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

$\begin{array}{ccc}X& \to & *\\ ↓& & ↓\\ *& \to & \Sigma X\end{array}\phantom{\rule{thinmathspace}{0ex}},$\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)