Operational Resolutions and State Transi- Tions in a Categorical Setting

The core of the mathematical development in this paper consists of lifting the — categorically — equivalent descriptions of physical systems by a (i) ‘state space’ or a (ii) ‘property lattice’ — see [14,20,25,26] — to an asymmetrical — i.e., not anymore isomorphic — duality on the level of: (i) ‘possible state’ transitions — ‘possible’ in the sense that an arbitrary initial state is mapped onto all possible outcome states for this