Schr\'{o}dinger's problem with cats: measurements and states in the Groupoid Picture of Quantum Mechanics

Schr\"{o}dinger's famous Gedankenexperiment involving a cat is used as a motivation to discuss the evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently. It is shown that the notion of classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. In accordance with Raggio's theorem, the impossibility of evolving the product state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution which is internal to the composite system itself is proved in the groupoid formalism.
Comment: 24 pages. A slightly different version this work will has appeared in Entropy. The main difference is that in the version published in Entropy no mention is made of Schr\"{o}dinger's cat Gedankenexperiment. Comments and suggestions are more than welcome!