Contents

# Contents

## Idea

For $S_\bullet$ a spectrum, its cylinder spectrum $Cyl(E)_\bullet$ has as component spaces the reduced cylinder spaces over the original component spaces:

$Cyl(E)_n \coloneqq I_+ \wedge E_n \,,$

i.e. the smash product (of pointed topological spaces) of $E_n$ with the unit inveral with a dijoint basepoint adjoined.

Cylinder spectra serve to define left homotopy of spectra as for other cylinder objects.

## References

Early lecture notes include

Last revised on April 14, 2016 at 16:07:21. See the history of this page for a list of all contributions to it.