BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Simon Willerton
DTSTART:20260528T170000Z
DTEND:20260528T180000Z
DTSTAMP:20260604T152626Z
UID:ToposInstituteColloquium/214
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ToposInstitu
 teColloquium/214/">The projection formula\, extranatural transformations a
 nd surface diagrams</a>\nby Simon Willerton as part of Topos Institute Col
 loquium\n\n\nAbstract\nThis talk is motivated by trying to understand how 
 closed monoidal categories fit into higher categorical frameworks\, in par
 ticular to understand why\, in higher categorical terms\, the projection f
 ormula -- f_!(a x f^*b) = f_!(a) x b -- holds for an adjunction f_! -| f^*
  when f^* strong closed monoidal.  The circle of ideas involves the notion
  of extranatural transformation\, which is key to a formal definition of c
 losed monoidal category.  These can be represented graphically using 'surf
 ace diagrams' and it transpires that these actually have a natural interpr
 etation in terms of the monoidal double category of categories\, functors 
 and profunctors.  Along the way we will see the notion of conjugation for 
 adjunctions of two variables which will help formalize the projection form
 ula result.\n
LOCATION:https://researchseminars.org/talk/ToposInstituteColloquium/214/
END:VEVENT
END:VCALENDAR