BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Andrey Lazarev (Lancaster University\, UK)
DTSTART:20201008T110000Z
DTEND:20201008T120000Z
DTSTAMP:20260423T024755Z
UID:LAGOON/18
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LAGOON/18/">
 Koszul duality for dg-categories and infinity-categories</a>\nby Andrey La
 zarev (Lancaster University\, UK) as part of Longitudinal Algebra and Geom
 etry Open ONline Seminar (LAGOON)\n\n\nAbstract\nDifferential graded (dg) 
 Koszul duality is a certain adjunction between the category of dg algebras
  and conilpotent dg coalgebras that becomes an equivalence on the levels o
 f homotopy categories. More precisely\, this adjunction is a Quillen equiv
 alence of the corresponding closed model categories. Various versions of t
 his result exist and play important roles in rational homotopy theory\, de
 formation theory\, representation theory and other related fields. We exte
 nd it to a Quillen equivalence between dg categories (generalizing dg alge
 bras) and a class of dg coalgebras\, more general than conilpotent ones. A
 s applications we describe explicitly and conceptually Lurie’s dg nerve 
 functor as well as its adjoint and characterize derived categories of (\\i
 nfty\,1)-categories as derived categories of comodules over simplicial cha
 in coalgebras.(joint work with J. Holstein)\n
LOCATION:https://researchseminars.org/talk/LAGOON/18/
END:VEVENT
END:VCALENDAR