BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:Split Extensions\, Actions and Crossed Modules in the Categories o
 f Hopf Algebras
DTSTART:20211116T141500
DTEND:20211116T151500
DTSTAMP:20260503T144718Z
UID:0090fa57d986bc99b9de4f247b2bab08991251502eb8e60754a44bdc
CATEGORIES:Conferences - Seminars
DESCRIPTION:Florence Sterck\, Université Catholique de Louvain/EPFL\nIn t
 his talk\, we will investigate some categorical properties of Hopf algebra
 s. The first part of the talk will be devoted to the category of cocommuta
 tive Hopf algebras over a field. The fact that this category is semi-abeli
 an will allow us to give a description of internal crossed modules (as de
 fined by Janelidze). In the second part of the talk\, we will study the no
 tion of split extensions of general Hopf algebras. In the category of grou
 ps\, split extensions have a lot of interesting properties. One of them is
  the fact that the category of split extensions is equivalent to the categ
 ory of group actions. Unfortunately\, this does not hold in any category\,
  for example\, the category of monoids does not have this property. Nevert
 heless\, D. Bourn\, A. Montoli\, N. Martins-Ferreira and M. Sobral proved 
 that there exists such an equivalence if the split extensions of monoids a
 re « Schreier extensions ». We will answer the question: Which condition
 s on the split extensions of Hopf algebras do we need to have an equivalen
 ce with the category of actions of Hopf algebras?
LOCATION:MA A1 12 https://plan.epfl.ch/?room==MA%20A1%2012
STATUS:CONFIRMED
END:VEVENT
END:VCALENDAR