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Relation Liftings on Preorders and Posets
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SYSNO ASEP 0368502 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Relation Liftings on Preorders and Posets Author(s) Bílková, Marta (UIVT-O) SAI, RID, ORCID
Kurz, A. (GB)
Petrisan, D. (GB)
Velebil, J. (CZ)Source Title Algebra and Coalgebra in Computer Science. - Berlin : Springer, 2011 / Corradini A. ; Klin B. ; Cirstea C. - ISSN 0302-9743 - ISBN 978-3-642-22943-5 Pages s. 115-129 Number of pages 15 s. Action CALCO 2011. International Conference /4./ Event date 30.08.2011-02.09.2011 VEvent location Winchester Country GB - United Kingdom Event type WRD Language eng - English Country DE - Germany Keywords relation lifting ; exact squares ; monotone relation ; coalgebraic logic Subject RIV BA - General Mathematics R&D Projects GAP202/11/1632 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10300504 - UIVT-O (2005-2011) EID SCOPUS 80053019499 DOI 10.1007/978-3-642-22944-2_9 Annotation 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. Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2012
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