8:07 AM
Hey, are there any other known proofs of straightening for infty-cat-valued functors? I know of Lurie's version and there is a short paper by Boavida that proves it a somewhat different way
1 hour later…
9:36 AM
10:30 AM
10:59 AM
@GijsHeuts . I was aware Heuts-Moerdijk I and II, but if possible I'm wondering if it's possible to avoid markings by showing that the weighted colimit lands in an honest model category of algebras for the slice monad. Those papers are very nice though and definitely in the direction I'm thinking about.
11:16 AM
To make my idea precise, given a simplicial set S, there is a slice of the Joyal model structure to sSet/S and a nice monad (-)x_S S^{\Delta^1} on sSet/S. There should be a simplicial model cat of algebras for this monad.
So the question is: Can you choose a weight C[S]^op-> sSet such that the weighted colimit lands in that category of algebras on the nose
Nikolaus and Haugseng and the other coauthor show this up to weak equivalence, but yeah, it depends on Lurie's machinery already
« first day (2028 days earlier) ← previous day next day → last day (1375 days later) »