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SUMMARY:Julie Bergner (University of Virginia)
DTSTART:20201130T150000Z
DTEND:20201130T160000Z
DTSTAMP:20260423T021359Z
UID:OATS/15
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OATS/15/">Va
 riants of the Waldhausen S-construction</a>\nby Julie Bergner (University 
 of Virginia) as part of Online algebraic topology seminar\n\n\nAbstract\nT
 he S-construction\, first defined in the setting of cofibration categories
  by Waldhausen\, gives a way to define the algebraic K-theory associated t
 o certain kinds of categorical input.  It was proved by Galvez-Carrillo\, 
 Kock\, and Tonks that the result of applying this construction to an exact
  category is a decomposition space\, also called a 2-Segal space\, and Dyc
 kerhoff and Kapranov independently proved the same result for the slightly
  more general input of proto-exact categories.  In joint work with Osorno\
 , Ozornova\, Rovelli\, and Scheimbauer\, we proved that these results can 
 be maximally generalized to the input of augmented stable double Segal spa
 ces\, so that the S-construction defines an equivalence of homotopy theori
 es.  In this talk\, we'll review the S-construction and the reasoning behi
 nd these stages of generalization.  Time permitting\, we'll discuss attemp
 ts to characterize those augmented stable double Segal spaces that corresp
 ond to cyclic spaces\, which is work in progress with Walker Stern.\n
LOCATION:https://researchseminars.org/talk/OATS/15/
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