The Microcosm Principle and Concurrency in Coalgebra Export

@incollection{citeulike:3778002, 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.}, author = {Hasuo, Ichiro and Jacobs, Bart and Sokolova, Ana}, citeulike-article-id = {3778002}, citeulike-linkout-0 = {http://dx.doi.org/10.1007/978-3-540-78499-9_18}, citeulike-linkout-1 = {http://www.springerlink.com/content/b20u0420736537n4}, doi = {10.1007/978-3-540-78499-9_18}, journal = {Foundations of Software Science and Computational Structures}, keywords = {category-theory, coalgebra, computation, concurrency}, pages = {246--260}, posted-at = {2008-12-12 01:33:49}, priority = {2}, title = {The Microcosm Principle and Concurrency in Coalgebra}, url = {http://dx.doi.org/10.1007/978-3-540-78499-9_18}, year = {2008} }

TY - CHAP ID - citeulike:3778002 L3 - citeulike-article-id:3778002 N2 - 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. JF - Foundations of Software Science and Computational Structures EP - 260 TI - The Microcosm Principle and Concurrency in Coalgebra SP - 246 KW - category-theory KW - coalgebra KW - computation KW - concurrency AU - Hasuo, Ichiro AU - Jacobs, Bart AU - Sokolova, Ana PY - 2008/// UR - http://dx.doi.org/10.1007/978-3-540-78499-9_18 ER -