 If \(f : \mathbf{A} \rightarrow \mathbf{C}\) is shortcut notation for the existence of the two functions above (the pair \(f\) of functions is called an infomorphism), then an arbitrary distributed system will consist of various classifications related by infomorphisms. For our purposes, it will suffice here to consider three classifications \(\mathbf{A}, \mathbf{B}, \mathbf{C}\) together with two infomorphisms 