@JonathanBeardsley it's not working here either

@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.

@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

@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.

@HarryGindi what's not working

The link to the Zulip?

@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.

@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?

Which paper?

arxiv.org/abs/1302.5756

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.

@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.

@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.