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SUMMARY:Defining limits in (∞\,n)-categories - Lyne Moser (Universität 
 Regensburg)
DTSTART:20240604T083000Z
DTEND:20240604T093000Z
UID:TALK217219@talks.cam.ac.uk
DESCRIPTION:An (&infin\;\,1)-category has been shown to support most theor
 ems and constructions of category theory and\, in particular\, limits in a
 n (&infin\;\,1)-category have been constructed as terminal objects in the 
 corresponding (&infin\;\,1)-category of cones. In this talk\, I will prese
 nt a generalization of this construction to the (&infin\;\,n)-categorical 
 setting for higher n\, focusing on the case where n=2. This is joint work 
 with Nima Rasekh and Martina Rovelli.&nbsp\; A good notion of limit in a (
 strict) 2-category is that of a 2-limit\, which is defined as a categorica
 lly enriched limit. Unlike its 1-categorical analogue\, a 2-limit cannot b
 e characterized as a 2-terminal object in the corresponding 2-category of 
 cones. Instead\, a passage to double categories allows such a characteriza
 tion and a 2-limit is equivalently a double terminal object in the corresp
 onding double category of cones. This issue extends to the &infin\;-settin
 g and we define limits in an (&infin\;\,2)-category as terminal objects in
  a double (&infin\;\,1)-category of cones. In particular\, we show that th
 is definition is equivalent to the established definition of (&infin\;\,2)
 -limits as (&infin\;\,1)-categorically enriched limits. The case of (&infi
 n\;\,n)-categories is analogous\, with limits defined in the setting of in
 ternal categories to (&infin\;\,n-1)-categories.
LOCATION:External
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