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Towards a construction of limits in (∞,2)-categories

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Speaker: 
Lyne Moser
Date: 
Mon, 2021-06-07 14:30 - 15:00
Parent event: 
MPIM Topology Seminar

Meeting ID: 916 5855 1117
Password: as before.
Contact: Aru Ray, Tobias Barthel,Viktoriya Ozornova
Slides are attached on the Talk's page or see our Nextcloud

An (∞,1)-category has been shown to support most theorems and constructions of category theory and, in particular, limits in an (∞,1)-category have been constructed as terminal objects in the (∞,1)-category of cones. In this talk, I will explain how to generalize this construction to (∞,2)-categories.

A good notion of limit in a 2-category is that of a 2-limit, defined as a limit enriched over categories. Unlike its 1-categorical analogue, a 2-limit cannot be characterized as a 2-terminal object in the 2-category of cones. Instead, we need to construct a "shifted2" 2-category of cones to formulate such a result. This issue extends to the ∞-setting and therefore defining limits in an (∞,2)-category is more involved than in the (∞,1)-categorical case. The results in the 2-categorical setting are joint work with tslil clingman, while those in the ∞-setting are work in progress with Nima Rasekh and Martina Rovelli. 



 



 

 

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