The Microcosm Principle and Concurrency in Coalgebra

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.

• Type: Conference
• Year: 2008
• Where: FOSSACS
• Authors: Ichiro Hasuo, Bart Jacobs, Ana Sokolova
• Keywords: FOSSACS 2008, Lax Natural Transformation, Microcosm Principle, Nested Manner, Software Engineering