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SUMMARY:2-Monads for Differential Calculus - Martin Hyland\, University of
  Cambridge
DTSTART:20100216T141500Z
DTEND:20100216T154500Z
UID:TALK23381@talks.cam.ac.uk
CONTACT:Nathan Bowler
DESCRIPTION:One approach to algebra from an advanced standpoint is based o
 n Kleisli bicategories. Various flavours of substitution are captured by s
 uitable 2-monads. This point of view has many applications. In this talk b
 ased on joint work with Christine Tasson I present an application to the s
 ubstitutions needed to support the Ehrhard-Regnier differential lambda cal
 culus. For that one needs to combine the free symmetric monoidal category 
 2-monad with the 2-monad for finite products. Known combinations (via dist
 ributive laws\, tensor or sum) are of no help. I shall establish the exist
 ence of a general colimit construction on 2-monads\, which does produce th
 e desired 2-monad
LOCATION:MR9\, Centre for Mathematical Sciences
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