BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Alexander Kurz (Chapman University) DTSTART:20261106T173000Z DTEND:20261106T181500Z DTSTAMP:20261030T095106Z UID:ThirdVWDC/7 DESCRIPTION:Title: From Zero-Dimensional to Continuous Dualities: A Double-Categorical Acco unt\nby Alexander Kurz (Chapman University) as part of Third Virtual W orkshop on Double Categories\n\n\nAbstract\nWe investigate how to systemat ically construct continuous dualities from zero-dimensional dualities\, em ploying well-known methods from algebra\, topology\, category theory\, and domain theory. While our method is general\, this paper focusses on the m ove from Stone spaces to compact Hausdorff spaces and the move from Priest ley spaces to compact ordered Hausdorff spaces. The engine of our approach is Stone duality for relations: on the space side quotienting by a preord er turns zero-dimensional spaces into continuous ones\, while distributive lattices with a proximity relation are their algebraic duals. Our duality for relations is inherently order-enriched. Double categories organise bo th functional and relational morphism in the same structure. The move from zero-dimensional to continuous dualities is then a three-step constructio n: extend a duality from functional to relational morphism\, split idempot ents\, restrict to maps.\n LOCATION:https://researchseminars.org/talk/ThirdVWDC/7/ END:VEVENT END:VCALENDAR