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SUMMARY:The co-end justifies the co-means - Philip Saville
DTSTART:20160219T110000Z
DTEND:20160219T120000Z
UID:TALK64599@talks.cam.ac.uk
CONTACT:Philip Saville
DESCRIPTION:Ends and coends are generalisations of limits and colimits: if
  you think of a colimit as a generalised `sum'\, then the corresponding co
 end is a kind of `integral'. They also have close connections to the Yoned
 a lemma and Kan extensions. I will recap the definitions of (co)limits\, t
 hen introduce (co)ends and their basic theory. In particular\, I will show
  how every limit is an end\, and every end is a limit. Finally I will try 
 to present examples of ends and coends at work\, and show how they can be 
 extremely useful tools for reasoning in category theory.\n\n\n*Covering:*\
 n* recap of definition of (co)limits\,\n* definition of (co)ends\,\n* basi
 c theory of (co)ends: relationship to limits\, Fubini theorem\n* (co)ends 
 in the wild: Kan extensions\, Yoneda\, other examples\n\n*Prerequisites:*\
 n* basic category theory: functors\, natural transformations\n* I will cov
 er the definition of limits and colimits\, having some intuition already w
 ill be useful (eg. as covered in Awodey's `Category Theory') 
LOCATION:Rainbow Room (FS07)\, Computer Laboratory
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