Timeline for Categorical formalism for higher non-abelian group cohomology / obstruction theory for gerbes?
Current License: CC BY-SA 3.0
13 events
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| Sep 22, 2021 at 15:46 | comment | added | W.Rether | Your construction of bandings (say the first half of the post) is extremely interesting to me. Do you have a source/reference for that? | |
| Dec 23, 2017 at 20:19 | history | edited | Saal Hardali | CC BY-SA 3.0 |
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| Oct 5, 2017 at 15:01 | comment | added | Saal Hardali | @YonatanHarpaz Nice! I hope this doesn't mean that this approach is hopeless. Is there any hope for abstract machinary which would spit out obstructions for non-abelian gerbes? Perhaps this is one of the few places where the only way to proceed is go to a higher category number? Perhaps if we had 2-deloopings or something of the sort? | |
| Sep 15, 2017 at 17:43 | comment | added | Yonatan Harpaz | If such a $\mathcal{K}$ existed then, taking the fiber over the base point $x_0 \in BOut(G)$, you would get a fiber sequence of the form $BInn(G) \to K(Z(G),2) \to \mathcal{K}_{x_0}$, and hence a fiber sequence of the form $\Omega\mathcal{K}_{x_0} \to BInn(G) \to K(Z(G),2)$. But the fiber of the map $BInn(G) \to K(Z(G),2)$ is $BG$, and $BG$ cannot be the loop space of something unless $G$ is abelian. | |
| Sep 14, 2017 at 17:53 | comment | added | Saal Hardali | @DylanWilson I agree, notice that in my question I phrased everything for $n=1$ anyway. | |
| Sep 14, 2017 at 16:54 | comment | added | Dylan Wilson | Ah, well that should be in Giraud, no? Aren't non-commutative things restricted to n\le 2? | |
| Sep 14, 2017 at 16:53 | history | edited | Saal Hardali | CC BY-SA 3.0 |
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| Sep 14, 2017 at 16:52 | comment | added | Saal Hardali | @DylanWilson Thanks so much! I tried to find this kind of statement in HTT for a long time. It seems that it's only applicable to the commutative case though and the non-commutative case is really crucial for me. | |
| Sep 14, 2017 at 12:27 | comment | added | Dylan Wilson | specifically 7.2.2.26 | |
| Sep 14, 2017 at 11:00 | history | edited | Saal Hardali | CC BY-SA 3.0 |
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| Sep 14, 2017 at 11:00 | comment | added | Dylan Wilson | Have you tried 7.2.2 in HTT? | |
| Sep 14, 2017 at 10:50 | history | edited | Saal Hardali | CC BY-SA 3.0 |
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| Sep 14, 2017 at 10:33 | history | asked | Saal Hardali | CC BY-SA 3.0 |