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Jonathan Beardsley
Jonathan Beardsley
00:22
@skd I don't have any answer to this question but it's interesting to me.
Tim Campion
Tim Campion
00:41
@GeoffroyHorel Since you're here, I might as well confirm the answer to Denis' question the other day: your model structure on simplicially-internal categories is not a simplicial model structure in any known way, is it? But probably it's also not known that no such simplicial enrichment exists, right?
 
3 hours later…
skd
skd
03:45
@JonathanBeardsley please let me know if you make any progress on this question!
 
4 hours later…
Geoffroy Horel
Geoffroy Horel
07:42
@TimCampion This model structure is simplicial. It is transferred from Rezk's model structure which is simplicial. The structure of a simplicial model category can be lifted along the right adjoint functor. The non-existence of a simplicial enrichment is for the category of simplicially enriched categories. Having a space of objects make things a lot easier.
 
4 hours later…
Tim Campion
Tim Campion
11:20
@GeoffroyHorel Wow, thanks -- I'm glad I asked! Now I see that you transfer the projective model structure. Do you know if a similar construction works with the Reedy or injective model structures?
 
2 hours later…
Geoffroy Horel
Geoffroy Horel
13:45
Ï don't know but I would bet against it. I think at the time I wrote this I had a counter-example (or at least a reasonable candidate for a counter-example) but I never actually wrote down the details anywhere. Now I have no idea what this conter-example was :)
 
7 hours later…
Charles Rezk
Charles Rezk
20:47
Congrats @TylerLawson annals.math.princeton.edu/articles/12861
 
3 hours later…
Jonathan Beardsley
Jonathan Beardsley
23:45
@CharlesRezk god this is so cool... so excited about it.
Anyone know about "deformation functors," and could maybe help me understand some of the basic ideas around them, w/r/t deformation theory
user351585
23:59
@JonathanBeardsley If you mean the functor of infinitesimal deformations of an abelian variety or a formal group or a Hodge structure or something along those lines, Schlessinger's "Functors of Artin rings" is very readable and quite useful

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