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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Cubes\, comonads\, and calculus - Kathryn Hess (EP
 FL - Ecole Polytechnique Fédérale de Lausanne)
DTSTART;TZID=Europe/London:20240619T093000
DTEND;TZID=Europe/London:20240619T103000
UID:TALK217396AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/217396
DESCRIPTION:Abstracting the framework common to most flavors o
 f functor calculus\, one can define a calculus on 
 a category M equipped with a distinguished class o
 f weak equivalences to be a functor that associate
 s to each object x of M a tower of objects in M th
 at are increasingly good approximations to x\, in 
 some well defined\, Taylor-type sense. &nbsp\;This
  definition dualizes in an obvious sense\, giving 
 rise to the notion of a cocalculus. &nbsp\; Such (
 co)calculi can be applied\, for example\, to testi
 ng whether morphisms in M are weak equivalences.In
  this talk\, after making the definition above pre
 cise\, I will describe machines for creating (co)c
 alculi on functor categories Fun (C\,M)\, naturall
 y in both the source C and the target M. The natur
 ality of this construction makes it possible to co
 mpare both different types calculi on the same fun
 ctor category\, as well as the same type of calcul
 us on different functor categories. &nbsp\;I will 
 briefly sketch a few examples.\nThe key mechanism 
 in the calculus machine is the natural constructio
 n of a comonad on a functor category Fun (D\,M) fr
 om a cubical family of commuting localizations of 
 D\, and dually for the cocalculus machine.&nbsp\;\
 n(Joint work with Brenda Johnson and with Kristine
  Bauer\, Robyn Brooks\, Julie Rasmusen\, and Bridg
 et Schreiner.)
LOCATION:External
CONTACT:
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