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2:03 AM
Is there a name for a model category that is cofibrantly generated by (I, J) but where I and J do NOT permit the small object argument? In particular, I do not require to have any cellularization. All it means is that fibrations have right lifting property with J and trivial fibrations have right lifting property with I.
 
 
5 hours later…
6:52 AM
@TomBac Bachmann Yeah, I was too eager there looks like @JeremyHahn Thanks for this.
Was this:arxiv.org/abs/1603.00047 the paper you were refering to?
 
 
10 hours later…
4:29 PM
@JeremyHahn to be honest, we only studied the nonperiodic version you get by slowly trying to deform Z x BU into Z rather than the periodic one that goes * -> QCP^infty -> ... -> Z x BU, though some of the formal steps are the same
 
In HTT, in the introduction to section 6.5.3 Lurie mentions that for a small infinity-site C, the hypersheafification of a presheaf F on C is obtained by the formula colim_{U} lim F(V) where U ranges over the hypercoverings in the presheaf category. I know that in the world of simplicial (pre)sheaves this is essentially the generalized Verdier hypercovering theorem, but I wonder whether there is a more direct proof of this statement available that does not use simplicial sheaves?
 
@asdq What about this? arxiv.org/pdf/1612.03800.pdf
 
 
4 hours later…
9:04 PM
@TimCampion do you have any idea about my question above? is this ever talked about?
 

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