BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:A model-categorical cotangent complex formalism (part 1)
DTSTART:20160322T101500
DTEND:20160322T113000
DTSTAMP:20260407T230518Z
UID:387cf1bde37cfb32ef0c27910cc6ed6301cdf96c126b6e42683277ce
CATEGORIES:Conferences - Seminars
DESCRIPTION:Matan Prasma\n(Radboud Universiteit Nijmegen)\nOne of the firs
 t applications of the theory of model categories was Quillen homology. Bui
 lding on the notion of Beck modules\, one defines the cotangent complex of
  an associative or commutative (dg)-algebra as the derived functor of its 
 abelianization. The latter is a (bi)module over the original algebra\, and
  its homology groups are called the (Andre'-)Quillen homology. The caveat 
 of this approach is that the cotangent complex is not defined as a functor
  on the category of all algebras but rather on a fixed slice thereof. To r
 emedy this\, Lurie's "cotangent complex formalism" (Higher Algebra & 7) us
 es the infinity-categorical Grothendieck construction and gives a general 
 "global" treatment for the cotangent complex of an algebra over a (coheren
 t) infinity-operad.\nIn this talk I will propose a way to parallel Lurie's
  formalism using model categories which is based on the model-categorical 
 Grothendieck construction as developed by Yonatan Harpaz and myself. We wi
 ll see how to define the tangent model category of a model category\, acco
 mpanied with an "abstract" cotangent complex functor. We will then identif
 y the tangent category of algebras over a dg-operad\, as the category of o
 peradic algebras and their modules and the abstract cotangent complex with
  the operadic cotangent complex. This latter result is an extension of the
  results in Higher Algebra (and following Bastera-Mandell) to the dg-case.
  At the cost of potentially restricting generality\, our approach offers a
  simplification to that of Lurie's in that one can avoid carrying a signif
 icant amount of coherent data.\nI will assume basic familiarity with (mode
 l) categories but not much more.\nThis is a joint work with Yonatan Harpaz
  and Joost Nuiten.
LOCATION:CM113
STATUS:CONFIRMED
END:VEVENT
END:VCALENDAR