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SUMMARY:Elementary embeddings for category theory - Andrew Brooke-Taylor (
 University of Leeds)
DTSTART:20180313T141500Z
DTEND:20180313T151500Z
UID:TALK101131@talks.cam.ac.uk
CONTACT:Tamara von Glehn
DESCRIPTION:Elementary embeddings do crop up in category theory\, but are 
 often viewed as being simply convenient morphisms of the category in quest
 ion.  In set theory much more is made of them\, in particular in the conte
 xt of large cardinal axioms\, where elementary embeddings of the whole set
 -theoretic universe are used to characterise the large cardinals.  In this
  talk I will show how some of the power of elementary embeddings can be us
 ed in a category theory context.  In particular\, I will use this perspect
 ive in presenting a result with Joan Bagaria\, in which we reduce the larg
 e cardinal assumption required to show that a (definable) full embedding i
 nto an accessible category must preserve lambda-directed colimits for some
  lambda.
LOCATION:MR5\, Centre for Mathematical Sciences
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