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1:55 AM
I think someone said something in here a while back, maybe it was @HarryGindi, that the relative nerve agrees with the usual simplicial nerve...? or something? I'd like to start with a simplicial model category, take bifibrant objects, then take the simplicial nerve, and say that this is equivalent to starting with the underlying relative category, taking the Hammock localization, then taking fibrant replacement, THEN taking the simplicial nerve. Will these two things agree?
 
2:12 AM
Ah, I guess this is Proposition 1.2.1 of Hinich's paper: arxiv.org/pdf/1311.4128.pdf
 
2:59 AM
@Gasterbiter So I couldn't find this in Lurie, but it's actually "Deferred Proposition E" in Section 31 of Charles Rezk's notes on quasicategories: faculty.math.illinois.edu/~rezk/595-fal16/quasicats.pdf
 
 
9 hours later…
12:02 PM
Given a group G and a space X, there is a stack (say F) of G-torsors with a morphism to X - in other words a morphism from Y to F is the same as a diagram Y <- E -> X where E -> Y is a G-torsor and E -> X is any morphism (not necessarily equivariant). Does this stack have a standard name?
 
12:24 PM
@JonathanBeardsley If I remember correctly, I think I said that Barwick and Kan show that their RelNerv is 'usually' (i.e. on fibrant RelCats) the same thing as the hc-nerve of the hammock. I think someone then showed that all left-proper combinatorial model cats are fibrant in the B-K model str on RelCat
Hinich's lemma proves what Rune was saying, though
 
 
1 hour later…
1:27 PM
FWIW I think F is equivalent to Y^G // G ...
 
 
1 hour later…
2:44 PM
any dynamical systems freaks in here?
 
 
1 hour later…
3:45 PM
I think the DS people would object to being called freaks, however descriptive it may be : ^ )
I've always wondered if homotopical methods could be applied to straight up analysis. It seems unlikely, but I wonder if anyone has ever thought about ir
*it
 
@HarryGindi see the 'conley index'
It assigns a finite homotopy type to a dynamical system with sufficient compactness properties. Thomas would know more about the dynamical applications. It is also used in Floer theory (finite-dimensional approximations to infinite dimensional dynamics) which spits out a stable homotopy type.
 
 
1 hour later…
4:57 PM
that's neat!
 
 
7 hours later…
11:33 PM
Was there a picture of all the different notions of $\infty$-categories in Barwick--Schommer-Pries that got removed in the most recent revision? I really liked that picture...
There was !
 

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