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SUMMARY:The homotopy coherent classification of fusion 2-categories - Thib
 ault  Décoppet (Harvard University)
DTSTART:20240613T150000Z
DTEND:20240613T153000Z
UID:TALK217351@talks.cam.ac.uk
DESCRIPTION:I will explain how to describe the space of all fusion 2-categ
 ories\, and monoidal equivalences. The starting point is the observation t
 hat every fusion 2-category is Morita connected. In particular\, an import
 ant part of our proof consists in understanding the Witt groups of braided
  fusion 1-categories. More precisely\, we prove that the functor sending a
  symmetric fusion 1-category to the associated Witt space preserves limits
 . This can be used to show that fusion 2-categories are classified by a si
 ngle non-degenerate braided fusion 1-category together with group-theoreti
 c data. As consequences of our classification\, we obtain Ocneanu rigidity
  and rank finiteness for fusion 2-categories\, as well as strong constrain
 ts on the associated hypergroups. This is joint work in progress with Hust
 on\, Johnson-Freyd\, Penneys\, Plavnik\, Nikshych\, Reutter\, and Yu.
LOCATION:External
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