A point-free perspective on lax extensions and predicate liftings

Goncharov S, Hofmann D, Nora P, Schröder L, Wild P (2023)

Publication Type: Journal article

Publication year: 2023

Journal

Mathematical Structures in Computer Science Cambridge University Press (CUP)

DOI: 10.1017/S096012952300035X

Abstract

Lax extensions of set functors play a key role in various areas, including topology, concurrent systems, and modal logic, while predicate liftings provide a generic semantics of modal operators. We take a fresh look at the connection between lax extensions and predicate liftings from the point of view of quantale-enriched relations. Using this perspective, we show in particular that various fundamental concepts and results arise naturally and their proofs become very elementary. Ultimately, we prove that every lax extension is induced by a class of predicate liftings; we discuss several implications of this result.

Authors with CRIS profile

Sergey Goncharov Lehrstuhl für Informatik 8 (Theoretische Informatik) Pedro Nora Lehrstuhl für Informatik 8 (Theoretische Informatik) Lutz Schröder Lehrstuhl für Informatik 8 (Theoretische Informatik) Paul Wild Lehrstuhl für Informatik 8 (Theoretische Informatik)

Involved external institutions

Center for Research & Development in Mathematics and Applications / Centro de Investigação e Desenvolvimento em Matemática e Aplicações (CIDMA) PT Portugal (PT)

How to cite

APA:

Goncharov, S., Hofmann, D., Nora, P., Schröder, L., & Wild, P. (2023). A point-free perspective on lax extensions and predicate liftings. Mathematical Structures in Computer Science. https://doi.org/10.1017/S096012952300035X

MLA:

Goncharov, Sergey, et al. "A point-free perspective on lax extensions and predicate liftings." Mathematical Structures in Computer Science (2023).

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