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Relation Liftings on Preorders and Posets

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Algebra and Coalgebra in Computer Science (CALCO 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6859))

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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.

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Author information

Authors and Affiliations

  1. Faculty of Philosophy, Charles University, Prague, Czech Republic

    Marta Bílková

  2. Department of Computer Science, University of Leicester, United Kingdom

    Alexander Kurz & Daniela Petrişan

  3. Faculty of Electrical Engineering, Czech Technical University, Prague, Czech Republic

    Jiří Velebil

Authors
  1. Marta Bílková
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  2. Alexander Kurz
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  3. Daniela Petrişan
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  4. Jiří Velebil
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università di Pisa, 56127, Pisa, Italy

    Andrea Corradini

  2. Faculty of Mathematics, Informatics, and Mechanics, University of Warsaw, ul. Banacha 2, 02-097, Warszawa, Poland

    Bartek Klin

  3. School of Electronics and Computer Science, University of Southampton, SO17 1BJ, Southampton, UK

    Corina Cîrstea

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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. https://doi.org/10.1007/978-3-642-22944-2_9

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  • DOI: https://doi.org/10.1007/978-3-642-22944-2_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22943-5

  • Online ISBN: 978-3-642-22944-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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