The Microcosm Principle and Concurrency in Coalgebra

  • Ichiro Hasuo
  • Bart Jacobs
  • Ana Sokolova
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4962)


Coalgebras are categorical presentations of state-based systems. In investigating parallel composition of coalgebras (realizing concurrency), we observe that the same algebraic theory is interpreted in two different domains in a nested manner, namely: in the category of coalgebras, and in the final coalgebra as an object in it. This phenomenon is what Baez and Dolan have called the microcosm principle, a prototypical example of which is “a monoid in a monoidal category.” In this paper we obtain a formalization of the microcosm principle in which such a nested model is expressed categorically as a suitable lax natural transformation. An application of this account is a general compositionality result which supports modular verification of complex systems.


Composition Operator Natural Transformation Algebraic Theory Monoidal Category Parallel Composition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Ichiro Hasuo
    • 1
    • 3
    • 4
  • Bart Jacobs
    • 1
  • Ana Sokolova
    • 2
  1. 1.Radboud University NijmegenThe Netherlands
  2. 2.University of SalzburgAustria
  3. 3.RIMSKyoto UniversityJapan
  4. 4.PRESTO Research Promotion ProgramJapan Science and Technology Agency 

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