BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lander Hermans (University of Antwerp) DTSTART:20241024T100000Z DTEND:20241024T110000Z DTSTAMP:20260409T132311Z UID:SecondVDCW/5 DESCRIPTION:Title: Virtual double categories as coloured box operads\nby Lander Herman s (University of Antwerp) as part of Second Virtual Workshop on Double Cat egories\n\n\nAbstract\nVirtual double categories are a 2-categorification of multicategories and compare to double categories as multicategories com pare to monoidal categories. In algebraic topology\, multicategories are a lso known as coloured operads and are extensively used to encode algebraic operations\, thus generalizing operads.\n\nBy viewing virtual double cate gories as coloured versions of box operads\, we shift our point of view: f rom objects of study to algebraic gadgets encoding higher operations. This is exemplified by our main application: we present a box operad Lax encod ing lax functors U->Cat(k) into the category of k-linear categories. They appear in algebraic geometry as prestacks generalizing structure sheaves a nd (noncommutative) deformations thereof.\n\nIn the second part of the tal k\, I will sketch key components of our main result: a Koszul duality for box operads. For example\, to every box operad we can associate a canonica l L_\\infty-algebra. A salient feature is that these results can be explai ned purely in terms of (virtual) double categorical diagrams\, or in our t erms\, stackings of boxes.\n\nIf time permits\, I will explain how it appl ies to Lax in order to tackle their deformation and homotopy theory.\n LOCATION:https://researchseminars.org/talk/SecondVDCW/5/ END:VEVENT END:VCALENDAR