Abstract
This is a review of the book ‘Memory Evolutive Systems; Hierarchy, Emergence, Cognition’, by A. Ehresmann and J.P. Vanbremeersch. I welcome the use of category theory and the notion of colimit as a way of describing how complex hierarchical systems can be organised, and the notion of categories varying with time to give a notion of an evolving system. In this review I also point out the relation of the notion of colimit to ideas of communication; the necessity of communications to be symbolic representations; and the use of an analogy with mathematics to spell out some of the necessities of such a mode of communication to be powerful, robust and efficient.
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Notes
See Brown and Porter (2006).
See for example the ‘n-category cafe’ http://golem.ph.utexas.edu/category/ and ‘the ncat lab’ http://ncatlab.org/nlab/show/HomePage.
See also Brown and Porter (2003).
Multidisciplinary Software Systems Research Corporation, http://www.mssrc.com.
References
Brown R, Porter T (2003) Category theory and higher dimensional algebra: potential descriptive tools in neuroscience. In: Singh N (ed) Proceedings of the international conference on theoretical neurobiology, Delhi, February 2003, National Brain Research Centre, Conference Proceedings 1, pp 80–92. arXiv:math/0306223
Brown R, Porter T (2006) Category theory: an abstract setting for analogy and comparison. In: What is category theory? Advanced studies in mathematics and logic. Polimetrica Publisher, Italy, pp 257–274
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Brown, R. Memory Evolutive Systems. Axiomathes 19, 271–280 (2009). https://doi.org/10.1007/s10516-009-9065-4
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DOI: https://doi.org/10.1007/s10516-009-9065-4