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UID:9162@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20260709T110000
DTEND;TZID=Europe/Paris:20260709T123000
DTSTAMP:20260707T092233Z
URL:https://www.i2m.univ-amu.fr/evenements/correspondences-between-codensi
 ty-and-coupling-based-liftings-a-practical-approach/
SUMMARY:Samuel Humeau (LIS): Correspondences between codensity and coupling
 -based liftings\, a practical approach.
DESCRIPTION:Samuel Humeau: The Kantorovich distance is a widely used metric
  between probability\ndistributions. The Kantorovich-Rubinstein duality st
 ates that it can be\ndefined in two equivalent ways: as a supremum\, based
  on non-expansive\nfunctions into [0\,1]\, and as an infimum\, based on pr
 obabilistic couplings.\nOrthogonally\, there are categorical generalisatio
 ns of both\npresentations proposed in the literature\, in the form of code
 nsity\nliftings and what we refer to as coupling-based liftings. Both lift
 \nendofunctors on the category Set of sets and functions to that of\npseud
 ometric spaces\, and both are parameterised by modalities from\ncoalgebrai
 c modal logic.\nA generalisation of the Kantorovich-Rubinstein duality has
  been more\nnebulous - it is known not to work in some cases. In this pape
 r we\npropose a compositional approach for obtaining such generalised\ndua
 lities for a class of functors\, which is closed under coproducts and\npro
 ducts. Our approach is based on an explicit construction of\nmodalities an
 d also applies to and extends known cases such as that of\nthe powerset fu
 nctor.
CATEGORIES:Séminaire,Logique et Interactions
LOCATION:Luminy - LIS\, salle 04.02\, Campus de Luminy\, Marseille\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=Campus de Luminy\, Marseill
 e\, France;X-APPLE-RADIUS=100;X-TITLE=Luminy - LIS\, salle 04.02:geo:0,0
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DTSTART:20260329T030000
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