#
nLab

Spectrum

### 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

## Idea

$Spectrum$ is the stable (infinity,1)-category of spectra. It is also denoted $Sp$, or sometimes $Spec$ although that can be confusing.

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

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

Revised on December 16, 2015 05:27:45
by

Urs Schreiber
(89.15.238.162)