nLab
Spectrum

Contents

Context

Homotopy theory

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

Stable Homotopy theory

Contents

Idea

SpectrumSpectrum is the stable (infinity,1)-category of spectra. It is also denoted SpSp, or sometimes SpecSpec although that can be confusing.

It is the free stable locally presentable (infinity,1)-category on one compact generator, namely the sphere spectrum.

SpSp is the stable (infinity,1)-category of quasicoherent infinity-stacks on Spec(S).

category: category

Last revised on September 16, 2018 at 04:27:12. See the history of this page for a list of all contributions to it.