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)

Abstract

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.

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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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