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International Workshop on Coalgebraic Methods in Computer Science

CMCS 2012: Coalgebraic Methods in Computer Science pp 150–169Cite as

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Lax Extensions of Coalgebra Functors

Lax Extensions of Coalgebra Functors

  • Johannes Marti18 &
  • Yde Venema18 
  • Conference paper
  • 602 Accesses

  • 7 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7399)

Abstract

We discuss the use of relation lifting in the theory of set-based coalgebra. On the one hand we prove that the neighborhood functor does not extend to a relation lifting of which the associated notion of bisimilarity coincides with behavorial equivalence.

On the other hand we argue that relation liftings may be of use for many other functors that do not preserve weak pullbacks, such as the monotone neighborhood functor. We prove that for any relation lifting L that is a lax extension extending the coalgebra functor T and preserving diagonal relations, L-bisimilarity captures behavioral equivalence. We also show that if T is finitary, it admits such an extension iff there is a separating set of finitary monotone predicate liftings for T.

Keywords

  • coalgebra
  • relation lifting
  • predicate lifting
  • bisimilarity

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Author information

Authors and Affiliations

  1. ILLC, University of Amsterdam, The Netherlands

    Johannes Marti & Yde Venema

Authors
  1. Johannes Marti
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  2. Yde Venema
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Editor information

Editors and Affiliations

  1. Research School of Information Sciences and Engineering, The Australian National University, 0200, Canberra, ACT, Australia

    Dirk Pattinson

  2. Department of Computer Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, 91058, Erlangen, Germany

    Lutz Schröder

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© 2012 IFIP International Federation for Information Processing

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Cite this paper

Marti, J., Venema, Y. (2012). Lax Extensions of Coalgebra Functors. In: Pattinson, D., Schröder, L. (eds) Coalgebraic Methods in Computer Science. CMCS 2012. Lecture Notes in Computer Science, vol 7399. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32784-1_9

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  • DOI: https://doi.org/10.1007/978-3-642-32784-1_9

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