Timeline for Computations in $\infty$-categories
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Dec 28, 2011 at 8:46 | comment | added | Justin Noel | This works if $Y$ is a simply connected product of Eilenberg-Maclane spaces. Using this and the 'fibre lemmas' of Bousfield-Kan we see that it works more generally, by induction up the Postnikov tower, for $Y$ $p$-nilpotent. I was thinking of these fibre lemmas as requiring this sort of hands on data. | |
| Dec 28, 2011 at 8:31 | comment | added | Justin Noel | Mike: I was thinking of the EMSS and the UASS. These two spectral sequences are associated to the Tot filtration on a cosimplicial space, where you want the totalization to be identified with something else. For example, in the UASS we try to compute the homotopy groups of $Tot(Top(X,\mathbb{F}_p^{\bullet} X))$ where $\pi_*\mathbb{F}_p X\cong \tilde{H}_*(X,\mathbb{F}_p)$. Our interest in this spectral sequence lies in the cases where this Tot has the homotopy type of the space of maps from $X$ to the $p$-completion of $Y$. | |
| Dec 28, 2011 at 7:54 | comment | added | Mike Shulman | Can you elaborate on what sort of "very specific details" you need to know about limits and colimits? | |
| Dec 27, 2011 at 15:45 | history | answered | Justin Noel | CC BY-SA 3.0 |