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Partial groups and higher Segal conditions

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  • UserJustin Lynd (University of Louisiana at Lafayette)
  • ClockTuesday 11 June 2024, 13:45-14:15
  • HouseExternal.

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TRHW01 - Workshop on topology, representation theory and higher structures

Partial groups are group-like structures where instead of a binary product, one has a total product defined only on a subset of words of the underlying set. They were introduced by Chermak ultimately for the purpose of studying the $p$-local structure of a finite group, which itself can be distilled into a special type of partial group called a locality.  Gonzalez showed that a partial group is really a special type of simplicial set.  I will explain how to view the category of partial groups 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.  I will outline some preliminary work in progress studying higher associativity of partial groupoids in the context of the Dyckerhoff—Kapranov higher Segal conditions.

This talk is part of the Isaac Newton Institute Seminar Series series.

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