nLab
Symmetric spectra
This page collects material related to the lecture notes
on stable homotopy theory in terms of symmetric spectra.
See also the Lectures on Equivariant Stable Homotopy Theory and on Global homotopy theory for the model on orthogonal spectra and equivariant stable homotopy theory.
Contents
Chapter I. Basics
1. Symmetric spectra
Basic Examples:
2. Properties of naive homotopy groups
3. Basic constructions
3.1 Symmetric spectra of simplicial sets
3.2 Constructions
3.3 Constructions involving ring spectra
4. Stable equivalences
5. Smash product
6. Homotopy groups
7. Relation to other kinds of spectra
7.1 Orthogonal spectra
7.2 Unitary spectra
7.3 Continuous and simplicial functors
7.4 $\Gamma$spaces
7.5 Permutative categories
7.6 Spectra as enriched functors
8. Naive versus true homotopy groups
History, credits, further reading
Chapter II. The stable homotopy category
1. The stable homotopy category
2. Triangulated structure
3. Derived smash product
4. Grading
5. Generator
6. Homology and cohomology
6.1 Generalized homology and cohomology
6.2 Ordinary homology and cohomology
6.3 Moore spectra
7. Finite spectra
8. Connective covers and Postnikov sections
9. Localization and completion
10. The Steenrod algebra
10.1 Examples and applications
10.2 Hopf algebra structure
10.3 The Adams spectral sequence
Chapter III. Model structures
1. Symmetric spectra in a simplicial category
2. Flat cofibrations
3. Level model structures
4. Stable model structures
5. Operads and their algebras
6. Model structures for algebras over an operad
7. Connective covers of structured spectra
Chapter IV. Module spectra
Model category theory
Compactly generated spaces
Simplicial sets
Equivariant homotopy theory
Errata

p. 273. the definition of Kronecker pairing (construction 6.13) is missign the application of the multiplication map

p. 331. the second “vertically” should be “horizontally”

p. 331. “with coordinated”

p. 333. “stable stemes”

p. 344. uncompiled source code “eqrefeqgeneral” etc.