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|Title:||Relation lifting, with an application to the many-valued cover modality|
Kurz, Alexander A.
|Publisher:||International Federation of Computational Logic|
|Citation:||Logical Methods in Computer Science, 2013, 9 (4), 8|
|Abstract:||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 enable us to compute predicate liftings of endofunctors of, for example, generalised (ultra)metric spaces. We illustrate this by studying the coalgebraic cover modality in this setting.|
|Rights:||Copyright © the authors, 2013. This is an Open Access article distributed under the terms of the Creative Commons Attribution No Derivatives Licence ( http://creativecommons.org/licenses/by-nd/2.0/ ) which permits use and distribution in any medium, provided the original work is properly cited and no modifications or adaptations are made.|
|Appears in Collections:||Published Articles, College of Science and Engineering|
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