BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ramón González Rodríguez (University of Vigo\, Spain) DTSTART:20260112T150000Z DTEND:20260112T160000Z DTSTAMP:20260423T035627Z UID:ENAAS/156 DESCRIPTION:Title: Quasigroupoids and weak Hopf quasigroups\nby Ramón González Rodrígu ez (University of Vigo\, Spain) as part of European Non-Associative Algebr a Seminar\n\n\nAbstract\nQuasigroupoids and weak Hopf quasigroups are non associative generalizations of groupoids and weak Hopf algebras. In this t alk we will show that the category of finite quasigroupoids is equivalent to the one of pointed cosemisimple weak Hopf quasigroups over a given fie ld K. As a consequence\, we obtain a categorical equivalence between the categories of quasigroups\, in the sense of Klim and Majid (i.e.\, loops w ith the inverse property)\, and the category of pointed cosemisimple Hopf quasigroups over K. On the other hand\, in this talk we introduce the not ion of exact factorization of a quasigroupoid and the notion of matched p air of quasigroupoids with common base. We prove that if (A\,H) is a match ed pair of quasigroupoids it is posible to construct a new quasigroupoid called the double cross product of A and H. Moreover\, we show that\, if a quasigroupoid B admits an exact factorization\, there exists a matched pair of quasigroupoids (A\,H) and an isomorphism of quasigroupoids betw een the double cross product of A and H and B. Finally\, we show that eve ry matched pair of quasigroupoids (A\,H) induces\, thanks to the quasigrou poid magma construction\, a pair (K[A]\, K[H]) of weak Hopf quasigroups an d a double crossed product of weak Hopf quasigroups isomorphic as weak Hop f quasigroups to the quasigroupoid magma of the double cross product gor upoid of A and H .\n LOCATION:https://researchseminars.org/talk/ENAAS/156/ END:VEVENT END:VCALENDAR