Skip to main content
SpringerLink
Log in
Book cover

International Conference on Algebra and Coalgebra in Computer Science

CALCO 2011: Algebra and Coalgebra in Computer Science pp 85–99Cite as

Finitary Functors: From Set to Preord and Poset

  • Conference paper

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

Abstract

We investigate how finitary functors on Set can be extended or lifted to finitary functors on Preord and Poset and discuss applications to coalgebra.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abramsky, S., Jung, A.: Domain Theory. In: Abramsky, S., Gabbay, D.M., Maibaum, T.S.E. (eds.) Handbook of Logic in Computer Science, vol. 3, pp. 1–168. Oxford Univ. Press, New York (1994)

    Google Scholar 

  2. Aczel, P., Mendler, N.: A Final Coalgebra Theorem. In: Dybjer, P., Pitts, A.M., Pitt, D.H., Poigné, A., Rydeheard, D.E. (eds.) Category Theory and Computer Science. LNCS, vol. 389, pp. 357–365. Springer, Heidelberg (1989)

    Chapter  Google Scholar 

  3. Adámek, J.: Final Coalgebras Are Ideal Completions of Initial Algebras. J. Logic Computat. 12(2), 217–242 (2002)

    Article  MATH  Google Scholar 

  4. Adámek, J., Trnková, V.: Automata and Algebras in Categories. Mathematics and Its Applications: East European Series, vol. 37. Kluwer Academic Publishers, Dordrecht (1990)

    MATH  Google Scholar 

  5. Bilková, M., Kurz, A., Petrişan, D., Velebil, J.: Relation Liftings on Preorders and Posets. In: Corradini, A., Klin, B., Crstea, C. (eds.) CALCO 2011. LNCS, vol. 6859, pp. 115–129. Springer, Heidelberg (2011)

    Google Scholar 

  6. Borceux, F.: Handbook of Categorical Algebra. In: Encycl. Mathem. Appl., vol. 50-52. Cambridge Univ. Press, Cambridge (1994)

    Google Scholar 

  7. Guitart, R.: Relations et Carrés Exacts. Ann. Sci. Math. Québec 4(2), 103–125 (1980)

    MathSciNet  MATH  Google Scholar 

  8. Hughes, J., Jacobs, B.: Simulations in Coalgebra. Theor. Comput. Sci. 327, 71–108 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kapulkin, K., Kurz, A., Velebil, J.: Expressivity of Coalgebraic Logic over Posets. In: Jacobs, B.P.F., Niqui, M., Rutten, J.J.M.M., Silva, A.M. (eds.) CMCS 2010 Short contributions, CWI Technical report SEN-1004, pp. 16–17 (2010)

    Google Scholar 

  10. Karazeris, P., Matzaris, A., Velebil, J.: Final Coalgebra in Accessible Categories, http://xxx.lanl.gov/abs/0905.4883

  11. Lambek, J.: Subequalizers. Canad. Math. Bull. 13, 337–349 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  12. Levy, P.: Similarity Quotients as Final Coalgebras. In: Hofmann, M. (ed.) FOSSACS 2011. LNCS, vol. 6604, pp. 27–41. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  13. Rutten, J.: Relators and Metric Bisimulations (Extended Abstract). In: Jacobs, B., Moss, L., Reichel, H., Rutten, J. (eds.) First Workshop on Coalgebraic Methods in Computer Science, CMCS 1998. Electr. Notes Theor. Comput. Sci., vol. 11, pp. 252–258 (1998)

    Google Scholar 

  14. Rutten, J.: Universal Coalgebra: A Theory of Systems. Theor. Comput. Sci. 249, 3–80 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  15. Thijs, A.: Simulation and Fixed Point Sematics, Ph. D. Thesis, University of Groningen (1996)

    Google Scholar 

  16. Velebil, J., Kurz, A.: Equational Presentations of Functors and Monads. Math. Struct. Comput. Sci. 21(2), 363–381 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  17. Worrell, J.: Coinduction for Recursive Data Types: Partial orders, Metric Spaces and Ω-Categories. In: Reichel, H. (ed.) Coalgebraic Methods in Computer Science, CMCS 2000. Electr. Notes Theor. Comput. Sci., vol. 33, pp. 337–356 (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University Politehnica of Bucharest, Romania

    Adriana Balan

  2. University of Leicester, UK

    Alexander Kurz

Authors
  1. Adriana Balan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alexander Kurz
    View author publications

    You can also search for this author in PubMed Google Scholar

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

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Balan, A., Kurz, A. (2011). Finitary Functors: From Set to Preord and Poset . 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_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-22944-2_7

  • 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)

Publish with us

Policies and ethics

Search

Navigation