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SUMMARY:Adrian Miranda (University of Manchester)
DTSTART:20241021T160000Z
DTEND:20241021T170000Z
DTSTAMP:20260409T130440Z
UID:SecondVDCW/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/SecondVDCW/2
 /">The pseudomonad perspective on double categories\, with applications to
  double profunctors</a>\nby Adrian Miranda (University of Manchester) as p
 art of Second Virtual Workshop on Double Categories\n\n\nAbstract\nJust as
  a category is a monad in the bicategory Span(Set)\, so a double category 
 is a pseudomonad in the analogous tricategory Span(Cat). Pseudo-bimodules 
 of between these give a notion of double profunctor\, and these in turn sp
 ecialise to recover double functors. Composition of double profunctors use
 s a two-dimensional colimit which\, unlike the reflexive coequalisers of t
 he standard internal category setting\, are stable under pullback in Cat. 
 We extend Grandis and Pare’s strictification results for double categori
 es and double functors to analogous strictification results for double pro
 functors. We recover the tricategory PsDblCat whose morphisms are double f
 unctors\, and describe work in progress\, joint with Nicola Gambino\, towa
 rds a tricategory PsDblProf whose morphisms are double profunctors. Finall
 y\, a dual specialisation of double profunctors will also be described giv
 ing a notion of double cofunctor\, establishing the tricategory that these
  maps form\, and providing a strictification result for them.\n
LOCATION:https://researchseminars.org/talk/SecondVDCW/2/
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