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SUMMARY:Commutation of Limits and Colimits -- a Cautionary Tale - Peter Jo
 hnstone\, DPMMS
DTSTART:20140128T141500Z
DTEND:20140128T151500Z
UID:TALK49707@talks.cam.ac.uk
CONTACT:Julia Goedecke
DESCRIPTION:The relation `limits of shape I commute with colimits of shape
  J in Set' induces a Galois connection between classes of limit shapes and
  classes of colimit shapes\, and it of some interest to determine the clos
 ed classes on either side. There are seven well-known closed classes for w
 hich the limit class is generated by finite\ncategories (equivalently\, fo
 r which the colimit class contains all filtered categories)\, and Martin H
 yland's student Marie Bjerrum conjectured that they were the only such cla
 sses. In the seminar I'll describe the evidence which Marie produced in su
 pport of\nthis conjecture\, as well as the infinite family of counterexamp
 les to it which I discovered the evening before her PhD viva. 
LOCATION:MR5\, Centre for Mathematical Sciences
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