BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nuiok Dicaire (University of Edinburgh) DTSTART:20211117T160000Z DTEND:20211117T170000Z DTSTAMP:20260423T053014Z UID:EmCats/4 DESCRIPTION:Title: L ocalisable monads\, from global to local\nby Nuiok Dicaire (University of Edinburgh) as part of Em-Cats\n\n\nAbstract\nMonads have many useful a pplications. In mathematics they are used to study algebras at the level o f theories rather than specific structures. In programming languages\, mon ads provide a convenient way to \nhandle computational side-effects which include\, roughly speaking\, things like interacting with external code or altering the state of the program's variables. An important question is t hen how to handle several instances of such side-effects or a graded colle ction of them. The general approach consists in defining many “small” monads and combining them together using distributive laws.\n\nIn this tal k\, we take a different approach and look for a pre-existing internal stru cture to a monoidal category that allows us to develop a fine-graining of monads. This uses techniques from tensor topology and provides an intrinsi c theory of local computational effects without needing to know how the co nstituent effects interact beforehand. We call the monads obtained "locali sable" and show how they are equivalent to monads in a specific 2-category . To motivate the talk\, we will consider two concrete applications in con currency and quantum theory. This is all covered in our recent paper: http s://arxiv.org/abs/2108.01756 .\n LOCATION:https://researchseminars.org/talk/EmCats/4/ END:VEVENT END:VCALENDAR