# nLab suspension object

### Context

#### Topology

topology

algebraic topology

## Theorems

#### Stable homotopy theory

stable homotopy theory

# Contents

## Definition

In an (∞,1)-category $C$, for any object $X$ its suspension object $\Sigma X$ is the homotopy pushout

$\array{ X &\to& {*} \\ \downarrow && \downarrow \\ {*} &\to& \Sigma X } \,,$

where ${*}$ is the terminal object.

This is the mapping cone of the terminal map $X \to {*}$. See there for more details.

This concept is dual to that of loop space object.

## Examples

• suspension object

Revised on September 2, 2012 22:17:57 by Urs Schreiber (89.204.139.178)