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SUMMARY:Alyssa Renata (Imperial College London)
DTSTART:20251212T140000Z
DTEND:20251212T150000Z
DTSTAMP:20260407T223458Z
UID:TheoryCSBham/65
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TheoryCSBham
 /65/">Stone Duality for Monads</a>\nby Alyssa Renata (Imperial College Lon
 don) as part of University of Birmingham theoretical computer science semi
 nar\n\nLecture held in LG23\, Computer Science.\n\nAbstract\nIn computer s
 cience\, monads are often interpreted as representing computation which in
 teract with some resource or environment. To what extent can we interpret 
 arbitrary monads in this way?\n\nTo answer this question\, I will associat
 e to each monad its topological behaviour category\, whose objects are und
 erstood as states of the environment\, and whose morphisms are transitions
  along states. I will also explain how to recover a monad from a topologic
 al category\, giving rise to an adjunction between the category of monads 
 on set and a category of topological categories.\n\nWe interpret this as a
  Stone-type adjunction because any Boolean algebra induces a monad of "if-
 then-else" programs\, whose behaviour category has space of objects the St
 one spectrum\, and the only morphisms are identity. If time permits\, I wi
 ll also explain the relationship between our behaviour category and the Za
 riski spectrum of commutative rings\, using an abstract framework of spect
 ra invented by Diers and Cole.\n\nThis is joint work with Richard Garner.\
 n
LOCATION:https://researchseminars.org/talk/TheoryCSBham/65/
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