Relation Liftings on Preorders and Posets

0368502 - ÚI 2012 RIV DE eng C - Conference Paper (international conference)
Bílková, Marta - Kurz, A. - Petrisan, D. - Velebil, J.
Relation Liftings on Preorders and Posets.
Algebra and Coalgebra in Computer Science. Berlin: Springer, 2011 - (Corradini, A.; Klin, B.; Cirstea, C.), s. 115-129. Lecture Notes in Computer Science, 6859. ISBN 978-3-642-22943-5. ISSN 0302-9743.
[CALCO 2011. International Conference /4./. Winchester (GB), 30.08.2011-02.09.2011]
R&D Projects: GA ČR GAP202/11/1632
Institutional research plan: CEZ:AV0Z10300504
Keywords : relation lifting * exact squares * monotone relation * coalgebraic logic
Subject RIV: BA - General Mathematics

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 coalgeraic logic over posets.
Permanent Link: http://hdl.handle.net/11104/0202829