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SUMMARY:Homotopy coherent companionships and conjunctions [MPIM]
DTSTART:20250210T100000Z
DTEND:20250210T110000Z
DTSTAMP:20260420T154000Z
UID:indico-event-244@math-events.uni-bonn.de
DESCRIPTION:Speakers: Jaco Ruit\n\nAbstract homotopy theory seminar\nCompa
 nionships and conjunctions play an important role in the theory of double 
 ∞-categories. Double ∞-categories are two-dimensional ∞-categorical 
 constructions that admit two directions of morphisms. They may be viewed a
 s a generalization of (∞\,2)-categories\, and\, from this perspective\, 
 companions and conjoints are the double categorical counterpart of adjoint
 s. We will give examples of companions and conjoints in a range of differe
 nt contexts. In particular\, we will elucidate their fundamental role in a
  double ∞-categorical approach to formal category theory.\nThe goal of t
 his talk is to discuss a result that asserts that every companionship/conj
 unction can uniquely be upgraded to a so-called homotopy coherent one\, an
 d if time permits\, we will say something about its proof. This result is 
 analogous to the celebrated result by Riehl—Verity that states that adju
 nctions in (∞\,2)-categories upgrade to homotopy coherent adjunctions in
  a unique way.\n\nhttps://math-events.uni-bonn.de/event/244/
LOCATION:MPIM\, Vivatsgasse\,  7 - Seminar Room (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/244/
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