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SUMMARY:Constructing Homotopy Bicategories of (oo\, 2)-Categories - Jack  
 Romo (University of Leeds)
DTSTART:20240529T083000Z
DTEND:20240529T091500Z
UID:TALK217204@talks.cam.ac.uk
DESCRIPTION:Across the multitude of definitions for a higher category\, a 
 dividing line can be found between two major camps of model. On one side l
 ives the &lsquo\;algebraic&rsquo\; models\, like B&eacute\;nabou&rsquo\;s 
 bicategories\, tricategories following Gurski and the models of Batanin an
 d Leinster\, Trimble and Penon. On the other end\, one finds the &lsquo\;n
 on-algebraic&rsquo\; models\, including those of Tamsamani and Paoli\, alo
 ng with quasicategories\, Segal n-categories\, complete n-fold Segal space
 s and more. The bridges between these models remain somewhat mysterious. P
 rogress has been made in certain instances\, as seen in the work of Tamsam
 ani\, Leinster\, Lack and Paoli\, Cottrell\, Campbell\, Nikolaus and other
 s. Nonetheless\, the correspondence remains incomplete\; indeed\, for inst
 ance\, there is no fully verified means in the literature to take an `alge
 braic&rsquo\; homotopy n-category of any known model of $(\\infty\, n)$-ca
 tegory for general $n$.In this talk\, I will explore current work in the p
 roblem of taking homotopy bicategories of non-algebraic $(\\infty\, 2)$-ca
 tegories\, with particular focus on the model of complete 2-fold Segal spa
 ces\, including a construction of my own. If time permits\, I will discuss
  potential applications of this problem to connecting extended TQFTs in th
 e world of (oo\, 2)-categories and in bicategories.
LOCATION:External
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