ORIGINAL PAPER On the Ehresmann–Vanbremeersch Theory and Mathematical Biology Paul C. Kainen Received: 9 June 2009 / Accepted: 9 July 2009 / Published online: 24 July 2009 Ó Springer Science+Business Media B.V. 2009 Abstract Category theory has been proposed as the ultimate algebraic model for biology. We review the Ehresmann–Vanbremeersch theory in the context of other mathematical approaches. Keywords Evolutionary systems  Memory  Biological theory  Aging of organic structures  Cognitive coherence 1 Introduction The Ehresmann–Vanbremeersch work is an abstract theory of biology, continuing and substantially extending the ideas of Rashevsky and Rosen. Before discussing the theory per se, it is fair to ask: Why should one care? In recent years, technological progress has made it necessary to control multiple sensors and effectors and to utilize common sense and context in carrying out computer operations. These requirements are no longer confined to the laboratory or industrial setting but now permeate daily life. The newest tools in computational mathematics, aimed at addressing these needs, include such fields as neural networks, fuzzy logic, and genetic algorithms, and are explicitly based on biologically inspired ideas. Older methods for handling such problems of ‘‘computational intelligence’’ including operations research and statistics were developed from applications to social and economic problems—insurance, gambling, and military logistics, rather than chemistry and physics. Thus, a strong motivation for studying biology in the abstract is the possibility of uncovering its mechanisms for coordinating movement, perception, behavior, and resources so that everything appears when and where needed. Even individual cells P. C. Kainen (&) Department of Mathematics, Georgetown University, Washington, DC 20057, USA e-mail: kainen@georgetown.edu 123 Axiomathes (2009) 19:225–244 DOI 10.1007/s10516-009-9071-6