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SUMMARY:Everything's a Kan extension - Philip Saville (University of Cambr
 idge)
DTSTART:20160129T110000Z
DTEND:20160129T120000Z
UID:TALK63831@talks.cam.ac.uk
CONTACT:Ian Orton
DESCRIPTION:Kan extensions are a fundamental construction in category theo
 ry. As Mac Lane puts it\, they "subsume all other fundamental concepts" in
  the field. I will give a brief introduction to Kan extensions: showing ho
 w the definition captures other important constructions\, and how Kan exte
 nsions are hidden in many familiar examples. I will also give (largely wit
 hout proof) some of the properties that make Kan extensions so useful.\n\n
 Covering:\n\n    * definition of Kan extensions\, their basic theory\n    
 * examples of Kan extensions\n    * other fundamental concepts as Kan exte
 nsions\n\nPrerequisites:\n\n    * basic category theory (natural transform
 ation\, functor)\n    * some familiarity with the definition of adjunction
 s (I will cover this in the talk\, but might be quite quick)\n\nMaterial\n
 \n    * most of the material covered will be taken from Mac Lane's 'Catego
 ries for the Working Mathematician' (chap. X)\; some will come from Awodey
 's 'Category Theory' (esp. pp. 186-192 for the Yoneda Lemma\, and pp. 208 
 - 234 for adjunctions and examples of Kan extensions)\n    * for more back
 ground the Wikipedia page on Kan extensions is pretty good\; the essay at 
 http://www.math.harvard.edu/theses/senior/lehner/lehner.pdf provides a rea
 sonably readable introduction as well. 
LOCATION:Rainbow Room (FS07)\, Computer Laboratory
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