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Quantaloids for Concurrency

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Abstract

S. Abramsky has introduced interaction categories as a new semantics for concurrent computation. We show that interaction categories can be naturally described in the language of quantaloids. More precisely, they are closely related to fix-points of a certain comonad on the category of quantaloids with biproducts.

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References

  1. Abramsky, S.: Interaction categories (extended abstract), in G. Burn, S. Gay and M. Ryan (eds.), Theory and Formal Methods 1993, Springer Workshops in Computing, Springer-Verlag, 1993, pp. 57-70.

  2. Abramsky, S.: Interaction categories I: Synchronous case, Deposited in the hypatia archive (http://hypatia.dcs.qmw.ac.uk).

  3. Abramsky, S., Gay, S. J. and Nagarajan, R.: Interaction categories and the foundation of the typed concurrent programming, in M. Broy (ed.), Deductive Program Design, Springer-Verlag, 1996, pp. 35-115.

  4. Abramsky, S., Gay, S. J. and Nagarajan, R.: Specification structures and propositions-as-types for concurrency, in Logics for Concurrency vs. Automata, LNCS 1043, Springer-Verlag, 1996.

  5. Adámek, J.: Free algebras and automata realizations in the language of categories, Comment. Math. Univ. Carolin. 15 (1974), 589-602.

    Google Scholar 

  6. Kameník, O.: Fix point semantics for synchronous processes, Preprint.

  7. Lambek, J.: Subequalizers, Canad. Math. Bull. 13 (1970), 337-349.

    Google Scholar 

  8. Rosenthal, K. I.: Free quantaloids, J. Pure Appl. Algebra 72 (1991), 67-82.

    Google Scholar 

  9. Rosenthal, K. I.: Girard quantaloids, Math. Structures Comput. Sci. 2 (1992), 93-108.

    Google Scholar 

  10. Rosenthal, K. I.: The Theory of Quantaloids, Addison Wesley, 1996.

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Authors and Affiliations

  1. Masaryk University, Janáčkovo nám. 2a, 662 95, Brno, Czech Republic

    Jiří Rosický

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  1. Jiří Rosický
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Rosický, J. Quantaloids for Concurrency. Applied Categorical Structures 9, 329–338 (2001). https://doi.org/10.1023/A:1011252012003

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