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SUMMARY:Fibrations and lax Limits of (∞\,2)-Categories
DTSTART:20210928T141500
DTEND:20210928T151500
DTSTAMP:20261005T050040Z
UID:fcef7182800b573bb4beb85a95347355bc68edb9153ba53143c29b25
CATEGORIES:Conferences - Seminars
DESCRIPTION:Edoardo Lanari\, Czech Academy of Sciences\nWe study four type
 s of (co)cartesian fibrations of $\\infty$-bicategories over a given base 
 $B$\, and prove that they encode the four variance flavors of $B$-indexed 
 diagrams of $\\infty$-categories. We then use this machinery to set up a g
 eneral theory of 2-(co)limits for diagrams valued in an $\\infty$-bicatego
 ry\, capable of expressing lax\, weighted and pseudo limits. When the $\\i
 nfty$-bicategory at hand arises from a model category tensored over marked
  simplicial sets\, we show that this notion of 2-(co)limit can be calculat
 ed as a suitable form of a weighted homotopy limit on the model categorica
 l level\, thus showing in particular the existence of these 2-(co)limits i
 n a wide range of examples. Next\, we extend this to $(\\infty\,2)$-catego
 ry valued diagrams and the corresponding fibrations\, and we provide motiv
 ating examples. We end by discussing a notion of cofinality appropriate to
  this setting and use it to deduce the unicity of 2-(co)limits\, once they
  exist.\n\nThis is joint work with A.Gagna and Y.Harpaz.
LOCATION:World Wide Web https://epfl.zoom.us/j/94351048760
STATUS:CONFIRMED
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