nLab
iterated loop space object

Context

Group Theory

Higher algebra

Contents

Idea

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 Γ-spaceinfinite loop space object
\simeq connective spectrum\simeq connective spectrum object
stabilizationspectrumspectrum object

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Created on February 9, 2012 23:43:20 by Urs Schreiber (89.204.130.229)