Abstract
Bigraph was proposed as a formal theoretical model in attempt to provide a rigorous platform for designing, simulating and analyzing ubiquitous computing systems. As the mathematical basis of bigraphs, bigraphical categories become important aspects of their theory and they are related to precategoy, category, s-category, wide category and symmetric partial monoidal category. However, we detect trouble spots in the construction of bigraphical quotient category and illustrate that not all s-category can be converted to the symmetric partial monoidal category by the support quotient. Both support quotient and lean-support quotient, hence, are not always the symmetric partial monoidal category. And, likewise, the quotient wide s-category may not the wide symmetric partial monoidal category in general. Also, quotient wide re-active system may not be abstract, consequently for the same reason. There-fore, we must make clear what conditions on s-category allow us to obtain a symmetric partial monoidal category, and ensure that the behavioral congruence is preserved for the abstract bigraphical reactive system.
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Xu, D., Li, X. (2019). On the Constructions of Bigraphical Categories. In: Ning, H. (eds) Cyberspace Data and Intelligence, and Cyber-Living, Syndrome, and Health. CyberDI CyberLife 2019 2019. Communications in Computer and Information Science, vol 1137. Springer, Singapore. https://doi.org/10.1007/978-981-15-1922-2_17
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DOI: https://doi.org/10.1007/978-981-15-1922-2_17
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