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SUMMARY:Partial groups and higher Segal conditions - Justin Lynd (Universi
 ty of Louisiana at Lafayette)
DTSTART:20240611T124500Z
DTEND:20240611T131500Z
UID:TALK217330@talks.cam.ac.uk
DESCRIPTION:Partial groups are group-like structures where instead of a bi
 nary product\, one has a total product defined only on a subset of words o
 f the underlying set. They were introduced by Chermak ultimately for the p
 urpose of studying the $p$-local structure of a finite group\, which itsel
 f can be distilled into a special type of partial group called a locality.
 &nbsp\; Gonzalez showed that a partial group is really a special type of s
 implicial set.&nbsp\; I will explain how to view the category of partial g
 roups as reflective subcategory of presheaves on the category of nonempty 
 finite sets and all functions\, which for example leads to a concrete way 
 for computing colimits of partial groups.&nbsp\; I will outline some preli
 minary work in progress studying higher associativity of partial groupoids
  in the context of the Dyckerhoff--Kapranov higher Segal conditions.
LOCATION:External
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