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SUMMARY:A Double (∞\,1)-Categorical Nerve for Double Categories
DTSTART:20200715T150000
DTEND:20200715T160000
DTSTAMP:20260510T032043Z
UID:9653bb39ce6a27632c227d2f2716b8ad2344899b88ab0d27db12a61d
CATEGORIES:Conferences - Seminars
DESCRIPTION:Lyne Moser\, École Polytechnique Fédérale de Lausanne\nA 2-
 category can be seen as an internal category to categories with discrete c
 ategory of objects\, i.e.\, a horizontal double category with only trivial
  vertical morphisms. Some aspects of 2-category theory\, such as 2-limits\
 , benefit from a passage to double categories. Going to the ∞-world\, we
  expect to have a similar picture\, which would allow one to develop aspec
 ts of (∞\,2)-category theory\, such as (∞\,2)-limits\, using double (
 ∞\,1)-categories.\n\nA double (∞\,1)-category was defined by Haugseng 
 as a Segal object in complete Segal spaces\, and then an (∞\,2)-category
  in the form of a 2-fold complete Segal space can be interpreted as a ``ho
 rizontal'' double (∞\,1)-category. In this talk\, I will consider a slig
 htly modified version of these double (∞\,1)-categories and give a nerve
  construction from double categories to double (∞\,1)-categories. This 
 nerve is right Quillen and homotopically fully faithful from the category 
 of double categories endowed with a model structure constructed in a joint
  work with Maru Sarazola and Paula Verdugo. By restricting along a ``homot
 opical'' horizontal embedding of 2-categories into double categories\, we 
 get a nerve from 2-categories into 2-fold complete Segal spaces\, which is
  also right Quillen and homotopically fully faithful. I will show that the
 se nerves are further compatible in a precise sense with the horizontal em
 bedding of 2-categories into double categories\, and this says that the 
 ∞-setting indeed extends the strict setting. 
LOCATION:World Wide Web https://epfl.zoom.us/j/94351048760
STATUS:CONFIRMED
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