Robert Rosen has proposed several characteristics to distinguish "simple" physical systems (or "mechanisms") from "complex" systems, such as living systems, which he calls "organisms". The Memory Evolutive Systems (MES) introduced by the authors in preceding papers are shown to provide a mathematical model, based on category theory, which satisfies his characteristics of organisms, in particular the merger of the Aristotelian causes. Moreover they identify the condition for the emergence of objects and systems of increasing complexity. As an application, the cognitive system of an animal is modeled by the "MES of cat-neurons" obtained by successive complexifications of his neural system, in which the emergence of higher order cognitive processes gives support to Mario Bunge's "emergentist monism."