categories

Chapter VIII. Bousfield localization of RR-modules and algebras

Chapter IX. Topological Hochschild homology and cohomology

Chapter X. Some basic constructions on spectra

Chapter XI. Spaces of linear isometries and technical theorems

Chapter XII. The monadic bar construction

Chapter XIII. Epilogue. The category of 𝕃\mathbb{L}-spectra under SS

category: reference

Last revised on January 11, 2021 at 06:53:18. See the history of this page for a list of all contributions to it.