BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tony Zorman (Universität Hamburg) DTSTART:20260617T090000Z DTEND:20260617T100000Z DTSTAMP:20260623T085542Z UID:EQuAL/59 DESCRIPTION:Title: C losed Reconstruction\nby Tony Zorman (Universität Hamburg) as part of European Quantum Algebra Lectures (EQuAL)\n\n\nAbstract\nStarting with a commutative ring R\, it is well-known that monoidal structures on the cate gory of H-modules\, for an R-algebra H\, that are compatible with the cano nical forgetful functor are in bijection with bialgebra structures on H. I f H is even Hopf\, then it is also possible to lift the closed structure f rom R-mod to H-mod.\n\nIn some cases one might be interested in first lift ing just the closed structure\, without any assumption of monoidal compati bility. This talk will focus on reconstruction of this kind\, more closely studying the question from the monadic point of view. While in the monoid al case\, oplax monoidal monads are the right notion\, in the closed world \, (lax) closed monads are inadequate for reconstruction purposes. The rig ht notion turns out to be that of a gabi-monad\, first outlined by Berger\ , Saracco\, and Vercruysse. In the algebraic setting\, lifting the closed structure in this way already implies that one started with a Hopf algebra . This\, however\, is not the case for monads: we give examples of gabi-mo nads that are not Hopf.\n\nThe talk is based on joint work in progress wit h Sebastian Halbig and Paolo Saracco.\n LOCATION:https://researchseminars.org/talk/EQuAL/59/ END:VEVENT END:VCALENDAR