Relation Liftings on Preorders and Posets

Authors

Marta Bílková, Academy of Sciences of the Czech Republic
Alexander Kurz, Chapman UniversityFollow
Daniela Petrişan, University of Leicester
Jiří Velebil, Czech Technical University in Prague

Document Type

Conference Proceeding

Publication Date

2011

Abstract

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.

Comments

This paper was originally presented at the Conference on Algebra and Coalgebra in Computer Science (CALCO) in 2011. DOI: 10.1007/978-3-642-22944-2_9

Recommended Citation

Bílková M., Kurz A., Petrişan D., Velebil J. (2011) Relation Liftings on Preorders and Posets. In: Corradini A., Klin B., Cîrstea C. (eds) Algebra and Coalgebra in Computer Science. CALCO 2011. Lecture Notes in Computer Science, vol 6859. Springer, Berlin, Heidelberg

Copyright

The authors