BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Bryce Clarke (Macquarie University) DTSTART:20220419T160000Z DTEND:20220419T170000Z DTSTAMP:20260423T052545Z UID:Intercats/9 DESCRIPTION:Title: Constructing lenses in double categories\nby Bryce Clarke (Macquarie University) as part of Intercats: Seminar on Categorical Interaction\n\n\ nAbstract\nLenses are a family of mathematical structures used to model bi directional transformations between systems. A common feature among all ki nds of lenses is that they consist of a "forwards" component and a "backwa rds" component. A double category is a 2-dimensional categorical structure consisting of objects\, two types of morphism (horizontal and vertical)\, and cells between them. A natural question arises: what if the forwards a nd backwards components of a lens were the horizontal and vertical morphis ms in a double category? \n\nIn this talk\, I advocate for a double catego rical approach to lenses\, and demonstrate how many examples of lenses\, p articularly those satisfying "lens laws"\, may be built from the horizonta l and vertical morphisms in a double category. A general process for const ructing lenses inside any double category\, called the "right-connected co mpletion"\, is introduced and is shown to satisfy a universal property. Fi nally\, we explore how many questions and properties of lenses may be unde rstood in the setting of double categories.\n LOCATION:https://researchseminars.org/talk/Intercats/9/ END:VEVENT END:VCALENDAR