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Timeline for How should I think about delooping?

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Oct 9, 2010 at 21:13 history edited Kevin H. Lin CC BY-SA 2.5
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Oct 8, 2010 at 22:56 comment added Mike Shulman (The linked article simplifies the situation by mentioning only connected spaces, which are of course automatically grouplike.)
Oct 8, 2010 at 22:54 comment added Mike Shulman That's not exactly right as stated -- to be a loop space X has to not only be an algebra over an $A_\infty$ operad, but must also be grouplike, i.e. $\pi_0$ of it is a group (under the monoid operation induced by the $A_\infty$ structure). Otherwise $\Omega B X$ is only a "group completion" of X.
Oct 8, 2010 at 21:38 vote accept Aaron Mazel-Gee
Oct 8, 2010 at 17:25 history answered Kevin H. Lin CC BY-SA 2.5