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SUMMARY:Multivariable adjunctions and mates - Eugenia Cheng\, Sheffield
DTSTART:20120228T141500Z
DTEND:20120228T150000Z
UID:TALK34889@talks.cam.ac.uk
CONTACT:Julia Goedecke
DESCRIPTION:In this talk I will present the notion of ``cyclic double mult
 icategory''\, as a structure in which to organise multivariable adjunction
 s and mates. The most common example of a 2-variable adjunction is the hom
 /tensor/cotensor trio of functors\; we generalise this situation to $n+1$ 
 functors of $n$ variables.  Furthermore\, we generalise the mates correspo
 ndence\, which enables us neatly to pass between natural transformations i
 nvolving left adjoints and those involving right adjoints.\n\nWhile the st
 andard mates correspondence is elegantly described using an isomorphism of
  double categories\, the multivariable version needs the framework of ``do
 uble multicategories''.  Moreover\, we show that the analogous isomorphism
 s of double multicategories give a cyclic action on the multimaps\, yieldi
 ng the notion of ``cyclic double multicategory''.\n\nThis is joint work wi
 th Nick Gurski and Emily Riehl\, and is motivated by and applied to Riehl'
 s approach to algebraic monoidal model categories. 
LOCATION:MR5\, Centre for Mathematical Sciences
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