# Suspension functor

From Topospaces

Template:Self-functor on topospaces

## Definition

The **suspension functor** is a functor from the category of topological spaces with continuous maps to itself, defined as follows:

- It sends each topological space to its suspension
- Given a continuous map , the induced map is the map naturally induced by quotienting out from the map given by .

## Iteration

The iteration of the suspension functor times is equivalent to taking the join with a -sphere.