nLab cylinder spectrum




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

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

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

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


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.