CATEGORIES OF REPRESENTATIONS OF PHYSICAL SYSTEMS

I present a review of the mathematical structures used to represent th e states and properties of physical systems in the Geneva School appro ach to the foundations of physics using the language of category theor y. After proving the equivalence of the categories of state spaces and property lattices I reformulate the classical decomposition of the pr operty lattice of a physical system as a universal category-theoretica l construction and summaries the notions of hemimorphism and adjoint.