2026-07-21T19:38:38Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:22786 2025-10-02T11:31:55Z ddc:004 open_access

Correspondences Between Codensity and Coupling-Based Liftings, a Practical Approach Humeau, Samuel Petrisan, Daniela Rot, Jurriaan Kantorovich distance behavioural metrics Kantorovich-Rubinstein duality functor liftings 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Samuel Humeau and Daniela Petrisan and Jurriaan Rot 2025 Is Part Of LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CSL.2025.29 urn:nbn:de:0030-drops-227861 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.29 eng https://creativecommons.org/licenses/by/4.0/legalcode