A Point-free Perspective on Lax extensions and Predicate liftings

12/23/2021

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by   Sergey Goncharov, et al.

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In this paper we have a fresh look at the connection between lax extensions and predicate liftings of a functor from the point of view of quantale-enriched relations. Using this perspective, in particular we show that various fundamental concepts and results arise naturally and their proofs become very elementary. Ultimately, we prove that every lax extension is represented by a class of predicate liftings and discuss several implications of this result.