Systems and categorical methods of global control

Abstract

The toposes and others categorical construction are the most universal mathematical construction of society’s decision. For example, Syntetical autonomous systems, such as a voting, a selection, analyze rational behaviour for an individual and a collective. A society consists of individual members and society’s decision is composed of its members’ decisions. Natural autonomous systems, such as biological, neural, social or cultural systems, are open, self-organized with a more or less large hierarchy of interacting complexity levels; they are able to memorize their experiences and to adapt to various conditions through a change of behavior. We study algorithms of society’s decision and we discuss the concept of voting and individual choice. Using ours algorithms, we arrive a number of interesting results. We give a mathematically exact characterization of rule for making decisions. These last 25 years, the Authors have developed a mathematical model for these systems, based on Category Theory. The aim of the paper is to give an overview of this model, called CAS.