BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Talks.cam//talks.cam.ac.uk//
X-WR-CALNAME:Talks.cam
BEGIN:VEVENT
SUMMARY:Universes for category theory - Zhen Lin Low\, DPMMS
DTSTART:20130507T131500Z
DTEND:20130507T141500Z
UID:TALK44715@talks.cam.ac.uk
CONTACT:Julia Goedecke
DESCRIPTION:The Grothendieck-Verdier universe axiom asserts that every set
  is a member of some set-theoretic universe U that is itself a set. One ca
 n then work with entities like the category of all U-sets or even the cate
 gory of all locally U-small categories\, where U is an "arbitrary\nbut fix
 ed" universe\, all without worrying about which set-theoretic operations o
 ne may legitimately apply to these entities.\nUnfortunately\, as soon as o
 ne allows the possibility of changing U\, one also has to face the fact th
 at universal constructions such as limits or adjoints or Kan extensions co
 uld\, in principle\, depend on the parameter U. The purpose of this talk i
 s to explain how one can\nprove that this is not the case\, at least in th
 e case of adjoints for accessible functors between locally presentable cat
 egories (and hence\, limits and Kan extensions)\, making explicit the idea
  that ``bounded''\nconstructions should not depend on the choice of U.
LOCATION:MR9\, Centre for Mathematical Sciences
END:VEVENT
END:VCALENDAR