Relation Liftings on Preorders and Posets

  • Marta Bílková
  • Alexander Kurz
  • Daniela Petrişan
  • Jiří Velebil
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6859)


The category Rel(Set) of sets and relations can be described as a category of spans and as the Kleisli category for the powerset monad. A set-functor can be lifted to a functor on Rel(Set) iff it preserves weak pullbacks. We show that these results extend to the enriched setting, if we replace sets by posets or preorders. Preservation of weak pullbacks becomes preservation of exact lax squares. As an application we present Moss’s coalgebraic over posets.


Left Adjoint Note Theor Monotone Relation Geometric Morphism Kleisli Category 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Marta Bílková
    • 1
  • Alexander Kurz
    • 2
  • Daniela Petrişan
    • 2
  • Jiří Velebil
    • 3
  1. 1.Faculty of PhilosophyCharles UniversityPragueCzech Republic
  2. 2.Department of Computer ScienceUniversity of LeicesterUnited Kingdom
  3. 3.Faculty of Electrical EngineeringCzech Technical UniversityPragueCzech Republic

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