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SUMMARY:Internal algebra classifiers and their applications - Michael Bata
 nin\, Macquarie University\, Australia
DTSTART:20130423T131500Z
DTEND:20130423T141500Z
UID:TALK43623@talks.cam.ac.uk
CONTACT:Julia Goedecke
DESCRIPTION:Given a map between two 2-monads S and T one can define a noti
 on of internal S-algebra inside a T-algebra. For example\, the category of
  monoids in a symmetric monoidal category is the category of internal alge
 bras of the free monoidal category monad inside an algebra of the free sym
 metric monoidal category monad. The category of internal algebras form a 2
 -functor which is representable under some conditions on S and T. The repr
 esenting object is called internal S-algebra classifier inside T-algebras.
  These internal algebra classifiers have remarkable properties which often
  allow to compute explicitly left adjoint functors between categories of a
 lgebras. This technique has numerous applications ranging from the constru
 ction of free monads in double categories and the explicit calculation of 
 various envelopes of operads and PROPs to the construction of transferred 
 model structures.  \n
LOCATION:MR15\, Centre for Mathematical Sciences
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