# nLab function spectrum

mapping space

### Stable homotopy theory

#### Stable Homotopy theory

stable homotopy theory

# Contents

## Idea

A function spectrum or mapping spectrum is the analog of a mapping space in the context of stable homotopy theory.

Given two spectra $X$ and $E$, their function spectrum $[X,E]$ is the internal hom in a suitable category of spectra.

In the context of generalized (Eilenberg-Steenrod) cohomology the generalized $E$-cohomology of a topological space $X$ is given by the homotopy groups of the mapping spectrum $[\Sigma_\infty X, E]$.

Revised on April 16, 2014 01:56:13 by Urs Schreiber (92.68.97.89)