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SUMMARY:Giry and the Machine - Ilias Garnier\, ENS Paris
DTSTART:20160429T130000Z
DTEND:20160429T140000Z
UID:TALK65108@talks.cam.ac.uk
CONTACT:Dominic Mulligan
DESCRIPTION:We present a general method - the Machine - to analyse and cha
 racterise in finitary terms natural transformations between (iterates of) 
 Giry-like functors in the category Pol of Polish spaces. The method relies
  on a detailed analysis of the structure of Pol and a small set of composa
 ble categorical conditions on the domain and codomain functors. We apply t
 he Machine to transformations from the Giry and positive measures functors
  to combinations of the Vietoris\, multiset\, Giry and positive measures f
 unctors. We also show that for some combinations of these functors\, there
  cannot exist more than one natural transformation between the functors\, 
 in particular the Giry monad has no natural transformations to itself apar
 t from the identity. Finally we show how the Dirichlet and Poisson process
 es can be constructed with the Machine.
LOCATION:FW26
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