BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nelson Niu (Topos Institute) DTSTART:20261105T200000Z DTEND:20261105T204500Z DTSTAMP:20261030T094934Z UID:ThirdVWDC/1 DESCRIPTION:Title: Loose Yoneda theory for equipments\nby Nelson Niu (Topos Institute) as part of Third Virtual Workshop on Double Categories\n\n\nAbstract\nWhil e applications for double categories and proarrow equipments abound in for mal category theory\, categorical systems theory\, and beyond\, their Yone da theory had only ever been developed for representable functors specifyi ng tight arrows\, by Paré. This is because in general\, there is no ordin ary representable double functor out of a (weak) double category: loose ar rows would need to be sent to tight arrows (functors)\, while tight arrows would need to be sent to loose ones (profunctors). In recent work\, Lambe rt\, Myers\, and Patterson resolve this issue by introducing twisted doubl e functors\, precisely the structure needed for a loose Hom functor. We re view this construction before presenting our Yoneda lemma and embedding fo r these twisted representables out of double categories when they have pro arrow equipments. This material is ongoing joint work with Lambert and Pat terson.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/1/ END:VEVENT END:VCALENDAR