nLab
k-monoidal infinity-group

Context

Group Theory

Higher algebra

Contents

Idea

An ordinary group is either an abelian group or not. For an ∞-group there is an infinite tower of notions ranging from completely non-abelian to completely abelian.

(∞,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

References

Section 5 of

Created on February 9, 2012 23:36:18 by Urs Schreiber (89.204.130.229)