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SUMMARY:Matt Feller (University of Virginia)
DTSTART:20211208T204500Z
DTEND:20211208T220000Z
DTSTAMP:20260423T004825Z
UID:rts/5
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/rts/5/">Gene
 ralizing 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 particu
 lar simplicial sets which behave like categories up to homotopy. Their the
 ory has been massively developed in the past two decades\, thanks largely 
 due to Joyal and Lurie\, and they have become vital tools in many areas of
  algebraic topology\, algebraic geometry\, and beyond. Due to the success 
 of quasi-categories\, it would be nice to extend the theory to up-to-homot
 opy versions of objects more general than categories\, such as the 2-Segal
  sets of Dyckerhoff-Kapranov and Gàlvez-Kock-Tonks. Such a generalization
  would ideally come with an associated model structure on the category 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-e
 nded task. In this talk\, I will explain how to use Cisinski's machinery t
 o construct model structures on the category of simplicial sets whose fibr
 ant objects generalize quasi-categories. In particular\, one of these mode
 l structures has fibrant objects precisely the simplicial sets that satisf
 y a lifting condition which captures the homotopical behavior of quasi-cat
 egories without the algebraic aspects.\n\nZoom Meeting ID: 954 8701 7543\n
 Passcode: 123708\n
LOCATION:https://researchseminars.org/talk/rts/5/
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