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Full-Text Articles in Computer Engineering
Relation Lifting, With An Application To The Many-Valued Cover Modality, Marta Bílková, Alexander Kurz, Daniela Petrişan, Jirí Velebil
Relation Lifting, With An Application To The Many-Valued Cover Modality, Marta Bílková, Alexander Kurz, Daniela Petrişan, Jirí Velebil
Engineering Faculty Articles and Research
We introduce basic notions and results about relation liftings on categories enriched in a commutative quantale. We derive two necessary and sufficient conditions for a 2-functor T to admit a functorial relation lifting: one is the existence of a distributive law of T over the “powerset monad” on categories, one is the preservation by T of “exactness” of certain squares. Both characterisations are generalisations of the “classical” results known for set functors: the first characterisation generalises the existence of a distributive law over the genuine powerset monad, the second generalises preservation of weak pullbacks.
The results presented in this paper …