Universes for category theory

Add to your list(s) Download to your calendar using vCal

• Zhen Lin Low, DPMMS
• Tuesday 07 May 2013, 14:15-15:15
• MR9, Centre for Mathematical Sciences.

If you have a question about this talk, please contact Julia Goedecke.

The Grothendieck-Verdier universe axiom asserts that every set is a member of some set-theoretic universe U that is itself a set. One can then work with entities like the category of all U-sets or even the category of all locally U-small categories, where U is an “arbitrary but fixed” universe, all without worrying about which set-theoretic operations one may legitimately apply to these entities. Unfortunately, as soon as one allows the possibility of changing U, one also has to face the fact that universal constructions such as limits or adjoints or Kan extensions could, in principle, depend on the parameter U. The purpose of this talk is to explain how one can prove that this is not the case, at least in the case of adjoints for accessible functors between locally presentable categories (and hence, limits and Kan extensions), making explicit the idea that ``bounded’‘ constructions should not depend on the choice of U.

This talk is part of the Category Theory Seminar series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• Category Theory Seminar
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• MR9, Centre for Mathematical Sciences
• School of Physical Sciences
• bld31
• ndb35's list
• yk373's list

Note that ex-directory lists are not shown.