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SUMMARY:Jaco Ruit (Utrecht University)
DTSTART:20241024T090000Z
DTEND:20241024T100000Z
DTSTAMP:20260409T131532Z
UID:SecondVDCW/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SecondVDCW/4
 /">A double ∞-categorical approach to formal ∞-category theory</a>\nby
  Jaco Ruit (Utrecht University) as part of Second Virtual Workshop on Doub
 le Categories\n\n\nAbstract\nFormal ∞-category theory starts with the ob
 servation that there are many variants of ∞-category theory\, for exampl
 e\, enriched ∞-categories\, internal ∞-categories\, and monoidal ∞-c
 ategories\, which come with specialized notions of adjunctions\, point-wis
 e Kan extensions\, and so on. It is natural to ask whether one can give a 
 uniform and synthetic treatment of the foundational concepts and theorems 
 for these different flavors of ∞-category theory. \n \nIn this talk\, we
  propose an extension of the ideas from formal (strict) category theory of
  Street-Walters\, Wood\, Verity\, and Shulman\, to the ∞-categorical con
 text\, and give a leisurely introduction to the theory of ∞-equipments. 
 These ∞-equipments are certain double ∞-categories in which many conce
 pts of category theory may be developed and expressed (using only the doub
 le categorical structure). We will present an overview and highlight some 
 of these aspects. Now\, since this approach yields category theories for t
 he objects of these ∞-equipments\, developing a category theory for a fl
 avor of ∞-categories is a question of constructing the right suitable am
 bient ∞-equipment. Throughout the talk\, we discuss some of these exampl
 es of ∞-equipments.\n
LOCATION:https://researchseminars.org/talk/SecondVDCW/4/
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