BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Memento EPFL// BEGIN:VEVENT SUMMARY:N-fold groupoids and n-groupoids in semi-abelian categories DTSTART:20260416T100000 DTEND:20260416T110000 DTSTAMP:20260403T222737Z UID:df4769ecde253ed30f25286dd77d02d76cb79b9a11e1f1fbe51fbba2 CATEGORIES:Conferences - Seminars DESCRIPTION:Nadja Egner\, UC Louvain\nThe notion of semi-abelian category\ , introduced by G. Janelidze\, L. Márki and W. Tholen in 2002\, generaliz es that of abelian category\, and captures the homological properties that the categories of groups\, associative algebras\, Lie algebras and cocomm utative Hopf algebras over a field have in common. Internal structures beh ave surprisingly well in semi-abelian categories. For example\, any intern al reflexive graph admits at most one internal category structure\, and th e categories of internal categories and internal groupoids are isomorphic. Moreover\, the category of internal groupoids is equivalent to the catego ry of internal crossed modules. The notion of internal crossed module in a ny semi-abelian category was introduced by G. Janelidze in 2003\, and reco vers in particular the classical notion of crossed module of groups. The f act that the category of internal groupoids in a semi-abelian category is itself semi-abelian implies that also the category of internal n-fold grou poids is well-behaved.\n \nIn this talk\, I will prove that the full subc ategory of internal n-groupoids in a semi-abelian category is a Birkhoff s ubcategory of the category of internal n-fold groupoids\, and provide a si mple description of the corresponding reflection for n=2. In the abelian c ontext\, the internal n-groupoids yield a torsion-free subcategory of the category of internal n-fold groupoids\, and it is possible to characterize (higher) central extensions and compute generalized Hopf formulae for hom ology. \n \nPart of this talk is based on joint work with Marino Gran\n   LOCATION:MA B1 504 https://plan.epfl.ch/?room==MA%20B1%20504 STATUS:CONFIRMED END:VEVENT END:VCALENDAR