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SUMMARY:Matt Feller (University of Virginia)
DTSTART:20211208T204500Z
DTEND:20211208T220000Z
DTSTAMP:20260404T132228Z
UID:rts/5
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/rts/5
 /">Generalizing quasi-categories via model structures on simplicial sets</
 a>\nby Matt Feller (University of Virginia) as part of Rochester topology 
 seminar\n\nLecture held in Hylan 1106A.\n\nAbstract\nQuasi-categories are 
 particular simplicial sets which behave like categories up to homotopy. Th
 eir theory has been massively developed in the past two decades\, thanks l
 argely due to Joyal and Lurie\, and they have become vital tools in many a
 reas of algebraic topology\, algebraic geometry\, and beyond. Due to the s
 uccess of quasi-categories\, it would be nice to extend the theory to up-t
 o-homotopy versions of objects more general than categories\, such as the 
 2-Segal sets of Dyckerhoff-Kapranov and Gàlvez-Kock-Tonks. Such a general
 ization would ideally come with an associated model structure on the categ
 ory of simplicial sets\, but finding a model structure with a more general
  class of fibrant objects than a given model structure is a nontrivial and
  open-ended task. In this talk\, I will explain how to use Cisinski's mach
 inery to construct model structures on the category of simplicial sets who
 se fibrant objects generalize quasi-categories. In particular\, one of the
 se model structures has fibrant objects precisely the simplicial sets that
  satisfy a lifting condition which captures the homotopical behavior of qu
 asi-categories without the algebraic aspects.\n\nZoom Meeting ID: 954 8701
  7543\nPasscode: 123708\n
LOCATION:https://stable.researchseminars.org/talk/rts/5/
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