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SUMMARY:Covariant fibrations and diagrams of spaces - Ieke Moerdijk (Radbo
 ud University)
DTSTART:20150310T141500Z
DTEND:20150310T151500Z
UID:TALK57933@talks.cam.ac.uk
CONTACT:Dr Ignacio Lopez Franco
DESCRIPTION:For a small category _A_\, I consider the category *sSets*^_A_
  of diagrams of \nsimplicial sets ("spaces") parametrized by _A_. The usua
 l homotopy colimit \nfunctor construction can be considered as a functor\n
 \n_h_!: *sSets* ^_A_ --> *sSets*/_NA_\,\n\nwhere _NA_ is the nerve of _A_.
  It is well known that this functor gives an \nequivalence of homotopy cat
 egories when A is  group (viewed as a \ncategory with one object). I will 
 show that _h_! _always_ gives an \nequivalence of homotopy categories\, in
  the following precise way: One \nequips *sSets*^_A_ with the projective m
 odel structure\, and *sSets*/_NA_ with \nthe covariant model structure. Th
 e talk is based on joint work with Gijs \nHeuts\, and simplifies the treat
 ment in Lurie's Higher Topos Theory.\n
LOCATION:MR3\, Centre for Mathematical Sciences
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