Reactive Colimit : a View of Internal Measurement Based on a Hamiltonian System

Consistent structure of a Hamiltonian dynamical system with constant energy is shown in terms of category theory. A colimit of the dynamical system corresponds to a set of pairs of an initial state and a final state. Expansion of the colimit based on a concept of internal measurement induces heterarchical structure in the dynamical system and derives interaction between the system and the other one. Dynamical change of potential functions derived from that expansion is relevant to a concept of emergence based on the viewpoint of the Hamiltonian system.