Timeline for $\Omega X$-action on spectral $X$-bundles

9 events

when toggle format	what		by	license	comment
Jun 22, 2015 at 20:10	vote	accept	Jonathan Beardsley
Jun 17, 2015 at 20:14	history	edited	Jonathan Beardsley	CC BY-SA 3.0	added 21 characters in body
Jun 16, 2015 at 14:04	comment	added	Sean Tilson		@QiaochuYuan It feels a bit like you are addressing the obvious part and not the interesting part of the question. I think Jon is aware of what you are saying, but I could be wrong. Heaven knows it has happened before.
Jun 16, 2015 at 3:11	comment	added	Qiaochu Yuan		@Jon: the data of an action of a grouplike $E_1$ space $G$ on an object of an $\infty$-category $C$ is precisely the data of a functor $BG \to C$. So the data of a functor $X \to C$ is precisely the data of a functor $B \Omega X \to C$, which is in turn precisely the data of an $\Omega X$-action on an object of $C$.
Jun 16, 2015 at 1:40	comment	added	Jonathan Beardsley		@QiaochuYuan that comment is not helpful at all. Obviously I understand that $X\simeq B\Omega X$. If I knew why that implied what I'm describing above, I wouldn't have asked the question.
Jun 14, 2015 at 21:21	comment	added	Qiaochu Yuan		$X$ needs to be a based and connected space.
Jun 14, 2015 at 16:36	comment	added	Tom Goodwillie		I think that the first occurrence of $X$ in the second paragraph was meant to be $\Omega X$.
Jun 14, 2015 at 16:13	answer	added	John Klein		timeline score: 9
Jun 14, 2015 at 15:42	history	asked	Jonathan Beardsley	CC BY-SA 3.0