3:03 AM
Uy.
That is kind of awful :)
If we're giving bad names anyway, "spin" is a name for the types of symmetries you might expect to find in SO
So we could call the cover of SL(n) the "shear" group
And then GL(n) is either the "hear group" or the "ghear group"
... I'll see myself out

7 hours later…
10:36 AM
I have a didactic question for those more experienced than me. It's not urgent (I'm not about to give such a class, I'm just idly considering it for next year -- there's plenty of time to change my mind!), but I think it is interesting. Suppose I wanted to give a master level course on some homotopy theory topic, and that I'd like to give it an ∞-categorical perspective, because I believe it is the more natural approach to the material, and also that's how I think about it.
Of course there's no way I can actually do the whole theory of ∞-categories in the course as a prelude. What's the best approach? Is there a reasonably self-contained fragment of ∞-categories that one can do in 1-2 lectures before moving on to the main topic (naturally blackboxing some theorems)? Is there another technique one can use? Or is the whole idea just impossible?
I have to say I like Lurie's approach to spend 1h defining ∞-categories and then proceeding as if everyone knew the theory, but it's not suited to a master-level course

6 hours later…
4:20 PM
Hi @TylerLawson, the $n$-lab makes me believe that the covers of $Gl(n,R)$ are known as "meta-linear groups" $Ml(n,R)$; apparently this name is popular in geometric quantization...

3 hours later…
6:58 PM
While we're talking about names of groups, what about the unitary analogue of String? I've sometimes called this the "unitary string group", or "StringU". But I hate it.
@DenisNardin. The only thing I know how to do is to pretend everyone else knows about $\infty$-categories. I feel like that works for me because I actually don't know much about $\infty$-categories (more precisely, I don't feel comfortable with quasicategories at all, so all my thinking is basically in some other model anyway).
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