[Mathematical model for an evolutive and hierarchical living system, based on the theory of categories].
The notion of an evolutive hierarchical system proposed here retains the following characteristics of some natural systems, like living organisms: they have an internal organization consisting of more or less complex components with interrelations; they maintain their organization in time although their components are changing; they may be studied at several complexity levels (e.g., molecular, cellular, ...). The idea is to model the state of the system at a given instant by a category, the state transition by a functor, a complex object by the (direct) limit of a pattern of linked objects (its own organization). The emergence of new properties for a complex object is measured, and a development process is described.
D000818:Animals; D005075:Biological Evolution; D008433:Mathematics; D008954:Models, Biological; D010802:Phylogeny
Un modèle mathématique pour un système vivant évolutif et hiérarchique, fondé sur la théorie des catégories.