Évènement

Samuel Humeau
LIS
https://perso.ens-lyon.fr/samuel.humeau/

Date(s) : 09/07/2026   iCal
11h00 - 12h30

The Kantorovich distance is a widely used metric between probability
distributions. The Kantorovich-Rubinstein duality states that it can be
defined in two equivalent ways: as a supremum, based on non-expansive
functions into [0,1], and as an infimum, based on probabilistic couplings.
Orthogonally, there are categorical generalisations of both
presentations proposed in the literature, in the form of codensity
liftings and what we refer to as coupling-based liftings. Both lift
endofunctors on the category Set of sets and functions to that of
pseudometric spaces, and both are parameterised by modalities from
coalgebraic modal logic.
A generalisation of the Kantorovich-Rubinstein duality has been more
nebulous - it is known not to work in some cases. In this paper we
propose a compositional approach for obtaining such generalised
dualities for a class of functors, which is closed under coproducts and
products. Our approach is based on an explicit construction of
modalities and also applies to and extends known cases such as that of
the powerset functor.

Emplacement
Luminy - LIS, salle 04.02

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