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CATEGORIES:Category Theory Seminar
SUMMARY:Universes for category theory - Zhen Lin Low\, DPM
MS
DTSTART;TZID=Europe/London:20130507T141500
DTEND;TZID=Europe/London:20130507T151500
UID:TALK44715AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/44715
DESCRIPTION:The Grothendieck-Verdier universe axiom asserts th
at every set is a member of some set-theoretic uni
verse U that is itself a set. One can then work wi
th entities like the category of all U-sets or eve
n the category of all locally U-small categories\,
where U is an "arbitrary\nbut fixed" universe\, a
ll without worrying about which set-theoretic oper
ations one may legitimately apply to these entitie
s.\nUnfortunately\, as soon as one allows the poss
ibility of changing U\, one also has to face the f
act that universal constructions such as limits or
adjoints or Kan extensions could\, in principle\,
depend on the parameter U. The purpose of this ta
lk is to explain how one can\nprove that this is n
ot the case\, at least in the case of adjoints for
accessible functors between locally presentable c
ategories (and hence\, limits and Kan extensions)\
, making explicit the idea that ``bounded''\nconst
ructions should not depend on the choice of U.
LOCATION:MR9\, Centre for Mathematical Sciences
CONTACT:Julia Goedecke
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