BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Nihil Shah (University of Cambridge) DTSTART:20260220T130000Z DTEND:20260220T140000Z DTSTAMP:20260421T135834Z UID:TheoryCSBham/70 DESCRIPTION:Title: No-go theorems for distributive laws: directed containers vs. unifor m sampling\nby Nihil Shah (University of Cambridge) as part of Univers ity of Birmingham theoretical computer science seminar\n\nLecture held in LG23\, Computer Science.\n\nAbstract\nMonads model effectful computation\, comonads model folding with a context. Given a comonad W and a monad M\, when can two computations WA -> MB and WB -> MC be composed? Power and Wat anabe demonstrate that the existence of a mixed distributive law WM -> MW gives a sufficient condition for obtaining a biKleisli category where such morphisms can be composed. In this talk\, I will demonstrate that\, for a wide class of (co)monads on the category of sets\, such laws do not exist . I first show that\, on the category of sets\, there is no mixed distribu tive law of the non-empty list comonad over the powerset monad. We then ge neralise the comonad demonstrating that a directed container W has a distr ibutive law over the powerset monad M if and only if W is a coreader comon ad. Finally\, we generalise this no-go theorem to all monads over the cate gory of sets which have a meaningful notion of "uniform sampling". If I ha ve time\, I will also go over transfer theorems which enable lifting these no-go theorems over Set to related (co)monads on a different category.\n\ nThis talk is derived from my previous joint work with Amin Karamlou appea ring in LICS 2024 (https://doi.org/10.1145/3661814.3662137).\n LOCATION:https://researchseminars.org/talk/TheoryCSBham/70/ END:VEVENT END:VCALENDAR