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SUMMARY:Cubes\, comonads\, and calculus - Kathryn Hess (EPFL - Ecole Polyt
 echnique Fédérale de Lausanne)
DTSTART:20240619T083000Z
DTEND:20240619T093000Z
UID:TALK217396@talks.cam.ac.uk
DESCRIPTION:Abstracting the framework common to most flavors of functor ca
 lculus\, one can define a calculus on a category M equipped with a disting
 uished class of weak equivalences to be a functor that associates to each 
 object x of M a tower of objects in M that are increasingly good approxima
 tions to x\, in some well defined\, Taylor-type sense. &nbsp\;This definit
 ion dualizes in an obvious sense\, giving rise to the notion of a cocalcul
 us. &nbsp\; Such (co)calculi can be applied\, for example\, to testing whe
 ther morphisms in M are weak equivalences.In this talk\, after making the 
 definition above precise\, I will describe machines for creating (co)calcu
 li on functor categories Fun (C\,M)\, naturally in both the source C and t
 he target M. The naturality of this construction makes it possible to comp
 are both different types calculi on the same functor category\, as well as
  the same type of calculus on different functor categories. &nbsp\;I will 
 briefly sketch a few examples.\nThe key mechanism in the calculus machine 
 is the natural construction of a comonad on a functor category Fun (D\,M) 
 from a cubical family of commuting localizations of D\, and dually for the
  cocalculus machine.&nbsp\;\n(Joint work with Brenda Johnson and with Kris
 tine Bauer\, Robyn Brooks\, Julie Rasmusen\, and Bridget Schreiner.)
LOCATION:External
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