nLab iterated loop space object



Group Theory

Higher algebra



The notion of iterated loop space in Top has direct generalization to any (∞,1)-category with (∞,1)-pullbacks.

(∞,1)-operad∞-algebragrouplike versionin Topgenerally
A-∞ operadA-∞ algebra∞-groupA-∞ space, e.g. loop spaceloop space object
E-k operadE-k algebrak-monoidal ∞-groupiterated loop spaceiterated loop space object
E-∞ operadE-∞ algebraabelian ∞-groupE-∞ space, if grouplike: infinite loop space \simeq ∞-spaceinfinite loop space object
\simeq connective spectrum\simeq connective spectrum object
stabilizationspectrumspectrum object


Created on February 9, 2012 at 23:42:26. See the history of this page for a list of all contributions to it.