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SUMMARY:Comonad cohomology of track categories - Simona Paoli (University 
 of Leicester)
DTSTART:20180306T141500Z
DTEND:20180306T151500Z
UID:TALK101128@talks.cam.ac.uk
CONTACT:Tamara von Glehn
DESCRIPTION:Simplicial categories are one of the models of (&infin\;\,1)-c
 ategories. They can be studied using the Postnikov decomposition\, whose s
 ections are categories enriched in simplicial n-types and whose k-invarian
 ts are defined in terms of the (S\,O)-cohomology of Dwyer\, Kan and Smith.
  The latter is defined topologically\, while the understanding of the k-in
 variants calls for an algebraic description. In this talk I illustrate the
  first step of this program\, for categories enriched in groupoids\, also 
 called track category. We define a comonad cohomology of track categories 
 and we show that\, under mild hypothesis on the track category\, its comon
 ad cohomology coincides up to a dimension shift\, with its (S\,O)-cohomolo
 gy\, therefore obtaining an algebraic formulation of the latter. This is j
 oint work with David Blanc.
LOCATION:MR5\, Centre for Mathematical Sciences
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