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7:44 AM
@JonathanBeardsley it's not working here either
 
 
2 hours later…
9:43 AM
@HarryGindi Is this the state-of-the-art in the justification of the Appendix in Gaitsgory-Rozenblyum? Would it get close to filling all the gaps? I am writing a paper using their correspondence machinery (stating carefully that it is conditional on their results!) and I would be very happy if that saga was finally complete.
 
 
6 hours later…
3:43 PM
@HarryGindi I'd say mostly for the dualities available in $\Theta_2$-sets, but as far as the monoidal structure itself that was already available from Verity's work
 
 
1 hour later…
5:02 PM
@SimonPepinLehalleur As Edoardo said, a lot of this stuff was already developed for complicial sets, and the recent work of Gagna-Harpaz-Lanari more or less gives you a way to apply this in concert with Lurie's (un)straightening theorem by completing the equivalence between 2-trivial complicial sets and scaled simplicial sets
However, Yuki's paper is also excellent and has a bunch of interesting (∞,2)-categorical combinatorics. I personally prefer the Θ-type models to complicial sets, mainly because the representable objects are all fibrant and represent the obvious elementary operations of n-category theory. I was very excited to see this come out, but Gagna-Harpaz-Lanari does give you, at least right now, a better toolbox.
 
5:56 PM
@HarryGindi what's not working
The link to the Zulip?
 
6:09 PM
@JonathanBeardsley yeah it says I need an invitation.
 
Did you read the conversation following my initial posting of the link
Others had that problem but seemed to resolve it.
 
6:22 PM
@JonathanBeardsley Did they resolve it or give up?
 
@HarryGindi People seemed satisfied with the answer (I did not try it)
 
It was resolved.
Click on the twitter link.
The one that Rune posted. Here: twitter.com/_julesh_/status/1242141831057616896
 
Weird
ok, worked
Just wanted to check it out, don't know if it's for me.
 
There's not much \infty-category stuff happening there.
I've been learning a bit about algebraic theories and their relationship to operads.
 
Did you read Clark's paper?
 
6:25 PM
There's also some interesting discussions happening around cybernetics and semiotics.
Which paper?
 
Operator categories in this paper are more or less algebraic theories
 
I have not read it in detail, but I am pretty familiar with it.
 
Well, if you're looking into the relationship between algebraic theories and ∞-operads, this basically the one-stop-shop
I read it a long time ago, so I don't know exactly which algebraic theories correspond to ∞-operads, but iirc this gives a framework to change back and forth between them
 
I see. Well yeah I'm not really looking to create more work for myself in interpreting something. I'm more just having things explained to me by logicians, which is nice.
 
7:24 PM
@HarryGindi Great. So is someone who understands Verity+Gagna-Harpaz-Lanari well going to write down and publish somewhere "Thm: the results in [GR,Appendix.] are true"? That would be really a public service for the poor end-users like me.
 
 
1 hour later…
8:39 PM
@SimonPepinLehalleur It probably depends on what you need from GR. If you just need the Gray tensor product and its basic properties, then check out Yuki Maehara's thesis -- he develops the Gray tensor product in 2-quasicategories (i.e. Theta_2 - sets). I believe this is the first model where this has been done other than complicial.
 

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